Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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×#4002 | C2 | semidirect |
| 3. #64921 | C2 | direct (N × H) |
| 13. #4002 | C22 | semidirect |
| 91. C2×C5 | #329 | semidirect |
| 111. C5 | C2×#329 | semidirect |
| 124. C2 | #64921 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4082 | 2 |
| C2×#4002 | 2 |
| #64921 | 2 |
| C2×#329 | 5 |