Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
640 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 2. C2×#64921 | C2 | semidirect |
| 3. #10604181 | C2 | semidirect |
| 4. C4×#4002 | C2 | semidirect |
| 49. #4002 | D4 | semidirect |
| 199. C4×C5 | #329 | semidirect |
| 295. C5 | #9685 | semidirect |
| 318. C4 | #64921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614915 | 2 |
| C2×#64921 | 2 |
| #10604181 | 2 |
| C4×#4002 | 2 |
| #9685 | 5 |