Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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. #65470 | C2 | semidirect |
| 4. C2×#3961 | C2 | semidirect |
| 7. #64722 | C2 | semidirect |
| 46. C2×Q32 | D5 | semidirect |
| 134. C5 | #2251 | 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 |
| #65470 | 2 |
| C2×#3961 | 2 |
| C2×#3960 | 2 |
| C2×#3932 | 2 |
| #64722 | 2 |
| #2251 | 5 |