Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
346 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. C22×C3×C5×Dic3 | C2 | semidirect |
| 3. C5×#3757 | C2 | semidirect |
| 4. C5×#3724 | C2 | semidirect |
| 5. C5×(C2×D3)⋊Dic3 | C2 | semidirect |
| 15. #63961 | C5 | direct (N × H) |
| 19. C22×C5×Dic3 | D3 | semidirect |
| 37. C22×C3×Dic3 | C2×C5 | semidirect |
| 38. #3757 | C2×C5 | semidirect |
| 39. #3724 | C2×C5 | semidirect |
| 40. (C2×D3)⋊Dic3 | C2×C5 | semidirect |
| 98. C22×Dic3 | C5×D3 | semidirect |
| 106. C32×C5 | #123 | semidirect |
| 168. C3×C5 | #929 | semidirect |
| 169. C3×C5 | #935 | semidirect |
| 194. C32 | C5×#123 | semidirect |
| 213. C5 | #63961 | direct (N × H) |
| 223. C3 | C5×#929 | semidirect |
| 224. C3 | C5×#935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#67 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C5×#3757 | 2 |
| C5×#3724 | 2 |
| C5×(C2×D3)⋊Dic3 | 2 |
| C5×#935 | 3 |
| C5×#929 | 3 |
| #63961 | 5 |