Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. C5×#536 | C2 | semidirect |
| 3. #65523 | C2 | semidirect |
| 4. #65516 | C2 | semidirect |
| 5. #65338 | C2 | semidirect |
| 6. #65337 | C2 | semidirect |
| 7. #65335 | C2 | semidirect |
| 8. #65334 | C2 | semidirect |
| 9. #65292 | C2 | semidirect |
| 11. C22×C5×Q8 | C22 | semidirect |
| 18. C5×C22⋊Q8 | C22 | semidirect |
| 19. C5×#117 | C22 | semidirect |
| 29. C2×#681 | C22 | semidirect |
| 30. C22×#168 | C22 | semidirect |
| 31. #3967 | C22 | semidirect |
| 32. #3967 | C22 | semidirect |
| 34. C22⋊#168 | C22 | semidirect |
| 37. #3940 | C22 | semidirect |
| 38. #3939 | C22 | semidirect |
| 79. #536 | D5 | semidirect |
| 123. C22×Q8 | C2×D5 | semidirect |
| 136. C22⋊Q8 | C2×D5 | semidirect |
| 142. #117 | C2×D5 | semidirect |
| 249. C5 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#536 | 2 |
| #66164 | 2 |
| #65523 | 2 |
| #65516 | 2 |
| #65338 | 2 |
| #65337 | 2 |
| #65335 | 2 |
| #65334 | 2 |
| #65292 | 2 |
| #3200 | 5 |