Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
366 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 366 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. C3×C5×#217 | C2 | semidirect |
| 4. C5×Dic3⋊Dic3 | C2 | semidirect |
| 5. C5×#3722 | C2 | semidirect |
| 15. #63966 | C5 | direct (N × H) |
| 20. C22×C5×Dic3 | D3 | semidirect |
| 22. C5×#217 | D3 | semidirect |
| 37. C22×C3×Dic3 | C2×C5 | semidirect |
| 38. C3×#217 | C2×C5 | semidirect |
| 39. Dic3⋊Dic3 | C2×C5 | semidirect |
| 40. #3722 | C2×C5 | semidirect |
| 103. C22×Dic3 | C5×D3 | semidirect |
| 105. #217 | C5×D3 | semidirect |
| 110. C32×C5 | #123 | semidirect |
| 175. C3×C5 | #886 | semidirect |
| 176. C3×C5 | #929 | semidirect |
| 203. C32 | C5×#123 | semidirect |
| 223. C5 | #63966 | direct (N × H) |
| 233. C3 | C5×#886 | semidirect |
| 234. C3 | C5×#929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C3×C5×#217 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×#3722 | 2 |
| C5×#929 | 3 |
| C5×#886 | 3 |
| #63966 | 5 |