Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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×#3947 | C2 | semidirect |
| 5. C2×#3946 | C2 | semidirect |
| 6. #65008 | C2 | direct (N × H) |
| 20. #3947 | C22 | semidirect |
| 21. #3946 | C22 | semidirect |
| 132. C2×C5 | #432 | semidirect |
| 160. C5 | C2×#432 | semidirect |
| 177. C2 | #65008 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic5 | 2 |
| C2×C5×C22⋊C8 | 2 |
| C2×C22⋊#168 | 2 |
| C2×#3947 | 2 |
| C2×#3946 | 2 |
| #65008 | 2 |
| C2×#432 | 5 |