Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. C5×#568 | C4 | semidirect |
| 7. C5×#410 | C4 | semidirect |
| 11. #64765 | C4 | semidirect |
| 14. #64760 | C4 | semidirect |
| 73. #568 | Dic5 | semidirect |
| 78. #410 | Dic5 | semidirect |
| 213. C5 | #7494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1884 | 2 |
| #10602612 | 2 |
| #10602592 | 2 |
| #7494 | 5 |