Classification of Hamiltonian non-abelian Painlevé type systems

All Hamiltonian non-abelian Painlevé systems of ${\mathrm{P}}_1-{\mathrm{P}}_6$ type with constant coefficients are found. For ${\mathrm{P}}_1-{\mathrm{P}}_5$ systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new ${\mathrm{P}}_3^{\mathrm{\prime }}$ and ${\mathrm{P}}_5$ systems thus obtained, we find isomonodromic Lax pairs for them.