Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
288 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10598618 | C2 | semidirect |
| 5. #10598617 | C2 | semidirect |
| 233. C5 | #11973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613647 | 2 |
| #10603828 | 2 |
| #10603821 | 2 |
| #10598618 | 2 |
| #10598617 | 2 |
| #11973 | 5 |