Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
418 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 103 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×#1746 | C2 | semidirect |
| 3. #10600591 | C2 | semidirect |
| 4. #10600525 | C2 | semidirect |
| 5. #10600225 | C2 | semidirect |
| 13. #64984 | C4 | semidirect |
| 14. #64983 | C4 | semidirect |
| 17. #64971 | C4 | semidirect |
| 56. #1746 | D5 | semidirect |
| 253. C5 | #9764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610201 | 2 |
| C5×#1746 | 2 |
| #10600591 | 2 |
| #10600525 | 2 |
| #10600225 | 2 |
| #9764 | 5 |