Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
350 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 85 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. #10600068 | C2 | semidirect |
| 3. D5×#335 | C2 | semidirect |
| 4. C5×#1365 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10597964 | C2 | semidirect |
| 57. #1365 | D5 | semidirect |
| 249. C5 | #11952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613664 | 2 |
| #10600068 | 2 |
| D5×#335 | 2 |
| C5×#1365 | 2 |
| #10598293 | 2 |
| #10598051 | 2 |
| #10597964 | 2 |
| #11952 | 5 |