Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 76 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. C5×#3796 | C2 | semidirect |
| 2. C5×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×Dic12 | C2 | semidirect |
| 4. C3×C5×D24 | C2 | semidirect |
| 5. C5×#3715 | C2 | semidirect |
| 15. #63810 | C5 | direct (N × H) |
| 22. C5×Dic12 | D3 | semidirect |
| 23. C5×D24 | D3 | semidirect |
| 33. #3796 | C2×C5 | semidirect |
| 34. C8×C3⋊D3 | C2×C5 | semidirect |
| 35. C3×Dic12 | C2×C5 | semidirect |
| 36. C3×D24 | C2×C5 | semidirect |
| 37. #3715 | C2×C5 | semidirect |
| 91. Dic12 | C5×D3 | semidirect |
| 92. D24 | C5×D3 | semidirect |
| 96. C32×C5 | #135 | semidirect |
| 149. C3×C5 | #912 | semidirect |
| 150. C3×C5 | #919 | semidirect |
| 167. C32 | C5×#135 | semidirect |
| 183. C5 | #63810 | direct (N × H) |
| 190. C3 | C5×#912 | semidirect |
| 191. C3 | C5×#919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3796 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×Dic12 | 2 |
| C3×C5×D24 | 2 |
| C5×#3715 | 2 |
| C5×#919 | 3 |
| C5×#912 | 3 |
| #63810 | 5 |