Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #66079 | C2 | semidirect |
| 3. C2×C5×#100 | C2 | semidirect |
| 4. #65504 | C2 | semidirect |
| 5. #65428 | C2 | semidirect |
| 6. #64780 | C2 | semidirect |
| 7. #64779 | C2 | semidirect |
| 12. C2×#687 | C4 | semidirect |
| 15. C2×#686 | C4 | semidirect |
| 65. C2×#100 | D5 | semidirect |
| 202. C5 | #1903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4078 | 2 |
| #66079 | 2 |
| C2×C5×#100 | 2 |
| #65504 | 2 |
| #65428 | 2 |
| #64780 | 2 |
| #64779 | 2 |
| #1903 | 5 |