| 1 | C7×C9×D5×C29 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×C3⋊#10596816 | — | 3 | 1 | no | maximal |
| 3 | C5×C7×C9×C29 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C7×Dic261 | — | 5 | 1 | no | maximal, Hall |
| 5 | C3×C7×D5×C29 | D3 | 1 | 1 | yes | characteristic |
| 6 | C9⋊#10596816 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 7 | C7×#10596816 | — | 9 | 1 | no | Hall |
| 8 | C2×C7×C9×C29 | — | 5 | 1 | no | — |
| 9 | C3×C5×C7×C29 | Dic3 | 1 | 1 | yes | characteristic |
| 10 | C9×D5×C29 | C2×C7 | 1 | 1 | yes | characteristic |
| 11 | C7×Dic87 | — | 15 | 1 | no | — |
| 12 | C7×D5×C29 | D9 | 1 | 1 | yes | characteristic |
| 13 | C7×C9×C29 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Hall |
| 14 | C3⋊#10596816 | — | 3 | 1 | no | — |
| 15 | C5×C9×C29 | C4×C7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 16 | C7×C9⋊AGL(1,𝔽5) | — | 29 | 1 | no | maximal, Hall |
| 17 | C2×C3×C7×C29 | — | 5 | 1 | no | — |
| 18 | Dic261 | — | 5 | 1 | no | Hall |
| 19 | C5×C7×C29 | Dic9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 20 | C3×D5×C29 | D3×C7 | 1 | 1 | yes | characteristic |
| 21 | C7×Dic29 | — | 45 | 1 | no | Hall |
| 22 | C7×C9×D5 | D29 | 1 | 1 | yes | characteristic |
| 23 | C3×C7×C29 | ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 24 | #10596816 | — | 9 | 1 | no | Hall |
| 25 | C2×C9×C29 | — | 5 | 1 | no | — |
| 26 | C3×C5×C29 | C7×Dic3 | 1 | 1 | yes | characteristic |
| 27 | C7×ΓL(1,𝔽16) | — | 87 | 1 | no | — |
| 28 | C2×C7×C29 | — | 5 | 1 | no | — |
| 29 | Dic87 | — | 15 | 1 | no | — |
| 30 | C5×C7×C9 | Dic29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 31 | D5×C29 | C7×D9 | 1 | 1 | yes | characteristic |
| 32 | C9×C29 | C7×AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Hall |
| 33 | C7×Dic9 | — | 145 | 1 | no | Hall |
| 34 | C3×C7×D5 | D87 | 1 | 1 | yes | characteristic |
| 35 | C7×C29 | C9⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Hall |
| 36 | C9⋊AGL(1,𝔽5) | — | 29 | 1 | no | Hall |
| 37 | C2×C3×C29 | — | 5 | 1 | no | — |
| 38 | C5×C29 | C7×Dic9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 39 | C7×AGL(1,𝔽5) | — | 261 | 1 | no | Hall |
| 40 | C2×C7×C9 | — | 5 | 1 | no | — |
| 41 | Dic29 | — | 45 | 1 | no | Hall |
| 42 | C3×C5×C7 | Dic87 | 1 | 1 | yes | characteristic |
| 43 | C9×D5 | C7×D29 | 1 | 1 | yes | characteristic |
| 44 | C3×C29 | C7×ΓL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 45 | C7×Dic3 | — | 435 | 1 | no | — |
| 46 | C7×D5 | D261 | 1 | 1 | yes | characteristic |
| 47 | C7×C9 | #10596816 | 1 | 1 | yes | characteristic, complemented, Hall |
| 48 | ΓL(1,𝔽16) | — | 87 | 1 | no | — |
| 49 | C2×C29 | — | 5 | 1 | no | — |
| 50 | C5×C9 | C7×Dic29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 51 | C2×C3×C7 | — | 5 | 1 | no | — |
| 52 | Dic9 | — | 145 | 1 | no | Hall |
| 53 | C5×C7 | Dic261 | 1 | 1 | yes | characteristic, complemented, Hall |
| 54 | C3×D5 | C7×D87 | 1 | 1 | yes | characteristic |
| 55 | C29 | C7×C9⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 56 | C4×C7 | — | 1305 | 1 | no | Hall |
| 57 | C3×C7 | C3⋊#10596816 | 1 | 1 | yes | characteristic |
| 58 | AGL(1,𝔽5) | — | 261 | 1 | no | Hall |
| 59 | C2×C9 | — | 5 | 1 | no | — |
| 60 | C3×C5 | C7×Dic87 | 1 | 1 | yes | characteristic |
| 61 | C2×C7 | — | 5 | 1 | no | — |
| 62 | Dic3 | — | 435 | 1 | no | — |
| 63 | D5 | C7×D261 | 1 | 1 | yes | characteristic |
| 64 | C9 | C7×#10596816 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 65 | C7 | C9⋊#10596816 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 66 | C2×C3 | — | 5 | 1 | no | — |
| 67 | C5 | C7×Dic261 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 68 | C4 | — | 1305 | 1 | no | Sylow |
| 69 | C3 | C7×C3⋊#10596816 | 1 | 1 | yes | characteristic |
| 70 | C2 | — | 5 | 1 | no | — |
Finite Group Databasebeta