Number of isomorphism types of finite groups of given order
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 0+ |
. |
1 |
1 |
1 |
2 |
1 |
2 |
1 |
5 |
2 |
2 |
1 |
5 |
1 |
2 |
1 |
14 |
1 |
5 |
1 |
| 20+ |
5 |
2 |
2 |
1 |
15 |
2 |
2 |
5 |
4 |
1 |
4 |
1 |
51 |
1 |
2 |
1 |
14 |
1 |
2 |
2 |
| 40+ |
14 |
1 |
6 |
1 |
4 |
2 |
2 |
1 |
52 |
2 |
5 |
1 |
5 |
1 |
15 |
2 |
13 |
2 |
2 |
1 |
| 60+ |
13 |
1 |
2 |
4 |
267 |
1 |
4 |
1 |
5 |
1 |
4 |
1 |
50 |
1 |
2 |
3 |
4 |
1 |
6 |
1 |
| 80+ |
52 |
15 |
2 |
1 |
15 |
1 |
2 |
1 |
12 |
1 |
10 |
1 |
4 |
2 |
2 |
1 |
231 |
1 |
5 |
2 |
| 100+ |
16 |
1 |
4 |
1 |
14 |
2 |
2 |
1 |
45 |
1 |
6 |
2 |
43 |
1 |
6 |
1 |
5 |
4 |
2 |
1 |
| 120+ |
47 |
2 |
2 |
1 |
4 |
5 |
16 |
1 |
2328 |
2 |
4 |
1 |
10 |
1 |
2 |
5 |
15 |
1 |
4 |
1 |
| 140+ |
11 |
1 |
2 |
1 |
197 |
1 |
2 |
6 |
5 |
1 |
13 |
1 |
12 |
2 |
4 |
2 |
18 |
1 |
2 |
1 |
| 160+ |
238 |
1 |
55 |
1 |
5 |
2 |
2 |
1 |
57 |
2 |
4 |
5 |
4 |
1 |
4 |
2 |
42 |
1 |
2 |
1 |
| 180+ |
37 |
1 |
4 |
2 |
12 |
1 |
6 |
1 |
4 |
13 |
4 |
1 |
1543 |
1 |
2 |
2 |
12 |
1 |
10 |
1 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 200+ |
52 |
2 |
2 |
2 |
12 |
2 |
2 |
2 |
51 |
1 |
12 |
1 |
5 |
1 |
2 |
1 |
177 |
1 |
2 |
2 |
| 220+ |
15 |
1 |
6 |
1 |
197 |
6 |
2 |
1 |
15 |
1 |
4 |
2 |
14 |
1 |
16 |
1 |
4 |
2 |
4 |
1 |
| 240+ |
208 |
1 |
5 |
67 |
5 |
2 |
4 |
1 |
12 |
1 |
15 |
1 |
46 |
2 |
2 |
1 |
56092 |
1 |
6 |
1 |
| 260+ |
15 |
2 |
2 |
1 |
39 |
1 |
4 |
1 |
4 |
1 |
30 |
1 |
54 |
5 |
2 |
4 |
10 |
1 |
2 |
4 |
| 280+ |
40 |
1 |
4 |
1 |
4 |
2 |
4 |
1 |
1045 |
2 |
4 |
2 |
5 |
1 |
23 |
1 |
14 |
5 |
2 |
1 |
| 300+ |
49 |
2 |
2 |
1 |
42 |
2 |
10 |
1 |
9 |
2 |
6 |
1 |
61 |
1 |
2 |
4 |
4 |
1 |
4 |
1 |
| 320+ |
1640 |
1 |
4 |
1 |
176 |
2 |
2 |
2 |
15 |
1 |
12 |
1 |
4 |
5 |
2 |
1 |
228 |
1 |
5 |
1 |
| 340+ |
15 |
1 |
18 |
5 |
12 |
1 |
2 |
1 |
12 |
1 |
10 |
14 |
195 |
1 |
4 |
2 |
5 |
2 |
2 |
1 |
| 360+ |
162 |
2 |
2 |
3 |
11 |
1 |
6 |
1 |
42 |
2 |
4 |
1 |
15 |
1 |
4 |
7 |
12 |
1 |
60 |
1 |
| 380+ |
11 |
2 |
2 |
1 |
20169 |
2 |
2 |
4 |
5 |
1 |
12 |
1 |
44 |
1 |
2 |
1 |
30 |
1 |
2 |
5 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 400+ |
221 |
1 |
6 |
1 |
5 |
16 |
6 |
1 |
46 |
1 |
6 |
1 |
4 |
1 |
10 |
1 |
235 |
