Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 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. Q8⋊#674 | C2 | semidirect |
| 5. #10598581 | C2 | semidirect |
| 243. C5 | #11638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611689 | 2 |
| #10603829 | 2 |
| #10603828 | 2 |
| Q8⋊#674 | 2 |
| #10598581 | 2 |
| #11638 | 5 |