Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 80 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×#3799 | C2 | semidirect |
| 2. C5×#3745 | C2 | semidirect |
| 3. C3×C5×Dic12 | C2 | semidirect |
| 4. C3×C5×D3×C8 | C2 | semidirect |
| 5. C5×#3717 | C2 | semidirect |
| 15. #63808 | C5 | direct (N × H) |
| 21. C5×Dic12 | D3 | semidirect |
| 26. C5×D3×C8 | D3 | semidirect |
| 33. #3799 | C2×C5 | semidirect |
| 34. #3745 | C2×C5 | semidirect |
| 35. C3×Dic12 | C2×C5 | semidirect |
| 36. C3×D3×C8 | C2×C5 | semidirect |
| 37. #3717 | C2×C5 | semidirect |
| 88. Dic12 | C5×D3 | semidirect |
| 93. D3×C8 | C5×D3 | semidirect |
| 94. C32×C5 | #135 | semidirect |
| 146. C3×C5 | #904 | semidirect |
| 147. C3×C5 | #919 | semidirect |
| 163. C32 | C5×#135 | semidirect |
| 179. C5 | #63808 | direct (N × H) |
| 186. C3 | C5×#904 | semidirect |
| 187. C3 | C5×#919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3799 | 2 |
| C5×#3745 | 2 |
| C3×C5×Dic12 | 2 |
| C3×C5×D3×C8 | 2 |
| C5×#3717 | 2 |
| C5×#919 | 3 |
| C5×#904 | 3 |
| #63808 | 5 |