Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11752342 | C2 | semidirect |
| 3. C3×#65686 | C2 | semidirect |
| 4. #11746496 | C2 | semidirect |
| 8. #91758 | C4 | semidirect |
| 9. C5×#874 | C4 | semidirect |
| 14. Dic5×D12 | C4 | semidirect |
| 23. #65686 | D3 | semidirect |
| 95. #874 | AGL(1,𝔽5) | semidirect |
| 265. C3×C5 | #1505 | semidirect |
| 313. C5 | #69432 | semidirect |
| 329. C3 | #10604594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752672 | 2 |
| #11752342 | 2 |
| C3×#65686 | 2 |
| #11746496 | 2 |
| #10604594 | 3 |
| #69432 | 5 |