Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 92 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. C2×C5×#627 | C2 | semidirect |
| 3. C3×C5×#217 | C2 | semidirect |
| 4. C5×#3722 | C2 | semidirect |
| 5. C5×Dic32 | C2 | semidirect |
| 14. #63953 | C5 | direct (N × H) |
| 19. C5×#217 | D3 | semidirect |
| 33. C2×#627 | C2×C5 | semidirect |
| 34. C3×#217 | C2×C5 | semidirect |
| 35. #3722 | C2×C5 | semidirect |
| 36. Dic32 | C2×C5 | semidirect |
| 89. #217 | C5×D3 | semidirect |
| 93. C32×C5 | #124 | semidirect |
| 150. C3×C5 | #885 | semidirect |
| 173. C32 | C5×#124 | semidirect |
| 190. C5 | #63953 | direct (N × H) |
| 200. C3 | C5×#885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C2×C5×#627 | 2 |
| C3×C5×#217 | 2 |
| C5×#3722 | 2 |
| C5×Dic32 | 2 |
| C5×#885 | 3 |
| #63953 | 5 |