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×#486 | C2 | semidirect |
| 4. #65377 | C2 | semidirect |
| 5. #65365 | C2 | semidirect |
| 6. #65065 | C2 | semidirect |
| 7. #65051 | C2 | semidirect |
| 8. #64982 | C2 | semidirect |
| 9. #64974 | C2 | semidirect |
| 13. C5×C4⋊Q8 | C22 | semidirect |
| 20. C2×#687 | C22 | semidirect |
| 21. C2×#677 | C22 | semidirect |
| 25. #4033 | C22 | semidirect |
| 28. #4015 | C22 | semidirect |
| 29. C5×#102 | C22 | semidirect |
| 30. C4×C5×C8 | C22 | semidirect |
| 32. #3946 | C22 | semidirect |
| 33. #3941 | C22 | semidirect |
| 34. C4×#168 | C22 | semidirect |
| 75. #486 | D5 | semidirect |
| 105. C4×D5 | SD16 | semidirect |
| 115. C4⋊Q8 | C2×D5 | semidirect |
| 130. #102 | 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×#486 | 2 |
| #65377 | 2 |
| #65365 | 2 |
| #65065 | 2 |
| #65051 | 2 |
| #64982 | 2 |
| #64974 | 2 |
| #3208 | 5 |