2 |
4 |
1 |
| 420+ |
41 |
1 |
2 |
2 |
14 |
2 |
4 |
1 |
4 |
2 |
4 |
1 |
775 |
1 |
4 |
1 |
5 |
1 |
6 |
1 |
| 440+ |
51 |
13 |
4 |
1 |
18 |
1 |
2 |
1 |
1396 |
1 |
34 |
1 |
5 |
2 |
2 |
1 |
54 |
1 |
2 |
5 |
| 460+ |
11 |
1 |
12 |
1 |
51 |
4 |
2 |
1 |
55 |
1 |
4 |
2 |
12 |
1 |
6 |
2 |
11 |
2 |
2 |
1 |
| 480+ |
1213 |
1 |
2 |
2 |
12 |
1 |
261 |
1 |
14 |
2 |
10 |
1 |
12 |
1 |
4 |
4 |
42 |
2 |
4 |
1 |
| 500+ |
56 |
1 |
2 |
1 |
202 |
2 |
6 |
6 |
4 |
1 |
8 |
1 |
10494213 |
15 |
2 |
1 |
15 |
1 |
4 |
1 |
| 520+ |
49 |
1 |
10 |
1 |
4 |
6 |
2 |
1 |
170 |
2 |
4 |
2 |
9 |
1 |
4 |
1 |
12 |
1 |
2 |
2 |
| 540+ |
119 |
1 |
2 |
2 |
246 |
1 |
24 |
1 |
5 |
4 |
16 |
1 |
39 |
1 |
2 |
2 |
4 |
1 |
16 |
1 |
| 560+ |
180 |
1 |
2 |
1 |
10 |
1 |
2 |
49 |
12 |
1 |
12 |
1 |
11 |
1 |
4 |
2 |
8681 |
1 |
5 |
2 |
| 580+ |
15 |
1 |
6 |
1 |
15 |
4 |
2 |
1 |
66 |
1 |
4 |
1 |
51 |
1 |
30 |
1 |
5 |
2 |
4 |
1 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 600+ |
205 |
1 |
6 |
4 |
4 |
7 |
4 |
1 |
195 |
3 |
6 |
1 |
36 |
1 |
2 |
2 |
35 |
1 |
6 |
1 |
| 620+ |
15 |
5 |
2 |
1 |
260 |
15 |
2 |
2 |
5 |
1 |
32 |
1 |
12 |
2 |
2 |
1 |
12 |
2 |
4 |
2 |
| 640+ |
21541 |
1 |
4 |
1 |
9 |
2 |
4 |
1 |
757 |
1 |
10 |
5 |
4 |
1 |
6 |
2 |
53 |
5 |
4 |
1 |
| 660+ |
40 |
1 |
2 |
2 |
12 |
1 |
18 |
1 |
4 |
2 |
4 |
1 |
1280 |
1 |
2 |
17 |
16 |
1 |
4 |
1 |
| 680+ |
53 |
1 |
4 |
1 |
51 |
1 |
15 |
2 |
42 |
2 |
8 |
1 |
5 |
4 |
2 |
1 |
44 |
1 |
2 |
1 |
| 700+ |
36 |
1 |
62 |
1 |
1387 |
1 |
2 |
1 |
10 |
1 |
6 |
4 |
15 |
1 |
12 |
2 |
4 |
1 |
2 |
1 |
| 720+ |
840 |
1 |
5 |
2 |
5 |
2 |
13 |
1 |
40 |
504 |
4 |
1 |
18 |
1 |
2 |
6 |
195 |
2 |
10 |
1 |
| 740+ |
15 |
5 |
4 |
1 |
54 |
1 |
2 |
2 |
11 |
1 |
39 |
1 |
42 |
1 |
4 |
2 |
189 |
1 |
2 |
2 |
| 760+ |
39 |
1 |
6 |
1 |
4 |
2 |
2 |
1 |
1090235 |
1 |
12 |
1 |
5 |
1 |
16 |
4 |
15 |
5 |
2 |
1 |
| 780+ |
53 |
1 |
4 |
5 |
172 |
1 |
4 |
1 |
5 |
1 |
4 |
2 |
137 |
1 |
2 |
1 |
4 |
1 |
24 |
1 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 800+ |
1211 |
2 |
2 |
1 |
15 |
1 |
4 |
1 |
14 |
1 |
113 |
1 |
16 |
2 |
4 |
1 |
205 |
1 |
2 |
11 |
| 820+ |
20 |
1 |
4 |
1 |
12 |
5 |
4 |
1 |
30 |
1 |
4 |
2 |
1630 |
2 |
6 |
1 |
9 |
13 |
2 |
1 |
| 840+ |
186 |
2 |
2 |
1 |
4 |
2 |
10 |
