Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 11. C5×#346 | C4 | semidirect |
| 12. C4×C5×C16 | C4 | semidirect |
| 61. #346 | Dic5 | semidirect |
| 62. C4×C16 | Dic5 | semidirect |
| 135. C5 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2108 | 2 |
| #10600689 | 2 |
| #10598311 | 2 |
| #10598309 | 2 |
| #10598298 | 2 |
| #12893 | 5 |