| 1 | C5×C9×D5×C31 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C31×#1042 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C52×C9×C31 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C9×AGL(1,𝔽5)×C31 | — | 5 | 1 | no | maximal |
| 5 | C9×Dic5×C31 | — | 5 | 1 | no | maximal |
| 6 | C3×C5×D5×C31 | C2×C3 | 1 | 1 | yes | characteristic |
| 7 | C31×#1042 | C9 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 8 | C9×D5×C31 | D5 | 1 | 1 | yes | characteristic |
| 9 | C2×C5×C9×C31 | — | 5 | 1 | no | — |
| 10 | C3×C52×C31 | C3×C4 | 1 | 1 | yes | characteristic |
| 11 | C3×AGL(1,𝔽5)×C31 | — | 5 | 1 | no | — |
| 12 | C3×Dic5×C31 | — | 5 | 1 | no | — |
| 13 | C5×D5×C31 | C2×C9 | 1 | 1 | yes | characteristic |
| 14 | C5×C9×C31 | — | 4 | 1 | no | — |
| 15 | C5×C9×C31 | Dic5 | 1 | 1 | yes | characteristic, complemented |
| 16 | C5×C9×C31 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 17 | C4×C9×C31 | — | 25 | 1 | no | Hall |
| 18 | C2×C3×C5×C31 | — | 5 | 1 | no | — |
| 19 | C3×D5×C31 | C3×D5 | 1 | 1 | yes | characteristic |
| 20 | C9×#1042 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 21 | C52×C31 | C4×C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 22 | AGL(1,𝔽5)×C31 | — | 5 | 1 | no | — |
| 23 | Dic5×C31 | — | 5 | 1 | no | — |
| 24 | C2×C9×C31 | — | 5 | 1 | no | — |
| 25 | C3×C5×C31 | — | 4 | 1 | no | — |
| 26 | C3×C5×C31 | C3×Dic5 | 1 | 1 | yes | characteristic |
| 27 | C3×C5×C31 | C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 28 | C5×C9×D5 | C2×C31 | 1 | 1 | yes | characteristic |
| 29 | C3×C4×C31 | — | 25 | 1 | no | — |
| 30 | C2×C5×C31 | — | 5 | 1 | no | — |
| 31 | D5×C31 | C9×D5 | 1 | 1 | yes | characteristic |
| 32 | C3×#1042 | C3×C31 | 1 | 1 | yes | characteristic |
| 33 | C9×C31 | #1042 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 34 | C52×C9 | C4×C31 | 1 | 1 | yes | characteristic, complemented, Hall |
| 35 | C2×C3×C31 | — | 5 | 1 | no | — |
| 36 | C9×AGL(1,𝔽5) | — | 5 | 1 | no | — |
| 37 | C9×Dic5 | — | 5 | 1 | no | — |
| 38 | C5×C31 | — | 4 | 1 | no | — |
| 39 | C5×C31 | C9×Dic5 | 1 | 1 | yes | characteristic, complemented |
| 40 | C5×C31 | C9×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×C5×D5 | C2×C3×C31 | 1 | 1 | yes | characteristic |
| 42 | C4×C31 | — | 25 | 1 | no | Hall |
| 43 | #1042 | C9×C31 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 44 | C3×C31 | C3×#1042 | 1 | 1 | yes | characteristic |
| 45 | C2×C5×C9 | — | 5 | 1 | no | — |
| 46 | C9×D5 | D5×C31 | 1 | 1 | yes | characteristic |
| 47 | C3×C52 | C3×C4×C31 | 1 | 1 | yes | characteristic |
| 48 | C2×C31 | — | 5 | 1 | no | — |
| 49 | C3×AGL(1,𝔽5) | — | 5 | 1 | no | — |
| 50 | C3×Dic5 | — | 5 | 1 | no | — |
| 51 | C5×D5 | C2×C9×C31 | 1 | 1 | yes | characteristic |
| 52 | C5×C9 | — | 4 | 1 | no | — |
| 53 | C5×C9 | Dic5×C31 | 1 | 1 | yes | characteristic, complemented |
| 54 | C5×C9 | AGL(1,𝔽5)×C31 | 1 | 1 | yes | characteristic, complemented |
| 55 | C4×C9 | — | 25 | 1 | no | Hall |
| 56 | C31 | C9×#1042 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 57 | C2×C3×C5 | — | 5 | 1 | no | — |
| 58 | C3×D5 | C3×D5×C31 | 1 | 1 | yes | characteristic |
| 59 | C52 | C4×C9×C31 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 60 | AGL(1,𝔽5) | — | 5 | 1 | no | — |
| 61 | Dic5 | — | 5 | 1 | no | — |
| 62 | C2×C9 | — | 5 | 1 | no | — |
| 63 | C3×C5 | — | 4 | 1 | no | — |
| 64 | C3×C5 | C3×Dic5×C31 | 1 | 1 | yes | characteristic |
| 65 | C3×C5 | C3×AGL(1,𝔽5)×C31 | 1 | 1 | yes | characteristic |
| 66 | C3×C4 | — | 25 | 1 | no | — |
| 67 | C2×C5 | — | 5 | 1 | no | — |
| 68 | D5 | C9×D5×C31 | 1 | 1 | yes | characteristic |
| 69 | C9 | C31×#1042 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 70 | C2×C3 | — | 5 | 1 | no | — |
| 71 | C5 | — | 4 | 1 | no | — |
| 72 | C5 | C9×Dic5×C31 | 1 | 1 | yes | characteristic, complemented |
| 73 | C5 | C9×AGL(1,𝔽5)×C31 | 1 | 1 | yes | characteristic, complemented |
| 74 | C4 | — | 25 | 1 | no | Sylow |
| 75 | C3 | C3×C31×#1042 | 1 | 1 | yes | characteristic |
| 76 | C2 | — | 5 | 1 | no | — |
Finite Group Databasebeta