Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×D4×Dic5 | C2 | semidirect |
| 2. #65934 | C2 | semidirect |
| 4. #65507 | C2 | semidirect |
| 5. #65442 | C2 | semidirect |
| 6. #65441 | C2 | semidirect |
| 7. #65322 | C2 | semidirect |
| 8. #65052 | C2 | semidirect |
| 9. #65046 | C2 | semidirect |
| 10. #65010 | C2 | semidirect |
| 11. #65008 | C2 | semidirect |
| 17. #4082 | C22 | semidirect |
| 24. D4×Dic5 | C22 | semidirect |
| 29. #4036 | C22 | semidirect |
| 30. #4033 | C22 | semidirect |
| 36. #3964 | C22 | semidirect |
| 38. #3949 | C22 | semidirect |
| 39. #3948 | C22 | semidirect |
| 40. #3947 | C22 | semidirect |
| 41. #3946 | C22 | semidirect |
| 42. #3939 | C22 | semidirect |
| 253. C5 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic5 | 2 |
| #65934 | 2 |
| C5×#447 | 2 |
| #65507 | 2 |
| #65442 | 2 |
| #65441 | 2 |
| #65322 | 2 |
| #65052 | 2 |
| #65046 | 2 |
| #65010 | 2 |
| #65008 | 2 |
| #3114 | 5 |