Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. C2×#3946 | C2 | semidirect |
| 5. #64770 | C2 | semidirect |
| 64. C2×Dic5 | M16 | semidirect |
| 146. C5 | #1851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#681 | 2 |
| C2×C5×C22⋊C8 | 2 |
| C4×C22⋊Dic5 | 2 |
| C2×#3946 | 2 |
| #64770 | 2 |
| #1851 | 5 |