Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
522 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10604719 | C2 | semidirect |
| 5. C8×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 6. #10598789 | C2 | semidirect |
| 7. #10598785 | C2 | semidirect |
| 9. C2×#4094 | C4 | semidirect |
| 17. C5×#408 | C4 | semidirect |
| 19. #65411 | C4 | semidirect |
| 20. #65391 | C4 | semidirect |
| 25. #64926 | C4 | semidirect |
| 26. #64926 | C4 | semidirect |
| 27. #64920 | C4 | semidirect |
| 28. #64920 | C4 | semidirect |
| 149. #408 | AGL(1,𝔽5) | semidirect |
| 385. C5 | #8240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610386 | 2 |
| #10604989 | 2 |
| #10604719 | 2 |
| C8×C22⋊AGL(1,𝔽5) | 2 |
| #10598789 | 2 |
| #10598785 | 2 |
| #8240 | 5 |