Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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×#2248 | C2 | semidirect |
| 2. #10602098 | C2 | semidirect |
| 4. C16×D20 | C2 | semidirect |
| 5. #10598284 | C2 | semidirect |
| 6. #10598281 | C2 | semidirect |
| 7. #10597992 | C2 | semidirect |
| 47. #2248 | D5 | semidirect |
| 80. C5×C16 | D8 | semidirect |
| 112. D20 | SD32 | semidirect |
| 185. C16 | #686 | semidirect |
| 215. C5 | #12432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2248 | 2 |
| #10602098 | 2 |
| #10602075 | 2 |
| C16×D20 | 2 |
| #10598284 | 2 |
| #10598281 | 2 |
| #10597992 | 2 |
| #12432 | 5 |