I am working on a condensed matter research project and we have just been introduced to the idea of symmetry. My question is, in two dimensions, how do the 17 plane groups help simplify condensed matter theory problems. If a specific case is needed to narrow the responses than working within a square lattice of say the Heisenberg model of a ferromagnet/antiferromagnet. I can see how it might be used to identify degenerate ground states, but I don't have the experience or knowledge to see the greater value of symmetry. Any advice/pointers/insights would be greatly appreciated. Thanks in advance