Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10614167 | C2 | semidirect |
| 4. C4×#3968 | C2 | semidirect |
| 5. #10598124 | C2 | semidirect |
| 315. C5 | #9188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2632 | 2 |
| #10614167 | 2 |
| #10602511 | 2 |
| C4×#3968 | 2 |
| #10598124 | 2 |
| #9188 | 5 |