Over the last 70 years there has been a major shift in the threats to global peace. While the 1950's and 1960's were characterised by the cold war and the arms race, many security threats are now characterised by group behaviours that are disruptive, subversive or extreme. In many cases such groups are loosely and chaotically organised, but their ideals are sociologically and psychologically embedded in group members to the extent that the group represents a major threat. As a result, insights into how human groups form, emerge and change are critical, but surprisingly limited insights into the mutability of human groups exist. In this paper we argue that important clues to understand the mutability of groups come from examining the evolutionary origins of human behaviour. In particular, groups have been instrumental in human evolution, used as a basis to derive survival advantage, leaving all humans with a basic disposition to navigate the world through social networking and managing their presence in a group. From this analysis we present five critical features of social groups that govern mutability, relating to social norms, individual standing, status rivalry, ingroup bias and cooperation. We argue that understanding how these five dimensions interact and evolve can provide new insights into group mutation and evolution. Importantly, these features lend themselves to digital modeling. Therefore computational simulation can support generative exploration of groups and the discovery of latent factors, relevant to both internal group and external group modelling. Finally we consider the role of online social media in relation to understanding the mutability of groups. This can play an active role in supporting collective behaviour, and analysis of social media in the context of the five dimensions of group mutability provides a fresh basis to interpret the forces affecting groups.