Analyzing directed interactions within brain networks of high spatial resolution is always associated with a limited interpretability due to the high amount of possible connections. Here, module detection algorithms have proven to helpfully subsume the information of the resulting networks for each proband. However, the between-subject comparison of clusters is not straightforward since identified modules are not matched to each other across different subjects. Tensor decomposition has successfully been applied for the detection of group-wide connectivity patterns. Yet, a thorough investigation of the effect of the involved analysis parameters and data properties on decomposition results has still been missing. In this study we filled this gap and found that - given appropriate parameter choices - tensor decomposition of functional connectivity data reveals meaningful, group-specific insights into the brain's information processing.