Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
526 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 12. C5×#500 | C4 | semidirect |
| 13. #65367 | C4 | semidirect |
| 17. #64971 | C4 | semidirect |
| 90. #500 | AGL(1,𝔽5) | semidirect |
| 125. C5×C8 | #103 | semidirect |
| 126. #168 | #103 | semidirect |
| 236. C8 | #4009 | semidirect |
| 237. C5 | #9823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#500 | 2 |
| #10604674 | 2 |
| #10604672 | 2 |
| #10603848 | 2 |
| C8×D5⋊C8 | 2 |
| #9823 | 5 |