Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 81 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×M32 | C2 | semidirect |
| 3. C2×#3951 | C2 | semidirect |
| 4. #64737 | C2 | semidirect |
| 5. #64736 | C2 | semidirect |
| 48. C2×M32 | D5 | semidirect |
| 152. C5 | #2148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4050 | 2 |
| C2×C5×M32 | 2 |
| C2×#3951 | 2 |
| #64737 | 2 |
| #64736 | 2 |
| #2148 | 5 |