Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #66161 | C2 | semidirect |
| 3. #65523 | C2 | semidirect |
| 4. #65504 | C2 | semidirect |
| 5. C2×#3964 | C2 | semidirect |
| 6. #65324 | C2 | semidirect |
| 7. #65324 | C2 | semidirect |
| 8. #65323 | C2 | semidirect |
| 9. #65322 | C2 | semidirect |
| 10. #65287 | C2 | semidirect |
| 11. #65284 | C2 | semidirect |
| 24. #4072 | C22 | semidirect |
| 26. C2×C4⋊Dic5 | C22 | semidirect |
| 33. C22⋊#168 | C22 | semidirect |
| 34. C22⋊#168 | C22 | semidirect |
| 35. #3940 | C22 | semidirect |
| 36. #3940 | C22 | semidirect |
| 37. #3940 | C22 | semidirect |
| 38. #3939 | C22 | semidirect |
| 39. #3939 | C22 | semidirect |
| 40. #3939 | C22 | semidirect |
| 242. C5 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#535 | 2 |
| #66161 | 2 |
| #65523 | 2 |
| #65504 | 2 |
| C2×#3964 | 2 |
| #65324 | 2 |
| #65323 | 2 |
| #65322 | 2 |
| #65287 | 2 |
| #65284 | 2 |
| #3096 | 5 |