Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10602178 | C2 | semidirect |
| 5. C5×#1365 | C2 | semidirect |
| 6. #10598055 | C2 | semidirect |
| 7. #10597960 | C2 | semidirect |
| 50. #1365 | D5 | semidirect |
| 73. #672 | SD16 | semidirect |
| 188. C5 | #12456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602178 | 2 |
| #10602165 | 2 |
| #10600072 | 2 |
| #10599371 | 2 |
| C5×#1365 | 2 |
| #10598055 | 2 |
| #10597960 | 2 |
| #12456 | 5 |