Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 13. #64884 | C4 | semidirect |
| 14. #64881 | C4 | semidirect |
| 17. C5×#334 | C4 | semidirect |
| 18. #64699 | C4 | semidirect |
| 19. #64677 | C4 | semidirect |
| 35. C8×AGL(1,𝔽5) | C8 | semidirect |
| 85. #334 | AGL(1,𝔽5) | semidirect |
| 198. C5 | #8266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604010 | 2 |
| C4×C8×AGL(1,𝔽5) | 2 |
| #10603814 | 2 |
| #10599320 | 2 |
| #10598583 | 2 |
| #8266 | 5 |