Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #65904 | C2 | semidirect |
| 4. #65455 | C2 | semidirect |
| 5. SD16×Dic5 | C2 | semidirect |
| 7. C4×#689 | C2 | semidirect |
| 8. #65140 | C2 | semidirect |
| 9. #65119 | C2 | semidirect |
| 10. #65057 | C2 | semidirect |
| 11. #65052 | C2 | semidirect |
| 215. C5 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66047 | 2 |
| #65904 | 2 |
| C5×#460 | 2 |
| #65455 | 2 |
| SD16×Dic5 | 2 |
| #65359 | 2 |
| C4×#689 | 2 |
| #65140 | 2 |
| #65119 | 2 |
| #65057 | 2 |
| #65052 | 2 |
| #3365 | 5 |