Summary: Perhaps the strongest notion of truth-revealing in a cost sharing mechanism is group strategyproofness. However, matters are not so clear-cut on fairness, and many different, sometimes even conflicting, notions of fairness have been proposed which have relevance in different situations. We present a large class of group strategyproof cost sharing methods, for submodular cost functions, satisfying a wide range of fairness criteria, thereby allowing the service provider to choose a method that best satisfies the notion of fairness that is most relevant to its application. Our class includes the Dutta-Ray egalitarian method as a special case. It also includes a new cost sharing method, which we call the opportunity egalitarian method.