Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. C22×#689 | C2 | semidirect |
| 5. C2×#3968 | C2 | semidirect |
| 6. C2×#3956 | C2 | semidirect |
| 7. #64778 | C2 | semidirect |
| 226. C5 | #2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#137 | 2 |
| C2×#4097 | 2 |
| C22×#689 | 2 |
| #65523 | 2 |
| C2×#3968 | 2 |
| C2×#3956 | 2 |
| #64778 | 2 |
| #2020 | 5 |