Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
| 3. C3×#6710 | C2 | semidirect |
| 4. #10623826 | C2 | semidirect |
| 5. #10623823 | C2 | semidirect |
| 23. #6710 | D3 | semidirect |
| 36. C2×#634 | D5 | semidirect |
| 109. C32×C5 | #137 | semidirect |
| 171. C3×C5 | #909 | semidirect |
| 172. C3×C5 | #951 | semidirect |
| 192. C32 | #4088 | semidirect |
| 210. C5 | #63831 | semidirect |
| 218. C3 | #91307 | semidirect |
| 219. C3 | #91321 | 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×#6817 | 2 |
| C3×#6710 | 2 |
| #10623826 | 2 |
| #10623823 | 2 |
| #91321 | 3 |
| #91307 | 3 |
| #63831 | 5 |