Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
382 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 10. C5×#500 | C4 | semidirect |
| 11. C5×#498 | C4 | semidirect |
| 12. C5×#487 | C4 | semidirect |
| 13. C5×#487 | C4 | semidirect |
| 117. #500 | Dic5 | semidirect |
| 118. #498 | Dic5 | semidirect |
| 119. #487 | Dic5 | semidirect |
| 120. #487 | Dic5 | semidirect |
| 294. C5 | #9280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3231 | 2 |
| #10615062 | 2 |
| #10602629 | 2 |
| #10602620 | 2 |
| #10598238 | 2 |
| #10598228 | 2 |
| #9280 | 5 |