Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10600079 | C2 | semidirect |
| 2. #10598855 | C2 | semidirect |
| 3. C8×D40 | C2 | semidirect |
| 4. C5×#1370 | C2 | semidirect |
| 5. #10598051 | C2 | semidirect |
| 39. #1370 | D5 | semidirect |
| 62. D40 | D8 | semidirect |
| 94. C5×C8 | D16 | semidirect |
| 177. C8 | D80 | semidirect |
| 180. C5 | #12424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600079 | 2 |
| #10598855 | 2 |
| C8×D40 | 2 |
| C5×#1370 | 2 |
| #10598051 | 2 |
| #12424 | 5 |