Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
342 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 9. C5×#424 | C4 | semidirect |
| 10. C5×#424 | C4 | semidirect |
| 13. C4×C5×M16 | C4 | semidirect |
| 14. C2×C4×C5×C8 | C4 | semidirect |
| 86. #424 | Dic5 | semidirect |
| 87. #424 | Dic5 | semidirect |
| 92. C4×M16 | Dic5 | semidirect |
| 93. C2×C4×C8 | Dic5 | semidirect |
| 217. C5 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2922 | 2 |
| #10602437 | 2 |
| #10598184 | 2 |
| #10598183 | 2 |
| #10598182 | 2 |
| #12864 | 5 |