| 1 | #578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #509 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×SD32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | 2−1+4 | — | 2 | 1 | no | — |
| 9 | #137 | — | 2 | 2 | no | — |
| 10 | #137 | — | 2 | 1 | no | — |
| 11 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 12 | #135 | — | 2 | 1 | no | — |
| 13 | #135 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×Q16 | — | 2 | 1 | no | — |
| 15 | C2×Q16 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×D8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #131 | C22 | 1 | 1 | yes | characteristic |
| 18 | SD32 | — | 2 | 2 | no | — |
| 19 | SD32 | — | 2 | 1 | no | — |
| 20 | D16 | — | 2 | 1 | no | — |
| 21 | M32 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C16 | C22 | 1 | 1 | yes | characteristic |
| 23 | #108 | C22 | 1 | 1 | yes | characteristic |
| 24 | #100 | — | 2 | 1 | no | — |
| 25 | #41 | — | 2 | 2 | no | — |
| 26 | #41 | — | 2 | 1 | no | — |
| 27 | #41 | — | 4 | 2 | no | — |
| 28 | #41 | — | 4 | 1 | no | — |
| 29 | #41 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×Q8 | — | 2 | 2 | no | — |
| 31 | C2×Q8 | — | 2 | 1 | no | — |
| 32 | C2×Q8 | — | 4 | 1 | no | — |
| 33 | C2×D4 | — | 2 | 1 | no | — |
| 34 | Q16 | — | 2 | 2 | no | — |
| 35 | Q16 | — | 2 | 1 | no | — |
| 36 | Q16 | D4 | 1 | 1 | yes | characteristic |
| 37 | Q16 | D4 | 1 | 2 | yes | — |
| 38 | SD16 | — | 2 | 2 | no | — |
| 39 | SD16 | — | 2 | 1 | no | — |
| 40 | SD16 | — | 4 | 1 | no | — |
| 41 | D8 | — | 2 | 1 | no | — |
| 42 | D8 | — | 2 | 1 | no | — |
| 43 | D8 | — | 4 | 1 | no | — |
| 44 | D8 | D4 | 1 | 1 | yes | characteristic |
| 45 | M16 | — | 2 | 1 | no | — |
| 46 | M16 | — | 2 | 1 | no | — |
| 47 | M16 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×C8 | — | 2 | 1 | no | — |
| 49 | C2×C8 | C23 | 1 | 1 | yes | characteristic |
| 50 | C16 | — | 2 | 1 | no | — |
| 51 | C16 | — | 2 | 1 | no | — |
| 52 | C23 | — | 4 | 1 | no | — |
| 53 | Q8 | — | 2 | 2 | no | — |
| 54 | Q8 | — | 2 | 1 | no | — |
| 55 | Q8 | — | 4 | 2 | no | — |
| 56 | Q8 | — | 4 | 1 | no | — |
| 57 | Q8 | D8 | 1 | 1 | yes | characteristic |
| 58 | D4 | — | 2 | 1 | no | — |
| 59 | D4 | — | 2 | 1 | no | — |
| 60 | D4 | — | 4 | 2 | no | — |
| 61 | D4 | — | 4 | 1 | no | — |
| 62 | D4 | — | 4 | 1 | no | — |
| 63 | D4 | — | 4 | 1 | no | — |
| 64 | D4 | D8 | 1 | 1 | yes | characteristic |
| 65 | C2×C4 | — | 2 | 1 | no | — |
| 66 | C2×C4 | — | 4 | 2 | no | — |
| 67 | C2×C4 | — | 4 | 2 | no | — |
| 68 | C2×C4 | — | 4 | 1 | no | — |
| 69 | C2×C4 | — | 4 | 1 | no | — |
| 70 | C2×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C8 | — | 2 | 1 | no | — |
| 72 | C8 | — | 4 | 1 | no | — |
| 73 | C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 75 | C22 | — | 2 | 1 | no | — |
| 76 | C22 | — | 4 | 1 | no | — |
| 77 | C22 | — | 8 | 1 | no | — |
| 78 | C22 | — | 16 | 1 | no | — |
| 79 | C22 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 80 | C4 | — | 2 | 1 | no | — |
| 81 | C4 | — | 4 | 2 | no | — |
| 82 | C4 | — | 4 | 1 | no | — |
| 83 | C4 | #120 | 1 | 1 | yes | characteristic |
| 84 | C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 85 | C2 | — | 2 | 1 | no | — |
| 86 | C2 | — | 4 | 1 | no | — |
| 87 | C2 | — | 8 | 1 | no | — |
| 88 | C2 | — | 16 | 1 | no | — |
| 89 | C2 | #447 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta