| 1 | C2×C5×C22⋊ΓL(1,𝔽8) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C22×C5×Dic7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C5×C22⋊ΓL(1,𝔽8) | C4 | 1 | 1 | yes | characteristic, complemented |
| 4 | C5×ΓL(1,𝔽8)⋊C4 | — | 4 | 1 | no | maximal |
| 5 | Dic7⋊A4 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 6 | C23×C5×C7 | C2×C3 | 1 | 1 | yes | characteristic |
| 7 | C2×C5×Dic7 | — | 3 | 1 | no | — |
| 8 | C2×C5×Dic7 | — | 3 | 1 | no | — |
| 9 | C4×C5×A4 | — | 7 | 1 | no | maximal, Hall |
| 10 | C2×C5×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 11 | C2×C22⋊ΓL(1,𝔽8) | C2×C5 | 1 | 1 | yes | characteristic |
| 12 | C22×C5×C7 | — | 3 | 1 | no | — |
| 13 | C22×C5×C7 | — | 3 | 1 | no | — |
| 14 | C22×C5×C7 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | C5×Dic7 | — | 3 | 1 | no | — |
| 16 | C5×Dic7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×C5×A4 | — | 7 | 1 | no | — |
| 18 | C22×Dic7 | C3×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 19 | C5×ΓL(1,𝔽8) | — | 4 | 1 | no | Hall |
| 20 | C22⋊ΓL(1,𝔽8) | C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 21 | ΓL(1,𝔽8)⋊C4 | — | 4 | 1 | no | — |
| 22 | C22×C4×C5 | — | 7 | 1 | no | Hall |
| 23 | C2×C5×C7 | — | 3 | 1 | no | — |
| 24 | C2×C5×C7 | — | 3 | 1 | no | — |
| 25 | C2×C5×C7 | C2×A4 | 1 | 1 | yes | characteristic |
| 26 | C5×A4 | — | 7 | 1 | no | — |
| 27 | C3×C4×C5 | — | 28 | 1 | no | — |
| 28 | C23×C7 | C2×C3×C5 | 1 | 1 | yes | characteristic |
| 29 | C2×Dic7 | — | 3 | 1 | no | — |
| 30 | C2×Dic7 | — | 3 | 1 | no | — |
| 31 | C4×A4 | — | 7 | 1 | no | Hall |
| 32 | C2×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 33 | C23×C5 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 34 | C2×C4×C5 | — | 21 | 1 | no | — |
| 35 | C2×C4×C5 | — | 21 | 1 | no | — |
| 36 | C5×C7 | C4×A4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 37 | C2×C3×C5 | — | 28 | 1 | no | — |
| 38 | C22×C7 | — | 3 | 1 | no | — |
| 39 | C22×C7 | — | 3 | 1 | no | — |
| 40 | C22×C7 | C3×C4×C5 | 1 | 1 | yes | characteristic, complemented |
| 41 | Dic7 | — | 3 | 1 | no | — |
| 42 | Dic7 | C5×A4 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×A4 | — | 7 | 1 | no | — |
| 44 | ΓL(1,𝔽8) | — | 4 | 1 | no | Hall |
| 45 | C22×C5 | — | 3 | 1 | no | — |
| 46 | C22×C5 | — | 3 | 1 | no | — |
| 47 | C22×C5 | ΓL(1,𝔽8)⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 48 | C4×C5 | — | 7 | 1 | no | — |
| 49 | C4×C5 | — | 21 | 1 | no | — |
| 50 | C22×C4 | — | 7 | 1 | no | Sylow |
| 51 | C3×C5 | — | 28 | 1 | no | Hall |
| 52 | C2×C7 | — | 3 | 1 | no | — |
| 53 | C2×C7 | — | 3 | 1 | no | — |
| 54 | C2×C7 | C2×C5×A4 | 1 | 1 | yes | characteristic |
| 55 | A4 | — | 7 | 1 | no | — |
| 56 | C3×C4 | — | 28 | 1 | no | — |
| 57 | C2×C5 | — | 3 | 1 | no | — |
| 58 | C2×C5 | — | 3 | 1 | no | — |
| 59 | C2×C5 | D7⋊A4 | 1 | 1 | yes | characteristic |
| 60 | C23 | C5×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 61 | C2×C4 | — | 21 | 1 | no | — |
| 62 | C2×C4 | — | 21 | 1 | no | — |
| 63 | C7 | C4×C5×A4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 64 | C2×C3 | — | 28 | 1 | no | — |
| 65 | C5 | Dic7⋊A4 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 66 | C22 | — | 3 | 1 | no | — |
| 67 | C22 | — | 3 | 1 | no | — |
| 68 | C22 | C5×ΓL(1,𝔽8)⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 69 | C4 | — | 7 | 1 | no | — |
| 70 | C4 | — | 21 | 1 | no | — |
| 71 | C3 | — | 28 | 1 | no | Sylow |
| 72 | C2 | — | 3 | 1 | no | — |
| 73 | C2 | — | 3 | 1 | no | — |
| 74 | C2 | C5×D7⋊A4 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta