Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
342 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 17. #65288 | C4 | semidirect |
| 18. #65288 | C4 | semidirect |
| 21. C4×#681 | C4 | semidirect |
| 22. C2×C4×#168 | C4 | semidirect |
| 309. C5 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614244 | 2 |
| C5×#1827 | 2 |
| #10602437 | 2 |
| #10598192 | 2 |
| #10598191 | 2 |
| #10598188 | 2 |
| #10598187 | 2 |
| #12864 | 5 |