Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 223. C5 | #10664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1985 | 2 |
| #10602415 | 2 |
| #10601215 | 2 |
| #10601214 | 2 |
| #10600634 | 2 |
| #10598151 | 2 |
| #10664 | 5 |