Black hole microstates, considered collectively as an ensemble, are believed to exhibit properties of quantum chaos, and in particular eigenvalue repulsion. The extent of the repulsion characterises how ‘strong’ the chaos is. In this talk, I will focus on the example of the supersymmetric black-hole microstates of the D1-D5(-P) system. I will explain how the ability to find ‘strong’ or ‘weak’ chaos is related to how the microstates are organised into some particular subgroups. Finally, I will show how this organisational problem translates into a statistical-mechanics problem.