Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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. C5×#493 | C2 | semidirect |
| 2. C2×#3958 | C2 | semidirect |
| 3. C4×D40 | C2 | semidirect |
| 4. #64782 | C2 | semidirect |
| 5. C4⋊#672 | C2 | semidirect |
| 31. D40 | D4 | semidirect |
| 34. #493 | D5 | semidirect |
| 72. C4×C5 | D16 | semidirect |
| 113. C5 | #2206 | semidirect |
| 123. C4 | #3958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#493 | 2 |
| C2×#3958 | 2 |
| C4×D40 | 2 |
| #64782 | 2 |
| C4⋊#672 | 2 |
| #2206 | 5 |