Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #65834 | C2 | semidirect |
| 3. C5×#417 | C2 | semidirect |
| 4. #65522 | C2 | semidirect |
| 5. #65420 | C2 | semidirect |
| 6. #65411 | C2 | semidirect |
| 7. C2×#3941 | C2 | semidirect |
| 8. #65089 | C2 | semidirect |
| 9. #65084 | C2 | semidirect |
| 10. #65053 | C2 | semidirect |
| 11. #65049 | C2 | semidirect |
| 26. #4036 | C22 | semidirect |
| 28. #4034 | C22 | semidirect |
| 29. C5×#103 | C22 | semidirect |
| 30. C5×#102 | C22 | semidirect |
| 31. #3967 | C22 | semidirect |
| 32. #3967 | C22 | semidirect |
| 33. #3964 | C22 | semidirect |
| 34. #3964 | C22 | semidirect |
| 37. #3947 | C22 | semidirect |
| 38. C8×Dic5 | C22 | semidirect |
| 85. #417 | D5 | semidirect |
| 140. #103 | C2×D5 | semidirect |
| 147. #102 | C2×D5 | semidirect |
| 244. C5 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66164 | 2 |
| #65834 | 2 |
| C5×#417 | 2 |
| #65522 | 2 |
| #65420 | 2 |
| #65411 | 2 |
| C2×#3941 | 2 |
| #65089 | 2 |
| #65084 | 2 |
| #65053 | 2 |
| #65049 | 2 |
| #3136 | 5 |