Can someone tell me which data structure supports insert/delete/maximum operation in O(1)?
@KennyTM's comment points out an important missing detail - insert where, and delete from where. So I am going to assume that you always want to insert and delete only from one end like a stack.
Insertion (push) and Delete (pop) are O(1).
To get Max in O(1), use an additional stack to record the current max which corresponds to the main stack.