Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
446 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 15. C8×#170 | C4 | semidirect |
| 16. C8×#170 | C4 | semidirect |
| 17. C5×#334 | C4 | semidirect |
| 18. #64700 | C4 | semidirect |
| 19. #64677 | C4 | semidirect |
| 35. #3993 | C8 | semidirect |
| 88. #334 | AGL(1,𝔽5) | semidirect |
| 108. #170 | #106 | semidirect |
| 111. C5×C8 | C4×C8 | semidirect |
| 114. #168 | C4×C8 | semidirect |
| 206. C8 | C8×AGL(1,𝔽5) | semidirect |
| 207. C5 | C8×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604033 | 2 |
| C4×#3993 | 2 |
| C8×D5⋊C8 | 2 |
| D5×#334 | 2 |
| #10598589 | 2 |
| C8×#106 | 5 |