Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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×C5×#362 | C2 | semidirect |
| 3. #10602862 | C2 | semidirect |
| 5. #10602214 | C2 | semidirect |
| 7. #10598219 | C2 | semidirect |
| 64. C2×#362 | D5 | semidirect |
| 287. C5 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3960 | 2 |
| C2×C5×#362 | 2 |
| #10602862 | 2 |
| C2×#64736 | 2 |
| #10602214 | 2 |
| #10601502 | 2 |
| #10598219 | 2 |
| #13440 | 5 |