Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. #64984 | C2 | semidirect |
| 4. C4×#672 | C2 | semidirect |
| 26. #672 | D4 | semidirect |
| 29. #493 | D5 | semidirect |
| 57. C4×C5 | D16 | semidirect |
| 88. C5 | #2246 | semidirect |
| 94. 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 |
| #64984 | 2 |
| C4×#672 | 2 |
| #2246 | 5 |