| 1 | #16861232 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q16×D127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #16861155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #16861154 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #16861152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #16861148 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | Q32×C127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #14523249 | — | 2 | 1 | no | — |
| 9 | Q8×D127 | — | 2 | 1 | no | — |
| 10 | Dic508 | C22 | 1 | 1 | yes | characteristic |
| 11 | #14523238 | — | 2 | 1 | no | — |
| 12 | #14523235 | — | 2 | 1 | no | — |
| 13 | D1016 | C22 | 1 | 1 | yes | characteristic |
| 14 | C8×D127 | C22 | 1 | 1 | yes | characteristic |
| 15 | C127⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 16 | Q16×C127 | C22 | 1 | 1 | yes | characteristic |
| 17 | Q16×C127 | C22 | 1 | 1 | yes | characteristic |
| 18 | C16×C127 | C22 | 1 | 1 | yes | characteristic |
| 19 | Dic254 | — | 2 | 1 | no | — |
| 20 | Dic254 | — | 4 | 1 | no | — |
| 21 | D508 | — | 2 | 1 | no | — |
| 22 | D508 | — | 4 | 1 | no | — |
| 23 | C4×D127 | — | 4 | 1 | no | — |
| 24 | C4×D127 | — | 4 | 1 | no | — |
| 25 | C4×D127 | D4 | 1 | 1 | yes | characteristic |
| 26 | C127⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 27 | Q8×C127 | — | 2 | 1 | no | — |
| 28 | Q8×C127 | — | 2 | 1 | no | — |
| 29 | C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 30 | C2×D127 | — | 4 | 1 | no | — |
| 31 | C2×D127 | D8 | 1 | 1 | yes | characteristic |
| 32 | C4×C127 | — | 4 | 1 | no | — |
| 33 | C4×C127 | — | 4 | 1 | no | — |
| 34 | C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 35 | Dic127 | — | 4 | 1 | no | — |
| 36 | Dic127 | D8 | 1 | 1 | yes | characteristic |
| 37 | C2×C127 | C2×D8 | 1 | 1 | yes | characteristic |
| 38 | D127 | — | 2 | 1 | no | — |
| 39 | D127 | — | 8 | 1 | no | — |
| 40 | C127 | #510 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 41 | #510 | — | 127 | 1 | no | maximal, Sylow |
| 42 | #135 | — | 127 | 1 | no | — |
| 43 | C2×Q16 | — | 127 | 1 | no | — |
| 44 | Q32 | — | 127 | 1 | no | — |
| 45 | Q32 | D127 | 1 | 1 | yes | characteristic, complemented |
| 46 | SD32 | — | 127 | 1 | no | — |
| 47 | SD32 | — | 127 | 1 | no | — |
| 48 | M32 | — | 127 | 1 | no | — |
| 49 | #41 | — | 254 | 1 | no | — |
| 50 | C2×Q8 | — | 254 | 1 | no | — |
| 51 | Q16 | — | 127 | 1 | no | — |
| 52 | Q16 | — | 254 | 1 | no | — |
| 53 | Q16 | C2×D127 | 1 | 1 | yes | characteristic |
| 54 | Q16 | C2×D127 | 1 | 1 | yes | characteristic |
| 55 | SD16 | — | 254 | 1 | no | — |
| 56 | D8 | — | 127 | 1 | no | — |
| 57 | C2×C8 | — | 127 | 1 | no | — |
| 58 | C16 | — | 127 | 1 | no | — |
| 59 | C16 | C2×D127 | 1 | 1 | yes | characteristic |
| 60 | Q8 | — | 2 | 1 | no | — |
| 61 | Q8 | — | 2 | 1 | no | — |
| 62 | Q8 | — | 508 | 1 | no | — |
| 63 | Q8 | — | 254 | 1 | no | — |
| 64 | D4 | — | 508 | 1 | no | — |
| 65 | D4 | — | 254 | 1 | no | — |
| 66 | C2×C4 | — | 127 | 1 | no | — |
| 67 | C2×C4 | — | 508 | 1 | no | — |
| 68 | C2×C4 | — | 508 | 1 | no | — |
| 69 | C8 | — | 127 | 1 | no | — |
| 70 | C8 | C22×D127 | 1 | 1 | yes | characteristic |
| 71 | C22 | — | 127 | 1 | no | — |
| 72 | C22 | — | 508 | 1 | no | — |
| 73 | C4 | — | 4 | 1 | no | — |
| 74 | C4 | — | 4 | 1 | no | — |
| 75 | C4 | — | 127 | 1 | no | — |
| 76 | C4 | — | 508 | 1 | no | — |
| 77 | C4 | D4×D127 | 1 | 1 | yes | characteristic |
| 78 | C2 | — | 1016 | 1 | no | — |
| 79 | C2 | — | 254 | 1 | no | — |
| 80 | C2 | D8×D127 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta