Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. This theory could potentially be used for conceptualising complex living systems. In a previous study, we analysed collective behaviour in {\it Plecoglossus altivelis}. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of $\Phi$ values (i.e., group integrity). Other measures, such as mutual information, did not show such characteristics. In this study, we follow up on our previous findings and introduce two new factors. First, we define the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from $\Delta t =5/120$ s to $\Delta t =120/120$ s). The results showed that we succeeded in classifying fish school according to their group size in terms of the degree of group integrity, despite the small group size. The concrete classification includes the followership for a two-fish school, fission--fusion for a three-fish school, emergence of leadership for a four-fish school, and emergence of Boid-like behaviour for a five-fish school. These minute classifications have never been revealed before. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT analysis.