Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
| 3. C2×#3930 | C2 | semidirect |
| 4. C22⋊#672 | C2 | semidirect |
| 5. #64727 | C2 | semidirect |
| 6. #64721 | C2 | semidirect |
| 7. C16×Dic5 | C2 | semidirect |
| 38. C5×C16 | D4 | semidirect |
| 42. C2×M32 | D5 | semidirect |
| 90. Dic5 | M32 | semidirect |
| 109. C16 | C22⋊D5 | semidirect |
| 132. C5 | #2169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×M32 | 2 |
| C8×C22⋊D5 | 2 |
| C2×#3930 | 2 |
| C22⋊#672 | 2 |
| #64727 | 2 |
| #64721 | 2 |
| C16×Dic5 | 2 |
| #2169 | 5 |