Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C4⋊#170 | C2 | semidirect |
| 5. #64918 | C2 | semidirect |
| 36. C5×C22⋊C4 | C8 | semidirect |
| 53. C2×C4×C5 | C2×C8 | semidirect |
| 85. C22×C5 | C4⋊C8 | semidirect |
| 115. C22⋊C4 | #170 | semidirect |
| 144. C2×C4 | C2×#170 | semidirect |
| 148. C5 | #1850 | semidirect |
| 153. C22 | C4⋊#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#170 | 2 |
| C2×C22⋊#170 | 2 |
| C2×C4⋊#170 | 2 |
| C22⋊C4×Dic5 | 2 |
| #64918 | 2 |
| #1850 | 5 |