Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 1. #10602083 | C2 | semidirect |
| 2. #10602075 | C2 | semidirect |
| 3. #10600070 | C2 | semidirect |
| 4. #10599369 | C2 | semidirect |
| 5. C5×#1361 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10597960 | C2 | semidirect |
| 53. #1361 | D5 | semidirect |
| 82. #672 | D8 | semidirect |
| 116. D20 | D16 | semidirect |
| 226. C5 | #12430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602083 | 2 |
| #10602075 | 2 |
| #10600070 | 2 |
| #10599369 | 2 |
| C5×#1361 | 2 |
| #10598051 | 2 |
| #10597960 | 2 |
| #12430 | 5 |