| 1 | C3×C31×(C5⋊D5)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C31×C3⋊#1044 | — | 3 | 1 | no | maximal |
| 3 | C31×#64480 | — | 3 | 3 | no | maximal |
| 4 | C3×C31×C52⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C3×C31×C5⋊D5 | D3 | 1 | 1 | yes | characteristic |
| 6 | C31×(C5⋊D5)⋊C3 | D3 | 1 | 3 | yes | — |
| 7 | C31×#1044 | — | 9 | 1 | no | Hall |
| 8 | C31×C52⋊C3 | Dic3 | 1 | 3 | yes | complemented |
| 9 | C3×C52×C31 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C31×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 11 | C31×C5⋊D5 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 12 | C31×C3⋊Dic3 | — | 25 | 1 | no | maximal, Hall |
| 13 | C3×D5×C31 | — | 15 | 2 | no | — |
| 14 | C3⋊#64480 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 15 | C52×C31 | C3⋊Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 16 | AGL(1,𝔽5)×C31 | — | 45 | 2 | no | — |
| 17 | C2×C32×C31 | — | 25 | 1 | no | — |
| 18 | C3×C5×C31 | — | 3 | 2 | no | — |
| 19 | C3×(C5⋊D5)⋊C3 | C2×C31 | 1 | 1 | yes | characteristic |
| 20 | Dic3×C31 | — | 75 | 1 | no | — |
| 21 | Dic3×C31 | — | 75 | 3 | no | — |
| 22 | D5×C31 | — | 15 | 2 | no | — |
| 23 | C3⋊#1044 | — | 3 | 1 | no | — |
| 24 | #64480 | — | 3 | 3 | no | — |
| 25 | C32×C31 | — | 25 | 1 | no | Hall |
| 26 | C3×C52⋊C3 | C4×C31 | 1 | 1 | yes | characteristic, complemented, Hall |
| 27 | C2×C3×C31 | — | 25 | 3 | no | — |
| 28 | C2×C3×C31 | — | 25 | 1 | no | — |
| 29 | C5×C31 | — | 3 | 2 | no | — |
| 30 | C3×C5⋊D5 | D3×C31 | 1 | 1 | yes | characteristic |
| 31 | (C5⋊D5)⋊C3 | D3×C31 | 1 | 3 | yes | — |
| 32 | C4×C31 | — | 225 | 1 | no | Hall |
| 33 | #1044 | — | 9 | 1 | no | Hall |
| 34 | C3×C31 | — | 25 | 3 | no | — |
| 35 | C3×C31 | #64480 | 1 | 1 | yes | characteristic, complemented |
| 36 | C3×C52 | Dic3×C31 | 1 | 1 | yes | characteristic, complemented |
| 37 | C52⋊C3 | Dic3×C31 | 1 | 3 | yes | complemented |
| 38 | C2×C31 | — | 25 | 1 | no | — |
| 39 | ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 40 | C5⋊D5 | C3⋊D3×C31 | 1 | 1 | yes | characteristic |
| 41 | C3⋊Dic3 | — | 25 | 1 | no | Hall |
| 42 | C31 | C3⋊#64480 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 43 | C3×D5 | — | 15 | 2 | no | — |
| 44 | C52 | C31×C3⋊Dic3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 45 | AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 46 | C2×C32 | — | 25 | 1 | no | — |
| 47 | C3×C5 | — | 3 | 2 | no | — |
| 48 | Dic3 | — | 75 | 1 | no | — |
| 49 | Dic3 | — | 75 | 3 | no | — |
| 50 | D5 | — | 15 | 2 | no | — |
| 51 | C32 | — | 25 | 1 | no | Sylow |
| 52 | C2×C3 | — | 25 | 3 | no | — |
| 53 | C2×C3 | — | 25 | 1 | no | — |
| 54 | C5 | — | 3 | 2 | no | — |
| 55 | C4 | — | 225 | 1 | no | Sylow |
| 56 | C3 | — | 25 | 3 | no | — |
| 57 | C3 | C31×#64480 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2 | — | 25 | 1 | no | — |
Finite Group Databasebeta