Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×#4070 | C2 | semidirect |
| 3. #65507 | C2 | semidirect |
| 4. #65496 | C2 | semidirect |
| 5. #65331 | C2 | semidirect |
| 6. #65329 | C2 | semidirect |
| 7. #65322 | C2 | semidirect |
| 8. #65259 | C2 | semidirect |
| 12. C22×Dic10 | C22 | semidirect |
| 20. C2×#687 | C22 | semidirect |
| 21. C2×C4⋊Dic5 | C22 | semidirect |
| 25. #4070 | C22 | semidirect |
| 27. C2×#681 | C22 | semidirect |
| 28. #3964 | C22 | semidirect |
| 30. C22⋊#168 | C22 | semidirect |
| 31. #3942 | C22 | semidirect |
| 32. #3939 | C22 | semidirect |
| 229. C5 | #3193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#121 | 2 |
| C2×#4070 | 2 |
| #65507 | 2 |
| #65496 | 2 |
| #65331 | 2 |
| #65329 | 2 |
| #65322 | 2 |
| #65259 | 2 |
| #3193 | 5 |