Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C5×#1365 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10598052 | C2 | semidirect |
| 7. #10597965 | C2 | semidirect |
| 57. #1365 | D5 | semidirect |
| 232. C5 | #11953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613665 | 2 |
| #10600068 | 2 |
| #10599360 | 2 |
| C5×#1365 | 2 |
| #10598293 | 2 |
| #10598052 | 2 |
| #10597965 | 2 |
| #11953 | 5 |