Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #10602630 | C2 | semidirect |
| 4. #10602616 | C2 | semidirect |
| 6. #10598161 | C2 | semidirect |
| 7. #10598157 | C2 | semidirect |
| 10. C5×#500 | C4 | semidirect |
| 11. C5×#492 | C4 | semidirect |
| 12. C5×#487 | C4 | semidirect |
| 13. C5×#486 | C4 | semidirect |
| 116. #500 | Dic5 | semidirect |
| 117. #492 | Dic5 | semidirect |
| 118. #487 | Dic5 | semidirect |
| 119. #486 | Dic5 | semidirect |
| 296. C5 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3182 | 2 |
| #10615010 | 2 |
| #10602630 | 2 |
| #10602616 | 2 |
| #10602606 | 2 |
| #10598161 | 2 |
| #10598157 | 2 |
| #9415 | 5 |