| 1 | #16860810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #16860800 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #16860798 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #16860797 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #16860795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×C251⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #41×C251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | Dic502 | C22 | 1 | 1 | yes | characteristic |
| 9 | D1004 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22⋊D251 | — | 2 | 1 | no | — |
| 11 | C4×D251 | — | 2 | 1 | no | — |
| 12 | C251⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C251⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | Q8×C251 | C22 | 1 | 1 | yes | characteristic |
| 15 | D4×C251 | — | 2 | 1 | no | — |
| 16 | D4×C251 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×C251 | — | 2 | 1 | no | — |
| 18 | C2×C4×C251 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C251 | — | 2 | 1 | no | — |
| 20 | C22×C251 | D4 | 1 | 1 | yes | characteristic |
| 21 | C2×D251 | — | 2 | 1 | no | — |
| 22 | C4×C251 | — | 2 | 1 | no | — |
| 23 | C4×C251 | D4 | 1 | 1 | yes | characteristic |
| 24 | C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 25 | Dic251 | — | 2 | 1 | no | — |
| 26 | C2×C251 | — | 2 | 1 | no | — |
| 27 | C2×C251 | — | 4 | 1 | no | — |
| 28 | C2×C251 | C2×D4 | 1 | 1 | yes | characteristic |
| 29 | D251 | — | 4 | 1 | no | — |
| 30 | C251 | #135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 31 | #135 | — | 251 | 1 | no | maximal, Sylow |
| 32 | #41 | — | 251 | 1 | no | — |
| 33 | #41 | D251 | 1 | 1 | yes | characteristic, complemented |
| 34 | Q16 | — | 251 | 1 | no | — |
| 35 | SD16 | — | 251 | 1 | no | — |
| 36 | SD16 | — | 251 | 1 | no | — |
| 37 | D8 | — | 251 | 1 | no | — |
| 38 | C2×C8 | — | 251 | 1 | no | — |
| 39 | Q8 | — | 251 | 1 | no | — |
| 40 | Q8 | C2×D251 | 1 | 1 | yes | characteristic |
| 41 | D4 | — | 2 | 1 | no | — |
| 42 | D4 | — | 502 | 1 | no | — |
| 43 | D4 | — | 251 | 1 | no | — |
| 44 | D4 | C2×D251 | 1 | 1 | yes | characteristic |
| 45 | C2×C4 | — | 2 | 1 | no | — |
| 46 | C2×C4 | — | 502 | 1 | no | — |
| 47 | C2×C4 | C2×D251 | 1 | 1 | yes | characteristic |
| 48 | C8 | — | 251 | 1 | no | — |
| 49 | C8 | — | 251 | 1 | no | — |
| 50 | C22 | — | 2 | 1 | no | — |
| 51 | C22 | — | 502 | 1 | no | — |
| 52 | C22 | C22⋊D251 | 1 | 1 | yes | characteristic |
| 53 | C4 | — | 2 | 1 | no | — |
| 54 | C4 | — | 502 | 1 | no | — |
| 55 | C4 | C22⋊D251 | 1 | 1 | yes | characteristic |
| 56 | C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 57 | C2 | — | 2 | 1 | no | — |
| 58 | C2 | — | 4 | 1 | no | — |
| 59 | C2 | — | 1004 | 1 | no | — |
| 60 | C2 | C2×C22⋊D251 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta