Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #66103 | C2 | semidirect |
| 2. #66100 | C2 | semidirect |
| 3. C5×#510 | C2 | semidirect |
| 4. #65483 | C2 | semidirect |
| 5. C2×#3960 | C2 | semidirect |
| 6. #65208 | C2 | semidirect |
| 7. #65207 | C2 | semidirect |
| 8. #65203 | C2 | semidirect |
| 9. D5×SD32 | C2 | semidirect |
| 10. #65197 | C2 | semidirect |
| 11. #65196 | C2 | semidirect |
| 15. C2×C5×Q16 | C22 | semidirect |
| 19. #4065 | C22 | semidirect |
| 21. D5×Q16 | C22 | semidirect |
| 24. #4050 | C22 | semidirect |
| 27. C5×Q32 | C22 | semidirect |
| 28. C5×SD32 | C22 | semidirect |
| 29. C5×M32 | C22 | semidirect |
| 30. #3961 | C22 | semidirect |
| 31. #3960 | C22 | semidirect |
| 32. #3960 | C22 | semidirect |
| 33. #3960 | C22 | semidirect |
| 34. #3959 | C22 | semidirect |
| 35. #3958 | C22 | semidirect |
| 36. C2×#672 | C22 | semidirect |
| 37. #3932 | C22 | semidirect |
| 38. D80 | C22 | semidirect |
| 39. #3930 | C22 | semidirect |
| 40. D5×C16 | C22 | semidirect |
| 81. #510 | D5 | semidirect |
| 130. C2×Q16 | C2×D5 | semidirect |
| 135. Q32 | C2×D5 | semidirect |
| 141. SD32 | C2×D5 | semidirect |
| 145. M32 | C2×D5 | semidirect |
| 233. C5 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66103 | 2 |
| #66100 | 2 |
| C5×#510 | 2 |
| #65483 | 2 |
| C2×#3960 | 2 |
| #65208 | 2 |
| #65207 | 2 |
| #65203 | 2 |
| D5×SD32 | 2 |
| #65197 | 2 |
| #65196 | 2 |
| #3416 | 5 |