  We extend the construction of the relativistic Toda chains as integrable
systems on the Poisson submanifolds in Lie groups beyond the case of A-series.
For the simply-laced case this is just a direct generalization of the
well-known relativistic Toda chains, and we construct explicitly the set of the
Ad-invariant integrals of motion on symplectic leaves, which can be described
by the Poisson quivers being just the blown up Dynkin diagrams. We also
demonstrate how to get the set of "minimal" integrals of motion, using the
co-multiplication rules for the corresponding Lie algebras. In the non
simply-laced case the corresponding Bogoyavlensky-Coxeter-Toda systems are
constructed using the Fock-Goncharov folding of the corresponding Poisson
submanifolds. We discuss also how this procedure can be extended for the affine
case beyond A-series, and consider explicitly an example from the affine
D-series.
