  We investigate Yang-Mills theories with arbitrary gauge group on $R^3\times
S^1$, whose symmetry is spontaneously broken by the Wilson loop. We show that
instantons are made of fundamental magnetic monopoles, each of which has a
corresponding root in the extended Dynkin diagram. The number of constituent
magnetic monopoles for a single instanton is the dual Coxeter number of the
gauge group, which also accounts for the number of instanton zero modes. In
addition, we show that there exists a novel type of the $S^1$ coordinate
dependent magnetic monopole solutions in $G_2,F_4,E_8$.
