| 1 | C3×D25×C31⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C31×#1035 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C31⋊C3×#1035 | C3 | 1 | 3 | yes | maximal, direct product factor |
| 4 | C3×C25×C31⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C3×AGL(1,𝔽5)×C31⋊C3 | — | 5 | 1 | no | maximal |
| 6 | C3×C31×D25 | C2×C3 | 1 | 1 | yes | characteristic |
| 7 | D25×C31⋊C3 | C2×C3 | 1 | 3 | yes | — |
| 8 | C31×#1035 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C3×D5×C31⋊C3 | — | 5 | 1 | no | — |
| 10 | C25×C31⋊C3 | C3×C4 | 1 | 3 | yes | complemented |
| 11 | C3×C25×C31 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×AGL(1,𝔽5)×C31 | — | 5 | 1 | no | — |
| 13 | AGL(1,𝔽5)×C31⋊C3 | — | 5 | 3 | no | — |
| 14 | C31×D25 | C2×C32 | 1 | 1 | yes | characteristic |
| 15 | C3×C5×C31⋊C3 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 16 | C3×C4×C31⋊C3 | — | 25 | 1 | no | Hall |
| 17 | C3×D5×C31 | — | 5 | 1 | no | — |
| 18 | D5×C31⋊C3 | — | 5 | 3 | no | — |
| 19 | C32×#1035 | — | 31 | 1 | no | maximal, Hall |
| 20 | C25×C31 | C32×C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 21 | AGL(1,𝔽5)×C31 | — | 5 | 1 | no | — |
| 22 | C2×C3×C31⋊C3 | — | 25 | 1 | no | — |
| 23 | C3×C5×C31 | C3×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 24 | C5×C31⋊C3 | C3×AGL(1,𝔽5) | 1 | 3 | yes | — |
| 25 | C32×D25 | — | 31 | 1 | no | — |
| 26 | C3×C4×C31 | — | 25 | 1 | no | — |
| 27 | C4×C31⋊C3 | — | 25 | 3 | no | — |
| 28 | D5×C31 | — | 5 | 1 | no | — |
| 29 | C3×#1035 | — | 31 | 3 | no | — |
| 30 | C3×#1035 | C31⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 31 | C3×C31⋊C3 | #1035 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 32 | C32×C25 | — | 31 | 1 | no | Hall |
| 33 | C2×C3×C31 | — | 25 | 1 | no | — |
| 34 | C2×C31⋊C3 | — | 25 | 3 | no | — |
| 35 | C32×AGL(1,𝔽5) | — | 155 | 1 | no | — |
| 36 | C5×C31 | C32×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 37 | C3×D25 | — | 31 | 3 | no | — |
| 38 | C3×D25 | C2×C31⋊C3 | 1 | 1 | yes | characteristic |
| 39 | C4×C31 | — | 25 | 1 | no | Hall |
| 40 | #1035 | C3×C31⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 41 | C3×C31 | C3×#1035 | 1 | 1 | yes | characteristic, complemented |
| 42 | C31⋊C3 | C3×#1035 | 1 | 3 | yes | direct product factor |
| 43 | C32×D5 | — | 155 | 1 | no | — |
| 44 | C3×C25 | — | 31 | 3 | no | — |
| 45 | C3×C25 | C4×C31⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×C31 | — | 25 | 1 | no | — |
| 47 | C3×AGL(1,𝔽5) | — | 5 | 1 | no | — |
| 48 | C3×AGL(1,𝔽5) | — | 155 | 3 | no | — |
| 49 | D25 | C2×C3×C31⋊C3 | 1 | 1 | yes | characteristic |
| 50 | C32×C5 | — | 31 | 1 | no | — |
| 51 | C32×C4 | — | 775 | 1 | no | Hall |
| 52 | C31 | C32×#1035 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 53 | C3×D5 | — | 5 | 1 | no | — |
| 54 | C3×D5 | — | 155 | 3 | no | — |
| 55 | C25 | C3×C4×C31⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 56 | AGL(1,𝔽5) | — | 5 | 1 | no | — |
| 57 | C2×C32 | — | 775 | 1 | no | — |
| 58 | C3×C5 | — | 31 | 3 | no | — |
| 59 | C3×C5 | AGL(1,𝔽5)×C31⋊C3 | 1 | 1 | yes | characteristic |
| 60 | C3×C4 | — | 775 | 3 | no | — |
| 61 | C3×C4 | — | 25 | 1 | no | — |
| 62 | D5 | — | 5 | 1 | no | — |
| 63 | C32 | — | 31 | 1 | no | Sylow |
| 64 | C2×C3 | — | 775 | 3 | no | — |
| 65 | C2×C3 | — | 25 | 1 | no | — |
| 66 | C5 | C3×AGL(1,𝔽5)×C31⋊C3 | 1 | 1 | yes | characteristic |
| 67 | C4 | — | 25 | 1 | no | Sylow |
| 68 | C3 | — | 31 | 3 | no | — |
| 69 | C3 | C31⋊C3×#1035 | 1 | 1 | yes | characteristic, direct product factor |
| 70 | C2 | — | 25 | 1 | no | — |
Finite Group Databasebeta