Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 65 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×#2227 | C2 | semidirect |
| 4. #10602171 | C2 | semidirect |
| 5. #10598256 | C2 | semidirect |
| 7. #10598049 | C2 | semidirect |
| 55. #2227 | D5 | semidirect |
| 234. C5 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611443 | 2 |
| C5×#2227 | 2 |
| #10602174 | 2 |
| #10602171 | 2 |
| #10598256 | 2 |
| #10598051 | 2 |
| #10598049 | 2 |
| #12385 | 5 |