Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #10602484 | C2 | semidirect |
| 5. #10602482 | C2 | semidirect |
| 6. #10598178 | C2 | semidirect |
| 7. #10598177 | C2 | semidirect |
| 11. C5×#484 | C4 | semidirect |
| 12. C5×#481 | C4 | semidirect |
| 16. C5×#451 | C4 | semidirect |
| 17. C5×#448 | C4 | semidirect |
| 152. #484 | Dic5 | semidirect |
| 153. #481 | Dic5 | semidirect |
| 157. #451 | Dic5 | semidirect |
| 158. #448 | Dic5 | semidirect |
| 401. C5 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3196 | 2 |
| #10614652 | 2 |
| #10602503 | 2 |
| #10602484 | 2 |
| #10602482 | 2 |
| #10598178 | 2 |
| #10598177 | 2 |
| #9331 | 5 |