Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
170 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. #10598658 | C2 | semidirect |
| 4. #10598656 | C2 | semidirect |
| 123. C5 | #13642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×M32 | 2 |
| #10598759 | 2 |
| #10598658 | 2 |
| #10598656 | 2 |
| #13642 | 5 |