Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 1. C5×#2110 | C2 | semidirect |
| 4. #10602213 | C2 | semidirect |
| 6. #10598301 | C2 | semidirect |
| 7. #10598163 | C2 | semidirect |
| 60. #2110 | D5 | semidirect |
| 265. C5 | #13129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2110 | 2 |
| #10602230 | 2 |
| #10602228 | 2 |
| #10602213 | 2 |
| #10600680 | 2 |
| #10598301 | 2 |
| #10598163 | 2 |
| #13129 | 5 |