Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 1. C2×D240 | C2 | semidirect |
| 2. C3×#65193 | C2 | semidirect |
| 3. C5×#4499 | C2 | semidirect |
| 4. #11745824 | C2 | semidirect |
| 5. #11745819 | C2 | semidirect |
| 12. C3×Dic40 | C22 | semidirect |
| 14. C3×D80 | C22 | semidirect |
| 15. C5×C3⋊C32 | C22 | semidirect |
| 17. #65193 | D3 | semidirect |
| 36. #4499 | D5 | semidirect |
| 40. Dic40 | C2×D3 | semidirect |
| 44. D80 | C2×D3 | semidirect |
| 65. C3⋊C32 | C2×D5 | semidirect |
| 148. C3×C5 | #2263 | semidirect |
| 174. C5 | #71509 | semidirect |
| 182. C3 | #10600166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D240 | 2 |
| C3×#65193 | 2 |
| C5×#4499 | 2 |
| #11745824 | 2 |
| #11745819 | 2 |
| #10600166 | 3 |
| #71509 | 5 |