Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
528 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 274 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. #65748 | C2 | direct (N × H) |
| 4. C2×C4⋊#170 | C2 | semidirect |
| 5. C2×C4×#170 | C2 | semidirect |
| 17. C4⋊#170 | C22 | semidirect |
| 18. C4×#170 | C22 | semidirect |
| 21. C22×C4×C5 | C8 | semidirect |
| 54. C2×C4×C5 | C2×C8 | semidirect |
| 108. C22×C4 | #170 | semidirect |
| 121. C2×C5 | #431 | semidirect |
| 144. C2×C4 | C2×#170 | semidirect |
| 148. C5 | C2×#431 | semidirect |
| 165. C2 | #65748 | 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×C22⋊#170 | 2 |
| #65748 | 2 |
| C2×C4⋊#170 | 2 |
| C2×C4×#170 | 2 |
| C2×#431 | 5 |