Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
734 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 1. #10617361 | C2 | semidirect |
| 3. #10604796 | C2 | semidirect |
| 4. #10604792 | C2 | semidirect |
| 5. #10604606 | C2 | semidirect |
| 6. #10603816 | C2 | semidirect |
| 7. #10603807 | C2 | semidirect |
| 142. C5×C8 | #131 | semidirect |
| 250. C8 | #4131 | semidirect |
| 251. C5 | #17962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617361 | 2 |
| #10613506 | 2 |
| #10604796 | 2 |
| #10604792 | 2 |
| #10604606 | 2 |
| #10603816 | 2 |
| #10603807 | 2 |
| #17962 | 5 |