Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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. C22×C5×C16 | C2 | semidirect |
| 2. #65404 | C2 | semidirect |
| 3. C2×D80 | C2 | semidirect |
| 4. #64729 | C2 | semidirect |
| 5. #64724 | C2 | semidirect |
| 28. C5×C16 | D4 | semidirect |
| 30. C22×C16 | D5 | semidirect |
| 58. C22×C5 | D16 | semidirect |
| 79. C16 | C22⋊D5 | semidirect |
| 98. C5 | #2215 | semidirect |
| 104. C22 | D80 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C16 | 2 |
| #65404 | 2 |
| C2×D80 | 2 |
| #64729 | 2 |
| #64724 | 2 |
| #2215 | 5 |