Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 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. C2×#64761 | C2 | semidirect |
| 5. #10598132 | C2 | semidirect |
| 7. C2×C5×C4⋊Q8 | C4 | semidirect |
| 9. C2×C5×C22⋊Q8 | C4 | semidirect |
| 13. C5×#391 | C4 | semidirect |
| 17. C4×C5×C22⋊C4 | C4 | semidirect |
| 146. C2×C4⋊Q8 | Dic5 | semidirect |
| 148. C2×C22⋊Q8 | Dic5 | semidirect |
| 157. #391 | Dic5 | semidirect |
| 162. C4×C22⋊C4 | Dic5 | semidirect |
| 446. C5 | #13091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2432 | 2 |
| C2×#65529 | 2 |
| #10602932 | 2 |
| C2×#64761 | 2 |
| #10598132 | 2 |
| #13091 | 5 |