Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. C4×C22⋊Dic5 | C2 | semidirect |
| 5. #65270 | C2 | semidirect |
| 6. C4⋊C4×Dic5 | C2 | semidirect |
| 7. #65240 | C2 | semidirect |
| 8. #65240 | C2 | semidirect |
| 9. C22⋊C4×Dic5 | C2 | semidirect |
| 13. C5×#123 | C4 | semidirect |
| 40. C22×C4×C5 | C2×C4 | semidirect |
| 50. C5×C4⋊C4 | C2×C4 | semidirect |
| 52. C5×C22⋊C4 | C2×C4 | semidirect |
| 110. #123 | Dic5 | semidirect |
| 164. C22×C4 | C2×Dic5 | semidirect |
| 170. C4⋊C4 | C2×Dic5 | semidirect |
| 176. C22⋊C4 | C2×Dic5 | semidirect |
| 223. C5 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#123 | 2 |
| #65510 | 2 |
| #65509 | 2 |
| C4×C22⋊Dic5 | 2 |
| #65270 | 2 |
| C4⋊C4×Dic5 | 2 |
| #65240 | 2 |
| C22⋊C4×Dic5 | 2 |
| #2374 | 5 |