Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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. #66159 | C2 | semidirect |
| 3. C2×#4097 | C2 | semidirect |
| 4. #65529 | C2 | semidirect |
| 5. #65525 | C2 | semidirect |
| 6. #65409 | C2 | semidirect |
| 7. #64776 | C2 | semidirect |
| 249. C5 | #2009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#575 | 2 |
| #66159 | 2 |
| C2×#4097 | 2 |
| #65529 | 2 |
| #65525 | 2 |
| #65409 | 2 |
| #64776 | 2 |
| #2009 | 5 |