Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C2×C5×Q32 | C2 | semidirect |
| 3. #65477 | C2 | semidirect |
| 4. C2×#3960 | C2 | semidirect |
| 5. #64784 | C2 | semidirect |
| 6. #64729 | C2 | semidirect |
| 7. #64727 | C2 | semidirect |
| 49. C2×Q32 | D5 | semidirect |
| 152. C5 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4065 | 2 |
| C2×C5×Q32 | 2 |
| #65477 | 2 |
| C2×#3960 | 2 |
| #64784 | 2 |
| #64729 | 2 |
| #64727 | 2 |
| #2189 | 5 |