Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 75 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. #11756443 | C2 | semidirect |
| 2. C3×C5×#496 | C2 | semidirect |
| 3. #11751175 | C2 | semidirect |
| 4. #11751172 | C2 | semidirect |
| 5. #11746361 | C2 | semidirect |
| 6. #11746286 | C2 | semidirect |
| 7. #11746285 | C2 | semidirect |
| 30. C5×#496 | D3 | semidirect |
| 68. C3×#496 | D5 | semidirect |
| 172. #496 | D15 | semidirect |
| 350. C3×C5 | #1656 | semidirect |
| 406. C5 | #71327 | semidirect |
| 424. C3 | #10602120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756443 | 2 |
| C3×C5×#496 | 2 |
| #11751175 | 2 |
| #11751172 | 2 |
| #11746361 | 2 |
| #11746286 | 2 |
| #11746285 | 2 |
| #10602120 | 3 |
| #71327 | 5 |