Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
622 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 216 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×C5×#634 | C2 | semidirect |
| 2. C3×C5×#235 | C2 | semidirect |
| 3. C5×#3805 | C2 | semidirect |
| 4. C5×#3795 | C2 | semidirect |
| 5. C5×D3×Dic6 | C2 | semidirect |
| 17. #64298 | C5 | direct (N × H) |
| 23. C5×#235 | D3 | semidirect |
| 33. C2×#634 | C2×C5 | semidirect |
| 34. C3×#235 | C2×C5 | semidirect |
| 35. #3805 | C2×C5 | semidirect |
| 36. #3795 | C2×C5 | semidirect |
| 37. D3×Dic6 | C2×C5 | semidirect |
| 92. #235 | C5×D3 | semidirect |
| 96. C32×C5 | 2−1+4 | semidirect |
| 152. C3×C5 | #1010 | semidirect |
| 167. C32 | C5×2−1+4 | semidirect |
| 184. C5 | #64298 | direct (N × H) |
| 191. C3 | C5×#1010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#634 | 2 |
| C3×C5×#235 | 2 |
| C5×#3805 | 2 |
| C5×#3795 | 2 |
| C5×D3×Dic6 | 2 |
| C5×#1010 | 3 |
| #64298 | 5 |