Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #65817 | C2 | semidirect |
| 5. #64747 | C2 | semidirect |
| 6. #64747 | C2 | semidirect |
| 7. #64746 | C2 | semidirect |
| 22. C24×C5 | Q8 | semidirect |
| 32. C22×C4×C5 | Q8 | semidirect |
| 129. C24 | Dic10 | semidirect |
| 144. C22×C4 | Dic10 | semidirect |
| 200. C5 | #2032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65817 | 2 |
| C2×C5×#99 | 2 |
| C2×#3966 | 2 |
| #64747 | 2 |
| #64746 | 2 |
| #2032 | 5 |