Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #10600083 | C2 | semidirect |
| 3. #10598851 | C2 | semidirect |
| 4. C8×D40 | C2 | semidirect |
| 5. C5×#1367 | C2 | semidirect |
| 6. #10598056 | C2 | semidirect |
| 7. #10598051 | C2 | semidirect |
| 50. #1367 | D5 | semidirect |
| 74. D40 | SD16 | semidirect |
| 209. C5 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600083 | 2 |
| #10600079 | 2 |
| #10598851 | 2 |
| C8×D40 | 2 |
| C5×#1367 | 2 |
| #10598056 | 2 |
| #10598051 | 2 |
| #12418 | 5 |