Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 2. C5×#2912 | C2 | semidirect |
| 3. #10615511 | C2 | semidirect |
| 4. #10601449 | C2 | semidirect |
| 5. C2×#64708 | C2 | semidirect |
| 9. #66087 | C4 | semidirect |
| 10. #66086 | C4 | semidirect |
| 15. C5×#427 | C22 | semidirect |
| 16. C2×C5×#106 | C22 | semidirect |
| 18. C2×#3944 | C22 | semidirect |
| 19. #64708 | C22 | semidirect |
| 20. #64708 | C22 | semidirect |
| 39. C2×Dic20 | C2×C4 | semidirect |
| 42. #4050 | C2×C4 | semidirect |
| 44. C2×D40 | C2×C4 | semidirect |
| 55. #2912 | D5 | semidirect |
| 104. #427 | C2×D5 | semidirect |
| 105. C2×#106 | C2×D5 | semidirect |
| 235. C5 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619064 | 2 |
| C5×#2912 | 2 |
| #10615511 | 2 |
| #10601449 | 2 |
| C2×#64708 | 2 |
| #33388 | 5 |