Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
362 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10598807 | C2 | semidirect |
| 64. C5×Q16 | M16 | semidirect |
| 170. Q16 | #704 | semidirect |
| 217. C5 | #11664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×Dic5 | 2 |
| #10604710 | 2 |
| #10604696 | 2 |
| #10598807 | 2 |
| #11664 | 5 |