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×#5083 | C2 | semidirect |
| 2. C3×#65377 | C2 | semidirect |
| 4. D12×#168 | C2 | semidirect |
| 5. #11746368 | C2 | semidirect |
| 6. #11745867 | C2 | semidirect |
| 7. #11745852 | C2 | semidirect |
| 26. #65377 | D3 | semidirect |
| 52. #5083 | D5 | semidirect |
| 270. C3×C5 | #1681 | semidirect |
| 318. C5 | #71201 | semidirect |
| 333. C3 | #10601832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5083 | 2 |
| C3×#65377 | 2 |
| #11747033 | 2 |
| D12×#168 | 2 |
| #11746368 | 2 |
| #11745867 | 2 |
| #11745852 | 2 |
| #10601832 | 3 |
| #71201 | 5 |