Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 13. #64879 | C4 | semidirect |
| 14. C8×#170 | C4 | semidirect |
| 26. C5×#97 | C8 | semidirect |
| 29. #3947 | C8 | semidirect |
| 102. #97 | #170 | semidirect |
| 167. C5 | #8138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604687 | 2 |
| #10600597 | 2 |
| #10598773 | 2 |
| #10598695 | 2 |
| #8138 | 5 |