2 |
51 |
2 |
10 |
1 |
10 |
1 |
4 |
5 |
12 |
1 |
12 |
1 |
| 860+ |
11 |
2 |
2 |
1 |
4725 |
1 |
2 |
3 |
9 |
1 |
8 |
1 |
14 |
4 |
4 |
5 |
18 |
1 |
2 |
1 |
| 880+ |
221 |
1 |
68 |
1 |
15 |
1 |
2 |
1 |
61 |
2 |
4 |
15 |
4 |
1 |
4 |
1 |
19349 |
2 |
2 |
1 |
| 900+ |
150 |
1 |
4 |
7 |
15 |
2 |
6 |
1 |
4 |
2 |
8 |
1 |
222 |
1 |
2 |
4 |
5 |
1 |
30 |
1 |
| 920+ |
39 |
2 |
2 |
1 |
34 |
2 |
2 |
4 |
235 |
1 |
18 |
2 |
5 |
1 |
2 |
2 |
222 |
1 |
4 |
2 |
| 940+ |
11 |
1 |
6 |
1 |
42 |
13 |
4 |
1 |
15 |
1 |
10 |
1 |
42 |
1 |
10 |
2 |
4 |
1 |
2 |
1 |
| 960+ |
11394 |
2 |
4 |
2 |
5 |
1 |
12 |
1 |
42 |
2 |
4 |
1 |
900 |
1 |
2 |
6 |
51 |
1 |
6 |
2 |
| 980+ |
34 |
5 |
2 |
1 |
46 |
1 |
4 |
2 |
11 |
1 |
30 |
1 |
196 |
2 |
6 |
1 |
10 |
1 |
2 |
15 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 1000+ |
199 |
1 |
4 |
1 |
4 |
2 |
2 |
1 |
954 |
1 |
6 |
2 |
13 |
1 |
23 |
2 |
12 |
2 |
2 |
1 |
| 1020+ |
37 |
1 |
4 |
2 |
49487365422 |
4 |
66 |
2 |
5 |
19 |
4 |
1 |
54 |
1 |
4 |
2 |
11 |
1 |
4 |
1 |
| 1040+ |
231 |
1 |
2 |
1 |
36 |
2 |
2 |
2 |
12 |
1 |
40 |
1 |
4 |
51 |
4 |
2 |
1028 |
1 |
5 |
1 |
| 1060+ |
15 |
1 |
10 |
1 |
35 |
2 |
4 |
1 |
12 |
1 |
4 |
4 |
42 |
1 |
4 |
2 |
5 |
1 |
10 |
1 |
| 1080+ |
583 |
2 |
2 |
6 |
4 |
2 |
6 |
1 |
1681 |
6 |
4 |
1 |
77 |
1 |
2 |
2 |
15 |
1 |
16 |
1 |
| 1100+ |
51 |
2 |
4 |
1 |
170 |
1 |
4 |
5 |
5 |
1 |
12 |
1 |
12 |
2 |
2 |
1 |
46 |
1 |
4 |
2 |
| 1120+ |
1092 |
1 |
8 |
1 |
5 |
14 |
2 |
2 |
39 |
1 |
4 |
2 |
4 |
1 |
254 |
1 |
42 |
2 |
2 |
1 |
| 1140+ |
41 |
1 |
2 |
5 |
39 |
1 |
4 |
1 |
11 |
1 |
10 |
1 |
157877 |
1 |
2 |
4 |
16 |
1 |
6 |
1 |
| 1160+ |
49 |
13 |
4 |
1 |
18 |
1 |
4 |
1 |
53 |
1 |
32 |
1 |
5 |
1 |
2 |
2 |
279 |
1 |
4 |
2 |
| 1180+ |
11 |
1 |
4 |
3 |
235 |
2 |
2 |
1 |
99 |
1 |
8 |
2 |
14 |
1 |
6 |
1 |
11 |
14 |
2 |
1 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 1200+ |
1040 |
1 |
2 |
1 |
13 |
2 |
16 |
1 |
12 |
5 |
27 |
1 |
12 |
1 |
2 |
69 |
1387 |
1 |
16 |
1 |
| 1220+ |
20 |
2 |
4 |
1 |
164 |
4 |
2 |
2 |
4 |
1 |
12 |
1 |
153 |
2 |
2 |
1 |
15 |
1 |
2 |
2 |
| 1240+ |
51 |
1 |
30 |
1 |
4 |
1 |
4 |
1 |
1460 |
1 |
55 |
4 |
5 |
1 |
12 |
2 |
14 |
1 |
4 |
1 |
| 1260+ |
131 |
1 |
2 |
2 |
42 |
3 |
6 |
1 |
5 |
5 |
4 |
1 |
44 |
1 |
