Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×#5551 | C2 | semidirect |
| 2. #11751116 | C2 | semidirect |
| 3. #11747037 | C2 | semidirect |
| 4. #11746912 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745858 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 33. D4⋊#168 | D3 | semidirect |
| 60. #5551 | D5 | semidirect |
| 105. C5×D12 | D8 | semidirect |
| 280. D12 | #686 | semidirect |
| 333. C3×C5 | #1625 | semidirect |
| 393. C5 | #68180 | semidirect |
| 412. C3 | #10602703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5551 | 2 |
| #11751116 | 2 |
| #11747037 | 2 |
| #11746912 | 2 |
| C3×D4⋊#168 | 2 |
| #11745858 | 2 |
| #11745837 | 2 |
| #10602703 | 3 |
| #68180 | 5 |