Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #65517 | C2 | semidirect |
| 4. C2×#3967 | C2 | semidirect |
| 5. #65379 | C2 | semidirect |
| 6. #65370 | C2 | semidirect |
| 7. #65340 | C2 | semidirect |
| 8. #65333 | C2 | semidirect |
| 9. C4×#689 | C2 | semidirect |
| 10. #65310 | C2 | semidirect |
| 94. C5×D4 | Q16 | semidirect |
| 207. D4 | #689 | semidirect |
| 225. C5 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Q8 | 2 |
| #65877 | 2 |
| #65517 | 2 |
| C2×#3967 | 2 |
| #65379 | 2 |
| #65370 | 2 |
| #65340 | 2 |
| #65333 | 2 |
| C4×#689 | 2 |
| #65310 | 2 |
| D4×#168 | 2 |
| #3299 | 5 |