Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 486 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. #10604696 | C2 | semidirect |
| 5. #10604688 | C2 | semidirect |
| 6. #10604339 | C2 | semidirect |
| 7. #10604277 | C2 | semidirect |
| 372. C5 | #9804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65049 | 2 |
| #10604953 | 2 |
| #10604926 | 2 |
| #10604696 | 2 |
| #10604688 | 2 |
| #10604339 | 2 |
| #10604277 | 2 |
| #9804 | 5 |