Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
252 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 252 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. #10602106 | C2 | semidirect |
| 2. #10602098 | C2 | semidirect |
| 3. #10600070 | C2 | semidirect |
| 5. C5×#1362 | C2 | semidirect |
| 6. #10598051 | C2 | semidirect |
| 7. #10597961 | C2 | semidirect |
| 52. #1362 | D5 | semidirect |
| 81. #672 | D8 | semidirect |
| 112. D20 | SD32 | semidirect |
| 215. C5 | #12432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602106 | 2 |
| #10602098 | 2 |
| #10600070 | 2 |
| #10599369 | 2 |
| C5×#1362 | 2 |
| #10598051 | 2 |
| #10597961 | 2 |
| #12432 | 5 |