Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×C5×Q16 | C2 | semidirect |
| 4. #64784 | C2 | semidirect |
| 6. #64709 | C2 | semidirect |
| 7. #64681 | C2 | semidirect |
| 15. #3960 | C4 | semidirect |
| 25. C5×Q16 | C2×C4 | semidirect |
| 37. #672 | C2×C4 | semidirect |
| 39. C4×Q16 | D5 | semidirect |
| 87. Q16 | C4×D5 | semidirect |
| 119. C5 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Q16 | 2 |
| C2×#3960 | 2 |
| C4×D40 | 2 |
| #64784 | 2 |
| #64711 | 2 |
| #64709 | 2 |
| #64681 | 2 |
| #2175 | 5 |