Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
338 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 40. #3998 | Q8 | semidirect |
| 253. C5 | #13265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610807 | 2 |
| C2×#64888 | 2 |
| #10604702 | 2 |
| #10598796 | 2 |
| #10598728 | 2 |
| #13265 | 5 |