Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 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. #64873 | C2 | direct (N × H) |
| 121. C2×C5 | #332 | semidirect |
| 146. C5 | C2×#332 | semidirect |
| 161. C2 | #64873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4034 | 2 |
| C2×#4004 | 2 |
| #64873 | 2 |
| C2×#332 | 5 |