Relative equilibria in dynamical systems on Lie groups (Lie群上の力学系における相対的平衡状態) In a dynamical system with symmetry, a solution curve or its initial point is called a relative equilibrium if the solution is also the orbit of a one-parameter subgroup of the symmetry group. Relative equilibria occur in various dynamical systems with symmetry and are closely related to the geometric structure of each dynamical system. It is already known that the system is in relative equilibrium if and only if the initial point is a critical point of the function called the augmented potential. However, the dynamical meanings of the augmented potential are still worth understanding deeply. This paper deals with simple Lagrangian systems with symmetry on Lie groups, in which each symmetry group is a subgroup of the configuration Lie group. For these systems, necessary and sufficient conditions for relative equilibria are given. These conditions can be viewed as an extension of the Lie-algebraic condition that Hern\'{a}ndez-Gardu\~{n}o {\it et al.} gave in the case that the symmetry group coincides with the configuration space. It is also shown that the Euler-Lagrange equations are written out explicitly by using the augmented potential. The expression allows of an interpretation of the augmented potential, and further, provides the conditions for relative equilibria in terms of the Euler-Lagrange equations.