Consider the simple cubic lattice. There are symmetry operations which preserve the lattice symmetry such as translations and rotations around certain axes. There are also symmetry operations that do not preserve the lattice such as a rotation of 1° around an axis that cuts two points of the same side of the cube.
For this example this is quite obvious, however it can become more complicated for more complicated lattices. My question is whether there is an automatable way to check this for arbitrary chains of operations. I am looking for something like a program/tool that allows me to input these chains of operations (for example in the form of matrices) and tests if this chain preserves the lattice (i.e. is compatible with the lattice).