| 1 | C3×C7×D5×C29 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7⋊#10596816 | — | 3 | 1 | no | maximal, Hall |
| 3 | C3×C5×C7×C29 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | Dic609 | — | 5 | 1 | no | maximal, Hall |
| 5 | C7×D5×C29 | D3 | 1 | 1 | yes | characteristic |
| 6 | C3⋊#10596816 | — | 7 | 1 | no | maximal, Hall |
| 7 | C2×C3×C7×C29 | — | 5 | 1 | no | — |
| 8 | C5×C7×C29 | Dic3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C3×D5×C29 | D7 | 1 | 1 | yes | characteristic |
| 10 | Dic203 | — | 15 | 1 | no | Hall |
| 11 | C3×C7×C29 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Hall |
| 12 | #10596816 | — | 21 | 1 | no | Hall |
| 13 | C3×C5×C29 | Dic7 | 1 | 1 | yes | characteristic, complemented, Hall |
| 14 | C3⋊(C7⋊AGL(1,𝔽5)) | — | 29 | 1 | no | maximal, Hall |
| 15 | C2×C7×C29 | — | 5 | 1 | no | — |
| 16 | Dic87 | — | 35 | 1 | no | Hall |
| 17 | D5×C29 | D21 | 1 | 1 | yes | characteristic |
| 18 | C3×C7×D5 | D29 | 1 | 1 | yes | characteristic |
| 19 | C7×C29 | ΓL(1,𝔽16) | 1 | 1 | yes | characteristic, complemented, Hall |
| 20 | C2×C3×C29 | — | 5 | 1 | no | — |
| 21 | C5×C29 | Dic21 | 1 | 1 | yes | characteristic, complemented, Hall |
| 22 | C7⋊AGL(1,𝔽5) | — | 87 | 1 | no | Hall |
| 23 | Dic29 | — | 105 | 1 | no | Hall |
| 24 | C3×C5×C7 | Dic29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 25 | C3×C29 | C7⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented, Hall |
| 26 | Dic21 | — | 145 | 1 | no | Hall |
| 27 | C7×D5 | D87 | 1 | 1 | yes | characteristic |
| 28 | ΓL(1,𝔽16) | — | 203 | 1 | no | Hall |
| 29 | C2×C29 | — | 5 | 1 | no | — |
| 30 | C2×C3×C7 | — | 5 | 1 | no | — |
| 31 | C5×C7 | Dic87 | 1 | 1 | yes | characteristic, complemented, Hall |
| 32 | C3×D5 | D203 | 1 | 1 | yes | characteristic |
| 33 | C29 | C3⋊(C7⋊AGL(1,𝔽5)) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 34 | Dic7 | — | 435 | 1 | no | Hall |
| 35 | C3×C7 | #10596816 | 1 | 1 | yes | characteristic, complemented, Hall |
| 36 | AGL(1,𝔽5) | — | 609 | 1 | no | Hall |
| 37 | C3×C5 | Dic203 | 1 | 1 | yes | characteristic, complemented, Hall |
| 38 | C2×C7 | — | 5 | 1 | no | — |
| 39 | Dic3 | — | 1015 | 1 | no | Hall |
| 40 | D5 | D609 | 1 | 1 | yes | characteristic |
| 41 | C7 | C3⋊#10596816 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 42 | C2×C3 | — | 5 | 1 | no | — |
| 43 | C5 | Dic609 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 44 | C4 | — | 3045 | 1 | no | Sylow |
| 45 | C3 | C7⋊#10596816 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 46 | C2 | — | 5 | 1 | no | — |
Finite Group Databasebeta