Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
698 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 129 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. C22×D80 | C2 | semidirect |
| 2. C2×#64984 | C2 | semidirect |
| 3. C2×#64729 | C2 | semidirect |
| 4. #10600569 | C2 | semidirect |
| 5. C5×#1374 | C2 | semidirect |
| 41. C2×D40 | D4 | semidirect |
| 46. C2×C5×C16 | D4 | semidirect |
| 55. #1374 | D5 | semidirect |
| 123. C2×C4×C5 | D16 | semidirect |
| 170. C2×C16 | D20 | semidirect |
| 266. C2×C4 | D80 | semidirect |
| 276. C5 | #13325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D80 | 2 |
| C2×#64984 | 2 |
| C2×#64729 | 2 |
| #10600569 | 2 |
| C5×#1374 | 2 |
| #13325 | 5 |