Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10610237 | C2 | semidirect |
| 5. #10601629 | C2 | semidirect |
| 6. #10601616 | C2 | semidirect |
| 7. #10598156 | C2 | semidirect |
| 334. C5 | #10100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614709 | 2 |
| #10614680 | 2 |
| #10610237 | 2 |
| C5×#1527 | 2 |
| #10601629 | 2 |
| #10601616 | 2 |
| #10598156 | 2 |
| #10100 | 5 |