Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 75 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. C5×D4×C16 | C2 | semidirect |
| 2. #10601640 | C2 | semidirect |
| 3. #10599853 | C2 | semidirect |
| 4. #10598051 | C2 | semidirect |
| 5. #10597991 | C2 | semidirect |
| 36. D4×C16 | D5 | semidirect |
| 60. C5×C16 | D8 | semidirect |
| 75. C5×D4 | D16 | semidirect |
| 142. C16 | #686 | semidirect |
| 156. D4 | D80 | semidirect |
| 168. C5 | #12430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C16 | 2 |
| #10601640 | 2 |
| #10599853 | 2 |
| #10598051 | 2 |
| #10597991 | 2 |
| #12430 | 5 |