Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 84 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. C3×#65161 | C2 | semidirect |
| 2. #11747996 | C2 | semidirect |
| 3. C2×#90938 | C2 | semidirect |
| 4. C2×#90937 | C2 | semidirect |
| 5. #11746312 | C2 | semidirect |
| 6. C5×#4491 | C2 | semidirect |
| 7. #11745927 | C2 | semidirect |
| 26. #65161 | D3 | semidirect |
| 46. C3×D40 | D4 | semidirect |
| 55. #4491 | D5 | semidirect |
| 120. D40 | D12 | semidirect |
| 144. C3×Dic5 | D16 | semidirect |
| 236. Dic5 | #826 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 304. C5 | #70889 | semidirect |
| 320. C3 | #10599995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65161 | 2 |
| #11747996 | 2 |
| C2×#90938 | 2 |
| C2×#90937 | 2 |
| #11746312 | 2 |
| C5×#4491 | 2 |
| #11745927 | 2 |
| #10599995 | 3 |
| #70889 | 5 |