| 1 | C3×C5×C7×ΓL(1,𝔽8) | C2 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 2 | C2×C3×C5×C72 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C5×C7×ΓL(1,𝔽8) | C3 | 1 | 3 | yes | maximal, direct product factor |
| 4 | C2×C3×C7×ΓL(1,𝔽8) | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C3×C5×C72 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 6 | C5×C7×ΓL(1,𝔽8) | C2×C3 | 1 | 3 | yes | direct product factor |
| 7 | C2×C32×C5×C7 | — | 7 | 1 | no | maximal |
| 8 | C2×C3×C5×ΓL(1,𝔽8) | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 9 | C2×C5×C72 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 10 | C3×C7×ΓL(1,𝔽8) | C2×C5 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 11 | C32×C5×C7 | — | 7 | 1 | no | — |
| 12 | C3×C5×ΓL(1,𝔽8) | C2×C7 | 1 | 1 | yes | characteristic, direct product factor |
| 13 | C2×C3×C72 | C3×C5 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C7×ΓL(1,𝔽8) | C3×C5 | 1 | 3 | yes | direct product factor |
| 15 | C5×C72 | C2×C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 16 | C2×C3×C5×C7 | — | 3 | 2 | no | — |
| 17 | C2×C3×C5×C7 | — | 7 | 3 | no | — |
| 18 | C2×C3×C5×C7 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 19 | C2×C3×C5×C7 | C3×C7 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×C5×ΓL(1,𝔽8) | C3×C7 | 1 | 3 | yes | direct product factor |
| 21 | C3×C72 | C2×C3×C5 | 1 | 1 | yes | characteristic, complemented |
| 22 | C7×ΓL(1,𝔽8) | C2×C3×C5 | 1 | 3 | yes | direct product factor |
| 23 | C2×C32×C7 | — | 7 | 1 | no | — |
| 24 | C2×C3×ΓL(1,𝔽8) | C5×C7 | 1 | 1 | yes | characteristic, direct product factor |
| 25 | C3×C5×C7 | — | 3 | 2 | no | — |
| 26 | C3×C5×C7 | — | 7 | 3 | no | — |
| 27 | C3×C5×C7 | C2×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 28 | C3×C5×C7 | C2×C3×C7 | 1 | 1 | yes | characteristic, complemented |
| 29 | C5×ΓL(1,𝔽8) | C2×C3×C7 | 1 | 3 | yes | direct product factor |
| 30 | C2×C72 | C32×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 31 | C2×C32×C5 | — | 7 | 1 | no | Hall |
| 32 | C2×C5×C7 | — | 3 | 2 | no | — |
| 33 | C2×C5×C7 | C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 34 | C2×C5×C7 | C32×C7 | 1 | 1 | yes | characteristic, complemented |
| 35 | C32×C7 | — | 7 | 1 | no | — |
| 36 | C3×ΓL(1,𝔽8) | C2×C5×C7 | 1 | 1 | yes | characteristic, direct product factor |
| 37 | C72 | C2×C32×C5 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 38 | C32×C5 | — | 7 | 1 | no | Hall |
| 39 | C2×C3×C7 | — | 3 | 2 | no | — |
| 40 | C2×C3×C7 | — | 7 | 3 | no | — |
| 41 | C2×C3×C7 | C5×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 42 | C2×C3×C7 | C3×C5×C7 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×ΓL(1,𝔽8) | C3×C5×C7 | 1 | 3 | yes | direct product factor |
| 44 | C5×C7 | — | 3 | 2 | no | — |
| 45 | C5×C7 | C2×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 46 | C5×C7 | C2×C32×C7 | 1 | 1 | yes | characteristic, complemented |
| 47 | C2×C3×C5 | — | 7 | 3 | no | — |
| 48 | C2×C3×C5 | C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 49 | C3×C7 | — | 3 | 2 | no | — |
| 50 | C3×C7 | — | 7 | 3 | no | — |
| 51 | C3×C7 | C2×C5×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 52 | C3×C7 | C2×C3×C5×C7 | 1 | 1 | yes | characteristic, complemented |
| 53 | ΓL(1,𝔽8) | C2×C3×C5×C7 | 1 | 3 | yes | direct product factor |
| 54 | C2×C32 | — | 7 | 1 | no | Hall |
| 55 | C3×C5 | — | 7 | 3 | no | — |
| 56 | C3×C5 | C2×C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 57 | C2×C7 | — | 3 | 2 | no | — |
| 58 | C2×C7 | C3×C5×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 59 | C2×C7 | C32×C5×C7 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×C5 | C3×C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 61 | C32 | — | 7 | 1 | no | Sylow |
| 62 | C7 | — | 3 | 2 | no | — |
| 63 | C7 | C2×C3×C5×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 64 | C7 | C2×C32×C5×C7 | 1 | 1 | yes | characteristic, complemented |
| 65 | C2×C3 | — | 7 | 3 | no | — |
| 66 | C2×C3 | C5×C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 67 | C5 | C2×C3×C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 68 | C3 | — | 7 | 3 | no | — |
| 69 | C3 | C2×C5×C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 70 | C2 | C3×C5×C7×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
Finite Group Databasebeta