| 1 | C2×C32×C5×C7×C29 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×Dic609 | — | 3 | 4 | no | maximal |
| 3 | C32×C5×C7×C29 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3⋊Dic609 | C5 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 5 | C2×C3×C5×C7×C29 | D3 | 1 | 4 | yes | — |
| 6 | C5×C3⋊Dic87 | — | 7 | 1 | no | maximal, Hall |
| 7 | C5×Dic203 | — | 9 | 1 | no | Hall |
| 8 | C2×C32×C7×C29 | C2×C5 | 1 | 1 | yes | characteristic |
| 9 | C3×C5×C7×C29 | Dic3 | 1 | 4 | yes | complemented |
| 10 | C2×C32×C5×C29 | D7 | 1 | 1 | yes | characteristic |
| 11 | Dic609 | — | 3 | 4 | no | — |
| 12 | C2×C5×C7×C29 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 13 | C32×C7×C29 | C4×C5 | 1 | 1 | yes | characteristic, complemented, Hall |
| 14 | C5×Dic87 | — | 21 | 4 | no | — |
| 15 | C32×C5×C29 | Dic7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 16 | C5×C3⋊Dic21 | — | 29 | 1 | no | maximal, Hall |
| 17 | C2×C3×C7×C29 | C5×D3 | 1 | 4 | yes | — |
| 18 | C3⋊Dic87 | — | 7 | 1 | no | Hall |
| 19 | C5×C7×C29 | C3⋊Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 20 | C2×C3×C5×C29 | D21 | 1 | 4 | yes | — |
| 21 | Dic203 | — | 9 | 1 | no | Hall |
| 22 | C2×C32×C5×C7 | D29 | 1 | 1 | yes | characteristic |
| 23 | C3×C7×C29 | C5×Dic3 | 1 | 4 | yes | complemented |
| 24 | C5×Dic29 | — | 63 | 1 | no | Hall |
| 25 | C2×C32×C29 | C5×D7 | 1 | 1 | yes | characteristic |
| 26 | C3×C5×C29 | Dic21 | 1 | 4 | yes | complemented |
| 27 | C5×Dic21 | — | 87 | 4 | no | — |
| 28 | C2×C7×C29 | C5×C3⋊D3 | 1 | 1 | yes | characteristic |
| 29 | Dic87 | — | 21 | 4 | no | — |
| 30 | C32×C5×C7 | Dic29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 31 | C2×C5×C29 | C3⋊D21 | 1 | 1 | yes | characteristic |
| 32 | C32×C29 | C5×Dic7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 33 | C3⋊Dic21 | — | 29 | 1 | no | Hall |
| 34 | C2×C3×C5×C7 | D87 | 1 | 4 | yes | — |
| 35 | C7×C29 | C5×C3⋊Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 36 | C5×C3⋊Dic3 | — | 203 | 1 | no | Hall |
| 37 | C2×C3×C29 | C5×D21 | 1 | 4 | yes | — |
| 38 | C5×C29 | C3⋊Dic21 | 1 | 1 | yes | characteristic, complemented, Hall |
| 39 | C5×Dic7 | — | 261 | 1 | no | Hall |
| 40 | C2×C32×C7 | C5×D29 | 1 | 1 | yes | characteristic |
| 41 | Dic29 | — | 63 | 1 | no | Hall |
| 42 | C3×C5×C7 | Dic87 | 1 | 4 | yes | complemented |
| 43 | C2×C32×C5 | D203 | 1 | 1 | yes | characteristic |
| 44 | C3×C29 | C5×Dic21 | 1 | 4 | yes | complemented |
| 45 | Dic21 | — | 87 | 4 | no | — |
| 46 | C2×C5×C7 | C3⋊D87 | 1 | 1 | yes | characteristic |
| 47 | C32×C7 | C5×Dic29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 48 | C5×Dic3 | — | 609 | 4 | no | — |
| 49 | C2×C29 | C5×C3⋊D21 | 1 | 1 | yes | characteristic |
| 50 | C32×C5 | Dic203 | 1 | 1 | yes | characteristic, complemented, Hall |
| 51 | C2×C3×C7 | C5×D87 | 1 | 4 | yes | — |
| 52 | C3⋊Dic3 | — | 203 | 1 | no | Hall |
| 53 | C5×C7 | C3⋊Dic87 | 1 | 1 | yes | characteristic, complemented, Hall |
| 54 | C2×C3×C5 | D609 | 1 | 4 | yes | — |
| 55 | C29 | C5×C3⋊Dic21 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 56 | Dic7 | — | 261 | 1 | no | Hall |
| 57 | C3×C7 | C5×Dic87 | 1 | 4 | yes | complemented |
| 58 | C4×C5 | — | 1827 | 1 | no | Hall |
| 59 | C2×C32 | C5×D203 | 1 | 1 | yes | characteristic |
| 60 | C3×C5 | Dic609 | 1 | 4 | yes | complemented |
| 61 | C2×C7 | C5×C3⋊D87 | 1 | 1 | yes | characteristic |
| 62 | Dic3 | — | 609 | 4 | no | — |
| 63 | C2×C5 | C3⋊D609 | 1 | 1 | yes | characteristic |
| 64 | C32 | C5×Dic203 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 65 | C7 | C5×C3⋊Dic87 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 66 | C2×C3 | C5×D609 | 1 | 4 | yes | — |
| 67 | C5 | C3⋊Dic609 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 68 | C4 | — | 1827 | 1 | no | Sylow |
| 69 | C3 | C5×Dic609 | 1 | 4 | yes | complemented |
| 70 | C2 | C5×C3⋊D609 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta