Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
712 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 111 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. #10602482 | C2 | semidirect |
| 5. #10598107 | C2 | semidirect |
| 7. C2×C5×C4⋊Q8 | C4 | semidirect |
| 8. C2×C5×#124 | C4 | semidirect |
| 13. C5×#391 | C4 | semidirect |
| 14. C5×#390 | C4 | semidirect |
| 139. C2×C4⋊Q8 | Dic5 | semidirect |
| 140. C2×#124 | Dic5 | semidirect |
| 149. #391 | Dic5 | semidirect |
| 150. #390 | Dic5 | semidirect |
| 414. C5 | #9443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2432 | 2 |
| #10615805 | 2 |
| #10602932 | 2 |
| #10602482 | 2 |
| #10598107 | 2 |
| #9443 | 5 |