Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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×#2254 | C2 | semidirect |
| 5. #10598293 | C2 | semidirect |
| 6. #10598292 | C2 | semidirect |
| 7. #10597991 | C2 | semidirect |
| 45. #2254 | D5 | semidirect |
| 72. C5×C16 | SD16 | semidirect |
| 163. C16 | #688 | semidirect |
| 188. C5 | #12456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2254 | 2 |
| #10602165 | 2 |
| #10602164 | 2 |
| #10599848 | 2 |
| #10598293 | 2 |
| #10598292 | 2 |
| #10597991 | 2 |
| #12456 | 5 |