Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. C5×#2155 | C2 | semidirect |
| 3. #10602216 | C2 | semidirect |
| 4. #10601493 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 56. #2155 | D5 | semidirect |
| 259. C5 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2155 | 2 |
| C2×#64738 | 2 |
| #10602216 | 2 |
| #10601493 | 2 |
| #10601483 | 2 |
| #10601451 | 2 |
| #10598217 | 2 |
| #13469 | 5 |