Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 352 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×#5084 | C2 | semidirect |
| 2. C3×#65377 | C2 | semidirect |
| 4. D12×#168 | C2 | semidirect |
| 5. #11746367 | C2 | semidirect |
| 6. #11745864 | C2 | semidirect |
| 7. #11745852 | C2 | semidirect |
| 26. #65377 | D3 | semidirect |
| 51. #5084 | D5 | semidirect |
| 263. C3×C5 | #1677 | semidirect |
| 310. C5 | #71200 | semidirect |
| 325. C3 | #10601927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5084 | 2 |
| C3×#65377 | 2 |
| #11747033 | 2 |
| D12×#168 | 2 |
| #11746367 | 2 |
| #11745864 | 2 |
| #11745852 | 2 |
| #10601927 | 3 |
| #71200 | 5 |