Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×C5×#137 | C2 | semidirect |
| 3. #66150 | C2 | semidirect |
| 4. C22×#688 | C2 | semidirect |
| 5. #65522 | C2 | semidirect |
| 6. #65476 | C2 | semidirect |
| 7. #65458 | C2 | semidirect |
| 8. #65420 | C2 | semidirect |
| 9. #65418 | C2 | semidirect |
| 11. C22×C5×Q8 | C22 | semidirect |
| 22. C2×C5×Q16 | C22 | semidirect |
| 23. C2×C5×SD16 | C22 | semidirect |
| 24. C2×C5×M16 | C22 | semidirect |
| 26. #4092 | C22 | semidirect |
| 29. C2×#688 | C22 | semidirect |
| 31. #4072 | C22 | semidirect |
| 32. C22×#168 | C22 | semidirect |
| 33. #3967 | C22 | semidirect |
| 34. #3964 | C22 | semidirect |
| 35. #3953 | C22 | semidirect |
| 36. #3952 | C22 | semidirect |
| 85. C2×#137 | D5 | semidirect |
| 138. C22×Q8 | C2×D5 | semidirect |
| 144. C2×Q16 | C2×D5 | semidirect |
| 147. C2×SD16 | C2×D5 | semidirect |
| 148. C2×M16 | C2×D5 | semidirect |
| 268. C5 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4149 | 2 |
| C2×C5×#137 | 2 |
| #66150 | 2 |
| C22×#688 | 2 |
| #65522 | 2 |
| #65476 | 2 |
| #65458 | 2 |
| #65420 | 2 |
| #65418 | 2 |
| #3009 | 5 |