Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×D240 | C2 | semidirect |
| 2. #11747996 | C2 | semidirect |
| 3. #11747766 | C2 | semidirect |
| 4. C2×#90939 | C2 | semidirect |
| 5. C5×#4509 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. #11745896 | C2 | semidirect |
| 28. #64721 | D3 | semidirect |
| 40. D120 | D4 | semidirect |
| 56. #4509 | D5 | semidirect |
| 143. C3×Dic5 | D16 | semidirect |
| 236. Dic5 | D48 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 304. C5 | #69286 | semidirect |
| 320. C3 | #10599995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D240 | 2 |
| #11747996 | 2 |
| #11747766 | 2 |
| C2×#90939 | 2 |
| C5×#4509 | 2 |
| C3×#64721 | 2 |
| #11745896 | 2 |
| #10599995 | 3 |
| #69286 | 5 |