| 1 |
G ≤ Sym(22) |
3-trans., on cosets of L3(4) (1st max.) |
| 2 |
G ≤ Sym(77) |
rank 3, on cosets of 24:A6 (2nd max.) |
| 3 |
G ≤ Sym(176a) |
rank 3, on cosets of A7 (3rd max.) |
| 4 |
G ≤ Sym(176b) |
rank 3, on cosets of A7 (4th max.) |
| 5 |
G ≤ Sym(231) |
rank 4, on cosets of 24:S5 (5th max.) |
| 6 |
G ≤ Sym(330) |
rank 5, on cosets of 23:L3(2) (6th max.) |
| 7 |
G ≤ Sym(462a) |
rank 5, on cosets of 24:A5 < 24:A6 |
| 8 |
G ≤ Sym(462b) |
rank 8, on cosets of 24:A5 < L3(4), 24:S5 |
| 9 |
G ≤ Sym(462c) |
rank 8, on cosets of 24:A5 < L3(4), 24:A6 |
| 10 |
G ≤ Sym(616) |
rank 5, on cosets of A6.23 (7th max.) |
| 11 |
G ≤ Sym(672) |
rank 6, on cosets of L2(11) (8th max.) |
| 12 |
G ≤ Sym(770) |
rank 9, on cosets of (A4 × A4):4 < 24:A6 |
| 13 |
G ≤ GL(10a,2) |
character 10a |
| 14 |
G ≤ GL(10b,2) |
character 10b |
| 15 |
G ≤ GL(34,2) |
character 34a |
| 16 |
G ≤ GL(98,2) |
character 98a |
| 17 |
G ≤ GL(21,3) |
character 21a |
| 18 |
G ≤ GL(49a,3) |
character 49a |
| 19 |
G ≤ GL(49b,3) |
character 49b |
| 20 |
G ≤ GL(55,3) |
character 55a |
| 21 |
G ≤ GL(99,3) |
character 99a |
| 22 |
G ≤ GL(210,3) |
character 210a |
| 23 |
G ≤ GL(231,3) |
character 231a |
| 24 |
G ≤ GL(70a,4) |
character 70a |
| 25 |
G ≤ GL(70b,4) |
character 70b |
| 26 |
G ≤ GL(21,5) |
character 21a |
| 27 |
G ≤ GL(55,5) |
character 55a |
| 28 |
G ≤ GL(98,5) |
character 98a |
| 29 |
G ≤ GL(133,5) |
character 133a |
| 30 |
G ≤ GL(210,5) |
character 210a |
| 31 |
G ≤ GL(280a,5) |
character 280a |
| 32 |
G ≤ GL(385,5) |
character 385a |
| 33 |
G ≤ GL(21,7) |
character 21a |
| 34 |
G ≤ GL(45,7) |
character 45a |
| 35 |
G ≤ GL(54,7) |
character 54a |
| 36 |
G ≤ GL(154,7) |
character 154a |
| 37 |
G ≤ GL(210,7) |
character 210a |
| 38 |
G ≤ GL(231,7) |
character 231a |
| 39 |
G ≤ GL(385,7) |
character 385a |
| 40 |
G ≤ GL(45a,9) |
character 45a |
| 41 |
G ≤ GL(20,11) |
character 20a |
| 42 |
G ≤ GL(45a,11) |
character 45a |
| 43 |
G ≤ GL(45b,11) |
character 45b |
| 44 |
G ≤ GL(55,11) |
character 55a |
| 45 |
G ≤ GL(99,11) |
character 99a |
| 46 |
G ≤ GL(154,11) |
character 154a |
| 47 |
G ≤ GL(190,11) |
character 190a |
| 48 |
G ≤ GL(231,11) |
character 231a |
| 49 |
G ≤ GL(385,11) |
character 385a |
| 50 |
G ≤ GL(45a,25) |
character 45a |
| 51 |
G ≤ GL(280a,49) |
character 280a |
| 52 |
G ≤ GL(280b,49) |
character 280b |
| 53 |
G ≤ GL(21,ℤ) |
character 21a |
| 54 |
G ≤ GL(55,ℤ) |
character 55a |
| 55 |
G ≤ GL(99,ℤ) |
character 99a |
| 56 |
G ≤ GL(154,ℤ) |
character 154a |
| 57 |
G ≤ GL(210,ℤ) |
character 210a |
| 58 |
G ≤ GL(231,ℤ) |
character 231a |