| 1 | C5×Q8×ΓL(1,𝔽8) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C5×C4⋊AGL(1,𝔽7) | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C4×C5×AGL(1,𝔽7) | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C5×#1161 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 5 | C2×C5×AGL(1,𝔽7) | C22 | 1 | 3 | yes | — |
| 6 | C4×C5×ΓL(1,𝔽8) | C22 | 1 | 3 | yes | — |
| 7 | C5×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 8 | #66659 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 9 | C5×C7×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C5×D28 | C2×C3 | 1 | 3 | yes | complemented |
| 11 | C4×C5×D7 | C2×C3 | 1 | 3 | yes | complemented |
| 12 | C3×C5×#41 | — | 7 | 1 | no | maximal, Hall |
| 13 | C2×C5×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 14 | C5×AGL(1,𝔽7) | — | 2 | 3 | no | — |
| 15 | Q8×ΓL(1,𝔽8) | C2×C5 | 1 | 1 | yes | characteristic, complemented |
| 16 | C4⋊AGL(1,𝔽7) | C2×C5 | 1 | 3 | yes | complemented |
| 17 | C4×AGL(1,𝔽7) | C2×C5 | 1 | 3 | yes | complemented |
| 18 | C2×C5×D7 | C22×C3 | 1 | 3 | yes | — |
| 19 | C4×C5×C7 | C22×C3 | 1 | 3 | yes | — |
| 20 | C5×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 21 | C3×C5×Q8 | — | 7 | 1 | no | — |
| 22 | C3×C5×D4 | — | 7 | 3 | no | — |
| 23 | C2×C3×C4×C5 | — | 7 | 3 | no | — |
| 24 | #1161 | C3×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 25 | C5×ΓL(1,𝔽8) | #41 | 1 | 1 | yes | characteristic, complemented, Hall |
| 26 | C2×AGL(1,𝔽7) | C22×C5 | 1 | 3 | yes | — |
| 27 | C4×ΓL(1,𝔽8) | C22×C5 | 1 | 3 | yes | — |
| 28 | ΓL(1,𝔽8)⋊C4 | C22×C5 | 1 | 1 | yes | characteristic |
| 29 | C5×#41 | — | 7 | 1 | no | Hall |
| 30 | C2×C5×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 31 | C5×D7 | — | 2 | 3 | no | — |
| 32 | C22×C3×C5 | — | 7 | 3 | no | — |
| 33 | C3×C4×C5 | — | 7 | 1 | no | — |
| 34 | C3×C4×C5 | — | 7 | 3 | no | — |
| 35 | C7×Q8 | C2×C3×C5 | 1 | 1 | yes | characteristic, complemented |
| 36 | D28 | C2×C3×C5 | 1 | 3 | yes | complemented |
| 37 | C4×D7 | C2×C3×C5 | 1 | 3 | yes | complemented |
| 38 | C3×#41 | — | 7 | 1 | no | Hall |
| 39 | C2×ΓL(1,𝔽8) | C23×C5 | 1 | 1 | yes | characteristic |
| 40 | AGL(1,𝔽7) | — | 2 | 3 | no | — |
| 41 | C5×Q8 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 42 | C5×D4 | — | 7 | 3 | no | — |
| 43 | C2×C4×C5 | — | 7 | 3 | no | — |
| 44 | C5×C7 | C3×#41 | 1 | 1 | yes | characteristic, complemented, Hall |
| 45 | C2×C3×C5 | — | 7 | 1 | no | — |
| 46 | C2×C3×C5 | — | 14 | 3 | no | — |
| 47 | C2×D7 | C22×C3×C5 | 1 | 3 | yes | — |
| 48 | C4×C7 | C22×C3×C5 | 1 | 3 | yes | — |
| 49 | Dic7 | C22×C3×C5 | 1 | 1 | yes | characteristic |
| 50 | C3×Q8 | — | 7 | 1 | no | — |
| 51 | C3×D4 | — | 7 | 3 | no | — |
| 52 | C2×C3×C4 | — | 7 | 3 | no | — |
| 53 | ΓL(1,𝔽8) | C5×#41 | 1 | 1 | yes | characteristic, complemented, Hall |
| 54 | C22×C5 | — | 7 | 3 | no | — |
| 55 | C4×C5 | — | 7 | 1 | no | — |
| 56 | C4×C5 | C2×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 57 | #41 | — | 7 | 1 | no | Sylow |
| 58 | C3×C5 | — | 7 | 1 | no | Hall |
| 59 | C2×C7 | C23×C3×C5 | 1 | 1 | yes | characteristic |
| 60 | D7 | — | 2 | 3 | no | — |
| 61 | C22×C3 | — | 7 | 3 | no | — |
| 62 | C3×C4 | — | 7 | 1 | no | — |
| 63 | C3×C4 | — | 7 | 3 | no | — |
| 64 | C2×C5 | — | 14 | 3 | no | — |
| 65 | C2×C5 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 66 | Q8 | C5×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 67 | D4 | — | 7 | 3 | no | — |
| 68 | C2×C4 | — | 7 | 3 | no | — |
| 69 | C7 | C3×C5×#41 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 70 | C2×C3 | — | 7 | 1 | no | — |
| 71 | C2×C3 | — | 14 | 3 | no | — |
| 72 | C5 | #66659 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 73 | C22 | — | 7 | 3 | no | — |
| 74 | C4 | — | 7 | 1 | no | — |
| 75 | C4 | C2×C5×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 76 | C3 | — | 7 | 1 | no | Sylow |
| 77 | C2 | — | 14 | 3 | no | — |
| 78 | C2 | C22×C5×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
Finite Group Databasebeta