Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
588 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 122 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. C2×#64931 | C2 | semidirect |
| 5. #10598725 | C2 | semidirect |
| 360. C5 | #9128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65754 | 2 |
| #10614542 | 2 |
| C2×#64931 | 2 |
| #10604900 | 2 |
| #10598725 | 2 |
| #9128 | 5 |