Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×C5×Q32 | C2 | semidirect |
| 3. Q16×Dic5 | C2 | semidirect |
| 5. #64784 | C2 | semidirect |
| 7. #64721 | C2 | semidirect |
| 42. C2×Q32 | D5 | semidirect |
| 129. C5 | #2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q32 | 2 |
| #65480 | 2 |
| Q16×Dic5 | 2 |
| C2×#3960 | 2 |
| #64784 | 2 |
| #64729 | 2 |
| #64721 | 2 |
| #2211 | 5 |