Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. #66055 | C2 | semidirect |
| 3. C5×#461 | C2 | semidirect |
| 4. #65464 | C2 | semidirect |
| 5. #65452 | C2 | semidirect |
| 6. #65374 | C2 | semidirect |
| 7. C4×#687 | C2 | semidirect |
| 8. #65137 | C2 | semidirect |
| 9. #65119 | C2 | semidirect |
| 10. #65107 | C2 | semidirect |
| 11. #65077 | C2 | semidirect |
| 83. #461 | D5 | semidirect |
| 114. Dic10 | SD16 | semidirect |
| 117. #168 | #41 | semidirect |
| 234. C5 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66055 | 2 |
| #65887 | 2 |
| C5×#461 | 2 |
| #65464 | 2 |
| #65452 | 2 |
| #65374 | 2 |
| C4×#687 | 2 |
| #65137 | 2 |
| #65119 | 2 |
| #65107 | 2 |
| #65077 | 2 |
| #3392 | 5 |