Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
628 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 125 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. Dic5×#99 | C2 | semidirect |
| 5. #10598186 | C2 | semidirect |
| 7. C2×D4×Dic5 | C4 | semidirect |
| 10. #65510 | C4 | semidirect |
| 16. #65225 | C4 | semidirect |
| 17. #65221 | C4 | semidirect |
| 18. C5×#353 | C4 | semidirect |
| 19. #64765 | C4 | semidirect |
| 45. C5×#99 | C2×C4 | semidirect |
| 47. #3966 | C2×C4 | semidirect |
| 68. C2×C5×D4 | C42 | semidirect |
| 89. C42×C5 | C42 | semidirect |
| 114. #353 | Dic5 | semidirect |
| 187. #99 | C2×Dic5 | semidirect |
| 230. C2×D4 | C4×Dic5 | semidirect |
| 262. C42 | C4×Dic5 | semidirect |
| 317. C5 | #12628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614903 | 2 |
| C2×C5×#353 | 2 |
| C2×#64765 | 2 |
| Dic5×#99 | 2 |
| #10598186 | 2 |
| #12628 | 5 |