Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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×SD32 | C2 | semidirect |
| 2. #65477 | C2 | semidirect |
| 4. C2×#3930 | C2 | semidirect |
| 5. #64784 | C2 | semidirect |
| 6. #64782 | C2 | semidirect |
| 7. #64724 | C2 | semidirect |
| 39. C5×C16 | D4 | semidirect |
| 41. C2×SD32 | 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×SD32 | 2 |
| #65477 | 2 |
| #65446 | 2 |
| C2×#3930 | 2 |
| #64784 | 2 |
| #64782 | 2 |
| #64724 | 2 |
| #2220 | 5 |