Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
522 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10603913 | C2 | semidirect |
| 4. #10603776 | C2 | semidirect |
| 6. #10598561 | C2 | semidirect |
| 7. #10598507 | C2 | semidirect |
| 8. C2×#4131 | C4 | semidirect |
| 11. #65776 | C4 | semidirect |
| 19. #65708 | C4 | semidirect |
| 20. #65701 | C4 | semidirect |
| 25. #64920 | C4 | semidirect |
| 28. #64869 | C4 | semidirect |
| 29. C5×#327 | C4 | semidirect |
| 30. #64757 | C4 | semidirect |
| 31. #64687 | C4 | semidirect |
| 32. #64672 | C4 | semidirect |
| 172. #327 | AGL(1,𝔽5) | semidirect |
| 415. C5 | #8240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617225 | 2 |
| #10604466 | 2 |
| #10603913 | 2 |
| #10603776 | 2 |
| #10599094 | 2 |
| #10598561 | 2 |
| #10598507 | 2 |
| #8240 | 5 |