Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
300 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #10604748 | C2 | semidirect |
| 4. #10604746 | C2 | semidirect |
| 6. #10598797 | C2 | semidirect |
| 7. #10598796 | C2 | semidirect |
| 256. C5 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605009 | 2 |
| C2×#64932 | 2 |
| #10604748 | 2 |
| #10604746 | 2 |
| #10600926 | 2 |
| #10598797 | 2 |
| #10598796 | 2 |
| #13126 | 5 |