Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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. #10613940 | C2 | semidirect |
| 3. #10602552 | C2 | semidirect |
| 4. #10602364 | C2 | semidirect |
| 5. #10598122 | C2 | semidirect |
| 51. C4⋊#168 | D4 | semidirect |
| 300. C5 | #9198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2619 | 2 |
| #10613940 | 2 |
| #10602552 | 2 |
| #10602364 | 2 |
| #10598122 | 2 |
| #9198 | 5 |