  We investigate the nature of the Mott-insulating phases of half-filled
2N-component fermionic cold atoms loaded into a one-dimensional optical
lattice. By means of conformal field theory techniques and large-scale DMRG
calculations, we show that the phase diagram strongly depends on the parity of
$N$. First, we single out charged, spin-singlet, degrees of freedom, that carry
a pseudo-spin ${\cal S}=N/2$ allowing to formulate a Haldane conjecture: for
attractive interactions, we establish the emergence of Haldane insulating
phases when $N$ is even, whereas a metallic behavior is found when $N$ is odd.
We point out that the $N=1,2$ cases do \emph{not} have the generic properties
of each family. The metallic phase for $N$ odd and larger than 1 has a
quasi-long range singlet pairing ordering with an interesting edge-state
structure. Moreover, the properties of the Haldane insulating phases with even
$N$ further depend on the parity of N/2. In this respect, within the low-energy
approach, we argue that the Haldane phases with N/2 even are not topologically
protected but equivalent to a topologically trivial insulating phase and thus
confirm the recent conjecture put forward by Pollmann {\it et al.} [Pollmann
{\it et al.}, arXiv:0909.4059 (2009)].
