Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
282 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #10598640 | C2 | semidirect |
| 23. #3998 | C8 | semidirect |
| 135. C5 | #11406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604702 | 2 |
| #10604687 | 2 |
| C2×#64722 | 2 |
| #10598640 | 2 |
| #11406 | 5 |