Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×C5×M32 | C2 | semidirect |
| 2. #65405 | C2 | semidirect |
| 4. C2×#3932 | C2 | semidirect |
| 5. #64729 | C2 | semidirect |
| 6. #64724 | C2 | semidirect |
| 7. #64723 | C2 | semidirect |
| 40. C5×C16 | D4 | semidirect |
| 42. C2×M32 | D5 | semidirect |
| 109. C16 | C22⋊D5 | semidirect |
| 132. C5 | #2220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×M32 | 2 |
| #65405 | 2 |
| #65404 | 2 |
| C2×#3932 | 2 |
| #64729 | 2 |
| #64724 | 2 |
| #64723 | 2 |
| #2220 | 5 |