Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
866 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 312 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. #10604316 | C2 | semidirect |
| 12. #65684 | C4 | semidirect |
| 206. C5 | #20539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65684 | 2 |
| #10606049 | 2 |
| #10604316 | 2 |
| #10604313 | 2 |
| #20539 | 5 |