Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 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×#2246 | C2 | semidirect |
| 2. #10602075 | C2 | semidirect |
| 3. C16×D20 | C2 | semidirect |
| 4. #10598281 | C2 | semidirect |
| 5. #10597991 | C2 | semidirect |
| 35. #2246 | D5 | semidirect |
| 59. C5×C16 | D8 | semidirect |
| 84. D20 | D16 | semidirect |
| 142. C16 | #686 | semidirect |
| 168. C5 | #12430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2246 | 2 |
| #10602075 | 2 |
| C16×D20 | 2 |
| #10598281 | 2 |
| #10597991 | 2 |
| #12430 | 5 |