Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 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×#1568 | C2 | semidirect |
| 3. #10601629 | C2 | semidirect |
| 5. #10601606 | C2 | semidirect |
| 7. #10600544 | C2 | semidirect |
| 17. #64983 | C4 | semidirect |
| 18. #64982 | C4 | semidirect |
| 21. #64970 | C4 | semidirect |
| 22. #64969 | C4 | semidirect |
| 77. #1568 | D5 | semidirect |
| 329. C5 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610199 | 2 |
| C5×#1568 | 2 |
| #10601629 | 2 |
| #10601625 | 2 |
| #10601606 | 2 |
| #10601599 | 2 |
| #10600544 | 2 |
| #9766 | 5 |