Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #65912 | C2 | semidirect |
| 3. C5×#460 | C2 | semidirect |
| 4. #65464 | C2 | semidirect |
| 5. #65458 | C2 | semidirect |
| 6. #65364 | C2 | semidirect |
| 7. #65316 | C2 | semidirect |
| 8. #65137 | C2 | semidirect |
| 9. #65122 | C2 | semidirect |
| 10. #65065 | C2 | semidirect |
| 11. #65049 | C2 | semidirect |
| 15. C2×C5×SD16 | C22 | semidirect |
| 17. C4×C5×Q8 | C22 | semidirect |
| 19. #4090 | C22 | semidirect |
| 20. C2×#688 | C22 | semidirect |
| 24. C2×#687 | C22 | semidirect |
| 25. C2×#677 | C22 | semidirect |
| 29. #4034 | C22 | semidirect |
| 34. C4×Dic10 | C22 | semidirect |
| 35. C5×C4⋊C8 | C22 | semidirect |
| 36. C5×#102 | C22 | semidirect |
| 37. #3964 | C22 | semidirect |
| 38. #3953 | C22 | semidirect |
| 40. C8×Dic5 | C22 | semidirect |
| 41. #3941 | C22 | semidirect |
| 42. C4⋊#168 | C22 | semidirect |
| 94. #460 | D5 | semidirect |
| 130. C4×D5 | SD16 | semidirect |
| 142. C2×SD16 | C2×D5 | semidirect |
| 156. C4×Q8 | C2×D5 | semidirect |
| 160. C4⋊C8 | C2×D5 | semidirect |
| 164. #102 | C2×D5 | semidirect |
| 276. C5 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#127 | 2 |
| #65912 | 2 |
| C5×#460 | 2 |
| #65464 | 2 |
| #65458 | 2 |
| #65364 | 2 |
| #65316 | 2 |
| #65137 | 2 |
| #65122 | 2 |
| #65065 | 2 |
| #65049 | 2 |
| #3208 | 5 |