As I understand, the assignment problem is in P as the Hungarian algorithm can solve it in polynomial time - O(n3). I also understand that the assignment problem is an integer linear programming problem, but the Wikipedia page states that this is NP-Hard. To me, this implies the assignment problem is in NP-Hard.
But surely the assignment problem can't be in both P and NP-Hard, otherwise P would equal NP? Does the Wikipedia page simply mean that the general algorithm for solving all ILP problems is NP-Hard? A few other sources state that ILP is NP-Hard so this is really confusing my understanding of complexity classes in general.