  We investigate ordered phases (s-wave superconducting (SC), antiferromagnetic
(AF) and charge ordered (CO) phases) of the half-filled Holstein-Hubbard model
using the dynamical mean-field theory in combination with a continuous time
quantum Monte Carlo impurity solver. We particularly focus on the parameter
regime where the electron-electron Coulomb interaction and the phonon mediated
retarded attractive interaction are both comparable to the bare electron
bandwidth to understand the interplay of these interactions and the retardation
effects due to finite phonon frequency \omega_0. Results for the transition
temperatures for SC and AF as a function of the effective interaction
U_eff(=U-\lambda with U the Coulomb repulsion and \lambda the phonon-mediated
attraction) show deviations from the the corresponding results in the
anti-adiabatic limit. These are analyzed by comparing with an effective static
model in the polaron picture. We also determine the phase diagram around
U_eff=0 at low, but nonzero temperatures to show that paramagnetic phases
appear between AF and CO when U and \lambda are small or large, while AF and CO
directly compete with each other at moderate U and \lambda.
