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Group fairness metrics are an established way of assessing the fairness of prediction-based decision-making systems. However, these metrics are still insufficiently linked to philosophical theories, and their moral meaning is often unclear. In this paper, we propose a comprehensive framework for group fairness metrics, which links them to more theories of distributive justice. The different group fairness metrics differ in their choices about how to measure the benefit or harm of a decision for the affected individuals, and what moral claims to benefits are assumed. Our unifying framework reveals the normative choices associated with standard group fairness metrics and allows an interpretation of their moral substance. In addition, this broader view provides a structure for the expansion of standard fairness metrics that we find in the literature. This expansion allows addressing several criticisms of standard group fairness metrics, specifically: (1) they are parity-based, i.e., they demand some form of equality between groups, which may sometimes be detrimental to marginalized groups; (2) they only compare decisions across groups but not the resulting consequences for these groups; and (3) the full breadth of the distributive justice literature is not sufficiently represented.