Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 1. #66062 | C2 | semidirect |
| 3. C5×#492 | C2 | semidirect |
| 4. #65458 | C2 | semidirect |
| 5. #65452 | C2 | semidirect |
| 6. #65374 | C2 | semidirect |
| 7. #65359 | C2 | semidirect |
| 8. #64983 | C2 | semidirect |
| 9. #64974 | C2 | semidirect |
| 13. C2×C5×SD16 | C22 | semidirect |
| 14. C5×C4⋊Q8 | C22 | semidirect |
| 17. Q8×Dic5 | C22 | semidirect |
| 18. C2×#688 | C22 | semidirect |
| 28. #4015 | C22 | semidirect |
| 29. C4×C5×C8 | C22 | semidirect |
| 30. #3964 | C22 | semidirect |
| 31. #3953 | C22 | semidirect |
| 33. #3946 | C22 | semidirect |
| 34. C4×#168 | C22 | semidirect |
| 73. #492 | D5 | semidirect |
| 105. C4×D5 | SD16 | semidirect |
| 113. C2×SD16 | C2×D5 | semidirect |
| 115. C4⋊Q8 | C2×D5 | semidirect |
| 133. C4×C8 | C2×D5 | semidirect |
| 223. C5 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| D5×#127 | 2 |
| C5×#492 | 2 |
| #65458 | 2 |
| #65452 | 2 |
| #65374 | 2 |
| #65359 | 2 |
| #64983 | 2 |
| #64974 | 2 |
| #3208 | 5 |