It depends on the type of parallelogram:
The classic generic-looking parallelogram, having no right angles, and having adjacent sides of unequal length, has no lines of symmetry (only point symmetry about the point of intersection of the diagonals).
Special types of parallelograms are as follows:
A square has 4 lines of symmetry: horizontal, vertical, and one containing each diagonal.
A non-square rhombus has two lines of symmetry: one containing each diagonal.
A non-square rectangle has two lines of symmetry: horizontal and vertical.
a rectangle has 2 axes of symmetry
It has 5 axes of symmetry
An isosceles triangle definitely has three axes of symmetry
A polygon need not have any axes of symmetry. It can have at most n axes where n is the number of sides that the polygon has.
4
There are infinitely many axes of symmetry in mathematics.
a rectangle has 2 axes of symmetry
It has 5 axes of symmetry
A square has 4 axes of symmetry.
A regular pentagon has five axes of symmetry.
An isosceles triangle definitely has three axes of symmetry
Not sure about a duodecagon, but a regular dodecagon has 12 axes of symmetry.
A polygon need not have any axes of symmetry. It can have at most n axes where n is the number of sides that the polygon has.
2 axes from angles to angles
a tetrahedron has 7 axis of symmetry
It has 1 line of symmetry
4