Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
564 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 97 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. C5×#3135 | C2 | semidirect |
| 2. #10615086 | C2 | semidirect |
| 4. #10602631 | C2 | semidirect |
| 5. #10602607 | C2 | semidirect |
| 6. #10600616 | C2 | semidirect |
| 7. #10598152 | C2 | semidirect |
| 79. #3135 | D5 | semidirect |
| 362. C5 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3135 | 2 |
| #10615086 | 2 |
| #10615033 | 2 |
| #10602631 | 2 |
| #10602607 | 2 |
| #10600616 | 2 |
| #10598152 | 2 |
| #10219 | 5 |