  We investigate the SU($N$) Hubbard model for the multi-component fermionic
optical lattice system, combining dynamical mean-field theory with the
continuous-time quantum Monte Carlo method. We obtain the finite temperature
phase diagrams with $N\le 6$ and find that low temperature properties depends
on the parity of the components. The magnetically ordered state competes with
the correlated metallic state in the system with the even number of components
$(N\ge 4)$, yielding the first-order phase transition. It is also clarified
that, in the odd-component system, the ordered state is realized at relatively
lower temperatures and the critical temperature is constant in the strong
coupling limit.
