Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11752676 | C2 | semidirect |
| 2. C5×#4843 | C2 | semidirect |
| 3. #11747026 | C2 | semidirect |
| 4. #11746906 | C2 | semidirect |
| 5. #11746303 | C2 | semidirect |
| 6. C3×#64703 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 32. #64703 | D3 | semidirect |
| 62. #4843 | D5 | semidirect |
| 101. C5×D12 | D8 | semidirect |
| 280. D12 | #686 | semidirect |
| 333. C3×C5 | #1625 | semidirect |
| 393. C5 | #68180 | semidirect |
| 412. C3 | #10601811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752676 | 2 |
| C5×#4843 | 2 |
| #11747026 | 2 |
| #11746906 | 2 |
| #11746303 | 2 |
| C3×#64703 | 2 |
| #11745837 | 2 |
| #10601811 | 3 |
| #68180 | 5 |