Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
180 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 17. #4016 | C8 | semidirect |
| 120. C5 | #7358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600620 | 2 |
| #10598689 | 2 |
| #7358 | 5 |