10 |
3 |
11 |
1 |
10 |
1 |
| 1280+ |
1116461 |
5 |
2 |
1 |
10 |
1 |
2 |
4 |
35 |
1 |
12 |
1 |
11 |
1 |
2 |
1 |
3609 |
1 |
4 |
2 |
| 1300+ |
50 |
1 |
24 |
1 |
12 |
2 |
2 |
1 |
18 |
1 |
6 |
2 |
244 |
1 |
18 |
1 |
9 |
2 |
2 |
1 |
| 1320+ |
181 |
1 |
2 |
51 |
4 |
2 |
12 |
1 |
42 |
1 |
8 |
5 |
61 |
1 |
4 |
1 |
12 |
1 |
6 |
1 |
| 1340+ |
11 |
2 |
4 |
1 |
11720 |
1 |
2 |
1 |
5 |
1 |
112 |
1 |
52 |
1 |
2 |
2 |
12 |
1 |
4 |
4 |
| 1360+ |
245 |
1 |
4 |
1 |
9 |
5 |
2 |
1 |
211 |
2 |
4 |
2 |
38 |
1 |
6 |
15 |
195 |
15 |
6 |
2 |
| 1380+ |
29 |
1 |
2 |
1 |
14 |
1 |
32 |
1 |
4 |
2 |
4 |
1 |
198 |
1 |
4 |
8 |
5 |
1 |
4 |
1 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 1400+ |
153 |
1 |
2 |
1 |
227 |
2 |
4 |
5 |
19324 |
1 |
8 |
1 |
5 |
4 |
4 |
1 |
39 |
1 |
2 |
2 |
| 1420+ |
15 |
4 |
16 |
1 |
53 |
6 |
4 |
1 |
40 |
1 |
12 |
5 |
12 |
1 |
4 |
2 |
4 |
1 |
2 |
1 |
| 1440+ |
5958 |
1 |
4 |
5 |
12 |
2 |
6 |
1 |
14 |
4 |
10 |
1 |
40 |
1 |
2 |
2 |
179 |
1 |
1798 |
1 |
| 1460+ |
15 |
2 |
4 |
1 |
61 |
1 |
2 |
5 |
4 |
1 |
46 |
1 |
1387 |
1 |
6 |
2 |
36 |
2 |
2 |
1 |
| 1480+ |
49 |
1 |
24 |
1 |
11 |
10 |
2 |
1 |
222 |
1 |
4 |
3 |
5 |
1 |
10 |
1 |
41 |
2 |
4 |
1 |
| 1500+ |
174 |
1 |
2 |
2 |
195 |
2 |
4 |
1 |
15 |
1 |
6 |
1 |
889 |
1 |
2 |
2 |
4 |
1 |
12 |
2 |
| 1520+ |
178 |
13 |
2 |
1 |
15 |
4 |
4 |
1 |
12 |
1 |
20 |
1 |
4 |
5 |
4 |
1 |
408641062 |
1 |
2 |
60 |
| 1540+ |
36 |
1 |
4 |
1 |
15 |
2 |
2 |
1 |
46 |
1 |
16 |
1 |
54 |
1 |
24 |
2 |
5 |
2 |
4 |
1 |
| 1560+ |
221 |
1 |
4 |
1 |
11 |
1 |
30 |
1 |
928 |
2 |
4 |
1 |
10 |
2 |
2 |
13 |
14 |
1 |
4 |
1 |
| 1580+ |
11 |
2 |
6 |
1 |
697 |
1 |
4 |
3 |
5 |
1 |
8 |
1 |
12 |
5 |
2 |
2 |
64 |
1 |
4 |
2 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 1600+ |
10281 |
1 |
10 |
1 |
5 |
1 |
4 |
1 |
54 |
1 |
8 |
2 |
11 |
1 |
4 |
1 |
51 |
6 |
2 |
1 |
| 1620+ |
477 |
1 |
2 |
2 |
56 |
5 |
6 |
1 |
11 |
5 |
4 |
1 |
1213 |
1 |
4 |
2 |
5 |
1 |
72 |
1 |
| 1640+ |
68 |
2 |
2 |
1 |
12 |
1 |
2 |
13 |
42 |
1 |
38 |
1 |
9 |
2 |
2 |
2 |
137 |
1 |
2 |
5 |
| 1660+ |
11 |
1 |
6 |
1 |
21507 |
5 |
10 |
1 |
15 |
1 |
4 |
1 |
34 |
2 |
60 |
2 |
4 |
5 |
2 |
1 |
| 1680+ |
1005 |
2 |
5 |
2 |
5 |
1 |
4 |
1 |
12 |
1 |
10 |
1 |
30 |
1 |
10 |
1 |
235 |
1 |
