Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
612 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 612 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 |
|---|---|---|
| 5. C23×C5×Q8 | C4 | semidirect |
| 12. C5×#385 | C4 | semidirect |
| 13. C5×#380 | C4 | semidirect |
| 49. #3965 | Q8 | semidirect |
| 103. C23×Q8 | Dic5 | semidirect |
| 113. #385 | Dic5 | semidirect |
| 115. #380 | Dic5 | semidirect |
| 320. C5 | #13293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2409 | 2 |
| #10602412 | 2 |
| C4×#3965 | 2 |
| #10598128 | 2 |
| #13293 | 5 |