Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
388 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. #65774 | C2 | semidirect |
| 3. #65758 | C2 | semidirect |
| 4. #65757 | C2 | semidirect |
| 5. #65709 | C2 | semidirect |
| 6. #65694 | C2 | semidirect |
| 7. D5⋊(C4⋊C8) | C2 | semidirect |
| 8. #65678 | C2 | semidirect |
| 89. C4×D5 | M16 | semidirect |
| 192. C5 | #2989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#711 | 2 |
| #65774 | 2 |
| #65758 | 2 |
| #65757 | 2 |
| #65709 | 2 |
| #65694 | 2 |
| D5⋊(C4⋊C8) | 2 |
| #65678 | 2 |
| #2989 | 5 |