Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C5×D4×Q8 | C2 | semidirect |
| 3. #65516 | C2 | semidirect |
| 4. #65514 | C2 | semidirect |
| 5. #65372 | C2 | semidirect |
| 6. #65370 | C2 | semidirect |
| 7. #65338 | C2 | semidirect |
| 8. #65334 | C2 | semidirect |
| 9. C4×#688 | C2 | semidirect |
| 10. #65310 | C2 | semidirect |
| 11. #65301 | C2 | semidirect |
| 78. D4×Q8 | D5 | semidirect |
| 230. C5 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Q8 | 2 |
| #65897 | 2 |
| #65516 | 2 |
| #65514 | 2 |
| #65372 | 2 |
| #65370 | 2 |
| #65338 | 2 |
| #65334 | 2 |
| C4×#688 | 2 |
| #65310 | 2 |
| #65301 | 2 |
| #3329 | 5 |