How many lines of symmetry does a parallelogram have?

General parallelogram has no lines of symmetry.
Some specific types of parallelogram do. See below.
Rhombus is a special type of parallelogram and it has two lines of symmetry – its diagonals.
Rectangle, which is not a square, has two lines of symmetry – two lines going through the midpoints of opposite sides.
Square is a special type of parallelogram with four lines of symmetry – two diagonals and two lines going through the midpoints of opposite sides.