6 |
1 |
| 1700+ |
50 |
309 |
4 |
2 |
39 |
7 |
2 |
1 |
11 |
1 |
36 |
2 |
42 |
2 |
2 |
5 |
40 |
1 |
2 |
2 |
| 1720+ |
39 |
1 |
12 |
1 |
4 |
3 |
2 |
1 |
47937 |
1 |
4 |
2 |
5 |
1 |
13 |
1 |
35 |
4 |
4 |
1 |
| 1740+ |
37 |
1 |
4 |
2 |
51 |
1 |
16 |
1 |
9 |
1 |
30 |
2 |
64 |
1 |
2 |
14 |
4 |
1 |
4 |
1 |
| 1760+ |
1285 |
1 |
2 |
1 |
228 |
1 |
2 |
5 |
53 |
1 |
8 |
2 |
4 |
2 |
2 |
4 |
260 |
1 |
6 |
1 |
| 1780+ |
15 |
1 |
110 |
1 |
12 |
2 |
4 |
1 |
12 |
1 |
4 |
5 |
1083553 |
1 |
12 |
1 |
5 |
1 |
4 |
1 |
| +++ |
+0 |
+1 |
+2 |
+3 |
+4 |
+5 |
+6 |
+7 |
+8 |
+9 |
+10 |
+11 |
+12 |
+13 |
+14 |
+15 |
+16 |
+17 |
+18 |
+19 |
| 1800+ |
749 |
1 |
4 |
2 |
11 |
3 |
30 |
1 |
54 |
13 |
6 |
1 |
15 |
2 |
2 |
9 |
12 |
1 |
10 |
1 |
| 1820+ |
35 |
2 |
2 |
1 |
1264 |
2 |
4 |
6 |
5 |
1 |
18 |
1 |
14 |
2 |
4 |
1 |
117 |
1 |
2 |
2 |
| 1840+ |
178 |
1 |
6 |
1 |
5 |
4 |
4 |
1 |
162 |
2 |
10 |
1 |
4 |
1 |
16 |
1 |
1630 |
2 |
2 |
2 |
| 1860+ |
56 |
1 |
10 |
15 |
15 |
1 |
4 |
1 |
4 |
2 |
12 |
1 |
1096 |
1 |
2 |
21 |
9 |
1 |
6 |
1 |
| 1880+ |
39 |
5 |
2 |
1 |
18 |
1 |
4 |
2 |
195 |
1 |
120 |
1 |
9 |
2 |
2 |
1 |
54 |
1 |
4 |
4 |
| 1900+ |
36 |
1 |
4 |
1 |
186 |
2 |
2 |
1 |
36 |
1 |
6 |
15 |
12 |
1 |
8 |
1 |
4 |
5 |
4 |
1 |
| 1920+ |
241004 |
1 |
5 |
1 |
15 |
4 |
10 |
1 |
15 |
2 |
4 |
1 |
34 |
1 |
2 |
4 |
167 |
1 |
12 |
1 |
| 1940+ |
15 |
1 |
2 |
1 |
3973 |
1 |
4 |
1 |
4 |
1 |
40 |
1 |
235 |
11 |
2 |
1 |
15 |
1 |
6 |
1 |
| 1960+ |
144 |
1 |
18 |
1 |
4 |
2 |
2 |
2 |
203 |
1 |
4 |
15 |
15 |
1 |
12 |
2 |
39 |
1 |
4 |
1 |
| 1980+ |
120 |
1 |
2 |
2 |
1388 |
1 |
6 |
1 |
13 |
4 |
4 |
1 |
39 |
1 |
2 |
5 |
4 |
1 |
66 |
1 |
| 2000+ |
963 |
1 |
... |
1 |
... |
2 |
4 |
4 |
12 |
2 |
... |
1 |
4 |
2 |
4 |
2 |
... |
1 |
2 |
2 |
For the determination of this groups see
here.
The groups up to size 2000 except 1024 are available in
GAP and
MAGMA.
Another references to our group list is on the page of
Eric W. Weisstein. Here will even find something history about
the determination of small finite groups.
A Bibliography on the determination of finite groups
was written by
Eamonn O'Brien.
The groups of order 1024 have yet not been determined, but have been
emumerated by
Bettina Eick
and
Eamonn O'Brien.
Home