Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#689 | C2 | semidirect |
| 5. C2×#3968 | C2 | semidirect |
| 6. #65493 | C2 | direct (N × H) |
| 7. C2×#3956 | C2 | semidirect |
| 8. C2×#3954 | C2 | semidirect |
| 25. C2×#689 | C22 | semidirect |
| 32. #3968 | C22 | semidirect |
| 33. #3956 | C22 | semidirect |
| 34. #3954 | C22 | semidirect |
| 210. C2×C5 | #473 | semidirect |
| 248. C5 | C2×#473 | semidirect |
| 265. C2 | #65493 | direct (N × H) |
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 |
| C2×#4094 | 2 |
| C22×#689 | 2 |
| C2×#3968 | 2 |
| #65493 | 2 |
| C2×#3956 | 2 |
| C2×#3954 | 2 |
| C2×#473 | 5 |