Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
350 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 41. #3998 | Q8 | semidirect |
| 263. C5 | #13268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65117 | 2 |
| #10604708 | 2 |
| #10604702 | 2 |
| #10598780 | 2 |
| #10598701 | 2 |
| #13268 | 5 |