| 1 | C31×#135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11758481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11758417 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11758416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11758415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11758414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C31⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #41×C31 | — | 2 | 1 | no | — |
| 9 | #92495 | — | 2 | 1 | no | — |
| 10 | Q16×C31 | C22 | 1 | 1 | yes | characteristic |
| 11 | SD16×C31 | — | 2 | 1 | no | — |
| 12 | D8×C31 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C8×C31 | C22 | 1 | 1 | yes | characteristic |
| 14 | Dic124 | C22 | 1 | 1 | yes | characteristic |
| 15 | D248 | C22 | 1 | 1 | yes | characteristic |
| 16 | #92470 | — | 2 | 1 | no | — |
| 17 | C31⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C31⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×C31 | — | 2 | 1 | no | — |
| 20 | D4×C31 | — | 2 | 1 | no | — |
| 21 | D4×C31 | — | 4 | 1 | no | — |
| 22 | C2×C4×C31 | — | 4 | 1 | no | — |
| 23 | C2×C4×C31 | D4 | 1 | 1 | yes | characteristic |
| 24 | C22⋊D31 | — | 4 | 1 | no | — |
| 25 | D124 | — | 2 | 1 | no | — |
| 26 | C4×D31 | — | 4 | 1 | no | — |
| 27 | Dic62 | — | 2 | 1 | no | — |
| 28 | C8×C31 | D4 | 1 | 1 | yes | characteristic |
| 29 | C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 30 | C22×C31 | — | 4 | 1 | no | — |
| 31 | C22×C31 | D8 | 1 | 1 | yes | characteristic |
| 32 | C2×D31 | — | 4 | 1 | no | — |
| 33 | C4×C31 | — | 4 | 1 | no | — |
| 34 | C4×C31 | D8 | 1 | 1 | yes | characteristic |
| 35 | C4×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 36 | Dic31 | — | 4 | 1 | no | — |
| 37 | #508 | — | 31 | 1 | no | maximal, Sylow |
| 38 | C2×C31 | — | 2 | 1 | no | — |
| 39 | C2×C31 | — | 8 | 1 | no | — |
| 40 | C2×C31 | C2×D8 | 1 | 1 | yes | characteristic |
| 41 | D31 | — | 8 | 1 | no | — |
| 42 | #135 | — | 31 | 1 | no | — |
| 43 | #135 | D31 | 1 | 1 | yes | characteristic, complemented |
| 44 | Q32 | — | 31 | 1 | no | — |
| 45 | SD32 | — | 31 | 1 | no | — |
| 46 | SD32 | — | 31 | 1 | no | — |
| 47 | D16 | — | 31 | 1 | no | — |
| 48 | C2×C16 | — | 31 | 1 | no | — |
| 49 | C31 | #508 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 50 | #41 | — | 2 | 1 | no | — |
| 51 | #41 | — | 62 | 1 | no | — |
| 52 | Q16 | — | 31 | 1 | no | — |
| 53 | Q16 | C2×D31 | 1 | 1 | yes | characteristic |
| 54 | SD16 | — | 2 | 1 | no | — |
| 55 | SD16 | — | 62 | 1 | no | — |
| 56 | D8 | — | 31 | 1 | no | — |
| 57 | D8 | C2×D31 | 1 | 1 | yes | characteristic |
| 58 | C2×C8 | C2×D31 | 1 | 1 | yes | characteristic |
| 59 | C16 | — | 31 | 1 | no | — |
| 60 | C16 | — | 31 | 1 | no | — |
| 61 | Q8 | — | 2 | 1 | no | — |
| 62 | Q8 | — | 62 | 1 | no | — |
| 63 | D4 | — | 2 | 1 | no | — |
| 64 | D4 | — | 4 | 1 | no | — |
| 65 | D4 | — | 62 | 1 | no | — |
| 66 | D4 | — | 124 | 1 | no | — |
| 67 | C2×C4 | — | 4 | 1 | no | — |
| 68 | C2×C4 | — | 124 | 1 | no | — |
| 69 | C2×C4 | C22⋊D31 | 1 | 1 | yes | characteristic |
| 70 | C8 | C22⋊D31 | 1 | 1 | yes | characteristic |
| 71 | C8 | C22×D31 | 1 | 1 | yes | characteristic |
| 72 | C22 | — | 4 | 1 | no | — |
| 73 | C22 | — | 124 | 1 | no | — |
| 74 | C22 | #92479 | 1 | 1 | yes | characteristic |
| 75 | C4 | — | 4 | 1 | no | — |
| 76 | C4 | — | 124 | 1 | no | — |
| 77 | C4 | #92479 | 1 | 1 | yes | characteristic |
| 78 | C4 | C2×C22⋊D31 | 1 | 1 | yes | characteristic |
| 79 | C2 | — | 2 | 1 | no | — |
| 80 | C2 | — | 8 | 1 | no | — |
| 81 | C2 | — | 248 | 1 | no | — |
| 82 | C2 | C2×#92479 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta