Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 4. #65410 | C2 | semidirect |
| 5. #65409 | C2 | semidirect |
| 6. #65012 | C2 | semidirect |
| 7. #65011 | C2 | semidirect |
| 8. #65010 | C2 | semidirect |
| 29. #3950 | C22 | semidirect |
| 30. #3949 | C22 | semidirect |
| 31. #3948 | C22 | semidirect |
| 32. #3948 | C22 | semidirect |
| 207. C5 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4072 | 2 |
| C2×#4070 | 2 |
| C5×#407 | 2 |
| #65410 | 2 |
| #65409 | 2 |
| #65012 | 2 |
| #65011 | 2 |
| #65010 | 2 |
| #3095 | 5 |