Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 127 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. #10601478 | C2 | semidirect |
| 5. #10598220 | C2 | semidirect |
| 12. C2×#3944 | C4 | semidirect |
| 14. C22×#672 | C4 | semidirect |
| 184. C5 | #12832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65429 | 2 |
| C5×#1813 | 2 |
| #10602805 | 2 |
| #10601478 | 2 |
| #10598220 | 2 |
| #12832 | 5 |