Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
686 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 272. C5 | #8356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617704 | 2 |
| C5×#1801 | 2 |
| #10602427 | 2 |
| #10601302 | 2 |
| #10601294 | 2 |
| #8356 | 5 |