Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C5×#1812 | C2 | semidirect |
| 3. #10602807 | C2 | semidirect |
| 5. #10598188 | C2 | semidirect |
| 8. C22×#676 | C4 | semidirect |
| 15. #65415 | C4 | semidirect |
| 16. #65408 | C4 | semidirect |
| 20. #65390 | C4 | semidirect |
| 72. #1812 | D5 | semidirect |
| 344. C5 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615526 | 2 |
| C5×#1812 | 2 |
| #10602807 | 2 |
| #10600849 | 2 |
| #10598188 | 2 |
| #12806 | 5 |