Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 62 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. D5×#634 | C2 | semidirect |
| 3. #10623826 | C2 | semidirect |
| 4. #10623808 | C2 | semidirect |
| 5. #10623805 | C2 | semidirect |
| 6. C5×#3716 | C2 | semidirect |
| 7. C3×#6649 | C2 | semidirect |
| 36. #6649 | D3 | semidirect |
| 51. #3716 | D5 | semidirect |
| 136. C32×C5 | #137 | semidirect |
| 209. C3×C5 | #909 | semidirect |
| 210. C3×C5 | #951 | semidirect |
| 233. C32 | #4061 | semidirect |
| 253. C5 | #63831 | semidirect |
| 262. C3 | #91260 | semidirect |
| 263. C3 | #91484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#634 | 2 |
| C3×#6772 | 2 |
| #10623826 | 2 |
| #10623808 | 2 |
| #10623805 | 2 |
| C5×#3716 | 2 |
| C3×#6649 | 2 |
| #91484 | 3 |
| #91260 | 3 |
| #63831 | 5 |