Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
724 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#66132 | C2 | semidirect |
| 3. C2×#91117 | C2 | semidirect |
| 4. #11748425 | C2 | semidirect |
| 5. #11745969 | C2 | semidirect |
| 11. C5×#940 | C4 | semidirect |
| 13. C5×#936 | C4 | semidirect |
| 22. #66132 | D3 | semidirect |
| 36. C2×C5×D12 | C2×C4 | semidirect |
| 38. C2×C5×Dic6 | C2×C4 | semidirect |
| 46. C4×C5×Dic3 | C2×C4 | semidirect |
| 50. C3×C4×Dic5 | D4 | semidirect |
| 99. #940 | Dic5 | semidirect |
| 101. #936 | Dic5 | semidirect |
| 127. C4×Dic5 | #67 | semidirect |
| 162. C2×D12 | C2×Dic5 | semidirect |
| 164. C2×Dic6 | C2×Dic5 | semidirect |
| 172. C4×Dic3 | C2×Dic5 | semidirect |
| 281. C3×C5 | #1911 | semidirect |
| 332. C5 | #71652 | semidirect |
| 348. C3 | #10602646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5805 | 2 |
| C3×#66132 | 2 |
| C2×#91117 | 2 |
| #11748425 | 2 |
| #11745969 | 2 |
| #10602646 | 3 |
| #71652 | 5 |