Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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×D5⋊M16 | C2 | semidirect |
| 3. C2×#4013 | C2 | semidirect |
| 4. #65761 | C2 | direct (N × H) |
| 5. C2×#4005 | C2 | semidirect |
| 20. D5⋊M16 | C22 | semidirect |
| 23. #4013 | C22 | semidirect |
| 24. #4005 | C22 | semidirect |
| 203. C2×C5 | #413 | semidirect |
| 249. C5 | C2×#413 | semidirect |
| 277. C2 | #65761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#709 | 2 |
| C2×D5⋊M16 | 2 |
| C2×#4013 | 2 |
| #65761 | 2 |
| C2×#4005 | 2 |
| C2×#413 | 5 |