Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #65813 | C2 | semidirect |
| 2. C2×#4021 | C2 | semidirect |
| 3. C5×#431 | C2 | semidirect |
| 4. #65134 | C2 | semidirect |
| 5. #65133 | C2 | semidirect |
| 6. #65028 | C2 | semidirect |
| 7. #65027 | C2 | semidirect |
| 9. #65020 | C2 | semidirect |
| 10. #64986 | C2 | semidirect |
| 11. #64985 | C2 | semidirect |
| 21. C2×Dic20 | C22 | semidirect |
| 24. C2×#677 | C22 | semidirect |
| 30. #4021 | C22 | semidirect |
| 31. C4×D20 | C22 | semidirect |
| 33. #4016 | C22 | semidirect |
| 34. C4×Dic10 | C22 | semidirect |
| 35. C5×C4⋊C8 | C22 | semidirect |
| 38. C4×C5×C8 | C22 | semidirect |
| 41. #3948 | C22 | semidirect |
| 42. #3948 | C22 | semidirect |
| 95. #431 | D5 | semidirect |
| 151. C4⋊C8 | C2×D5 | semidirect |
| 158. C4×C8 | C2×D5 | semidirect |
| 259. C5 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65813 | 2 |
| C2×#4021 | 2 |
| C5×#431 | 2 |
| #65134 | 2 |
| #65133 | 2 |
| #65028 | 2 |
| #65027 | 2 |
| #65021 | 2 |
| #65020 | 2 |
| #64986 | 2 |
| #64985 | 2 |
| #3211 | 5 |