Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 396 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. #10600594 | C2 | semidirect |
| 5. #10600525 | C2 | semidirect |
| 6. #10600226 | C2 | semidirect |
| 17. #64983 | C4 | semidirect |
| 18. #64982 | C4 | semidirect |
| 21. #64970 | C4 | semidirect |
| 22. #64969 | C4 | semidirect |
| 76. #1746 | 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×#1746 | 2 |
| #10600594 | 2 |
| #10600591 | 2 |
| #10600525 | 2 |
| #10600226 | 2 |
| #10600225 | 2 |
| #9766 | 5 |