| 1 | C3×D17×C13⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3⋊#11725133 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11725133⋊C3 | — | 3 | 1 | no | maximal |
| 4 | C3×C17×C13⋊C3 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C3×C13×D17 | C2×C3 | 1 | 1 | yes | characteristic |
| 6 | D17×C13⋊C3 | — | 2 | 1 | no | — |
| 7 | D17×C13⋊C3 | D3 | 1 | 1 | yes | characteristic |
| 8 | #11725133 | — | 3 | 1 | no | Hall |
| 9 | C3×C13×C17 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C17×C13⋊C3 | — | 2 | 1 | no | — |
| 11 | C17×C13⋊C3 | Dic3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×C3⋊#595 | — | 13 | 1 | no | maximal, Hall |
| 13 | C3⋊(Dic13⋊C3) | — | 17 | 1 | no | maximal, Hall |
| 14 | C13×D17 | C3×D3 | 1 | 1 | yes | characteristic |
| 15 | C32×D17 | — | 13 | 1 | no | — |
| 16 | C2×C3×C13⋊C3 | — | 17 | 1 | no | — |
| 17 | C13×C17 | C3×Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 18 | C3⋊#595 | — | 13 | 1 | no | — |
| 19 | C3×#595 | — | 39 | 1 | no | — |
| 20 | Dic39 | — | 17 | 1 | no | — |
| 21 | Dic13⋊C3 | — | 51 | 1 | no | — |
| 22 | C32×C17 | — | 13 | 1 | no | Hall |
| 23 | C3×C13⋊C3 | #595 | 1 | 1 | yes | characteristic, complemented, Hall |
| 24 | C3×D17 | — | 13 | 1 | no | — |
| 25 | C3×D17 | — | 26 | 1 | no | — |
| 26 | C3×D17 | D13⋊C3 | 1 | 1 | yes | characteristic |
| 27 | C2×C3×C13 | — | 17 | 1 | no | — |
| 28 | C2×C13⋊C3 | — | 17 | 1 | no | — |
| 29 | C2×C13⋊C3 | — | 34 | 1 | no | — |
| 30 | #595 | — | 39 | 1 | no | Hall |
| 31 | Dic13 | — | 51 | 1 | no | Hall |
| 32 | C3×C17 | — | 13 | 1 | no | — |
| 33 | C3×C17 | — | 26 | 1 | no | — |
| 34 | C3×C17 | Dic13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C3×C13 | C3×#595 | 1 | 1 | yes | characteristic, complemented |
| 36 | C13⋊C3 | — | 2 | 1 | no | — |
| 37 | C13⋊C3 | C3⋊#595 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×Dic3 | — | 221 | 1 | no | Hall |
| 39 | D17 | C3⋊(D13⋊C3) | 1 | 1 | yes | characteristic |
| 40 | C2×C13 | — | 17 | 1 | no | — |
| 41 | C2×C32 | — | 221 | 1 | no | — |
| 42 | C17 | C3⋊(Dic13⋊C3) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 43 | C13 | C3×C3⋊#595 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 44 | C3×C4 | — | 663 | 1 | no | — |
| 45 | Dic3 | — | 221 | 1 | no | — |
| 46 | C32 | — | 13 | 1 | no | Sylow |
| 47 | C2×C3 | — | 17 | 1 | no | — |
| 48 | C2×C3 | — | 442 | 1 | no | — |
| 49 | C2×C3 | — | 221 | 1 | no | — |
| 50 | C4 | — | 663 | 1 | no | Sylow |
| 51 | C3 | — | 13 | 1 | no | — |
| 52 | C3 | — | 26 | 1 | no | — |
| 53 | C3 | #11725133⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C2 | — | 17 | 1 | no | — |
Finite Group Databasebeta