Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
558 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 4. #10602383 | C2 | semidirect |
| 5. #10598109 | C2 | semidirect |
| 8. C5×#400 | C4 | semidirect |
| 9. C5×#399 | C4 | semidirect |
| 10. C5×#398 | C4 | semidirect |
| 12. C5×#397 | C4 | semidirect |
| 119. #400 | Dic5 | semidirect |
| 120. #399 | Dic5 | semidirect |
| 121. #398 | Dic5 | semidirect |
| 123. #397 | Dic5 | semidirect |
| 333. C5 | #9012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2395 | 2 |
| #10614035 | 2 |
| C4×#3966 | 2 |
| #10602383 | 2 |
| #10598109 | 2 |
| #9012 | 5 |