Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
326 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 16. C5×#333 | C4 | semidirect |
| 17. C5×#332 | C4 | semidirect |
| 108. #333 | Dic5 | semidirect |
| 109. #332 | Dic5 | semidirect |
| 254. C5 | #9584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1542 | 2 |
| #10602632 | 2 |
| #10602617 | 2 |
| #10601543 | 2 |
| #10601234 | 2 |
| #10598227 | 2 |
| #10598198 | 2 |
| #9584 | 5 |