Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
346 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 14. #64861 | C4 | semidirect |
| 167. C5 | #12659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64890 | 2 |
| C2×#64861 | 2 |
| C4×#3947 | 2 |
| #10598780 | 2 |
| #12659 | 5 |