Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 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. C5×#2209 | C2 | semidirect |
| 4. Q16×#168 | C2 | semidirect |
| 5. #10598284 | C2 | semidirect |
| 7. #10598046 | C2 | semidirect |
| 47. #2209 | D5 | semidirect |
| 208. C5 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2209 | 2 |
| #10602090 | 2 |
| #10601707 | 2 |
| Q16×#168 | 2 |
| #10598284 | 2 |
| #10598051 | 2 |
| #10598046 | 2 |
| #12429 | 5 |