Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4838 | C2 | semidirect |
| 2. #11747071 | C2 | semidirect |
| 4. #11746964 | C2 | semidirect |
| 5. #11746303 | C2 | semidirect |
| 6. C3×#64705 | C2 | semidirect |
| 7. #11745869 | C2 | semidirect |
| 29. #64705 | D3 | semidirect |
| 55. #4838 | D5 | semidirect |
| 97. C5×C3⋊C8 | D8 | semidirect |
| 239. C3⋊C8 | #686 | semidirect |
| 274. C3×C5 | #1685 | semidirect |
| 322. C5 | #68398 | semidirect |
| 337. C3 | #10601660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4838 | 2 |
| #11747071 | 2 |
| #11747033 | 2 |
| #11746964 | 2 |
| #11746303 | 2 |
| C3×#64705 | 2 |
| #11745869 | 2 |
| #10601660 | 3 |
| #68398 | 5 |