On the number of metrizable group topologies on countable groups

If a countable group $G$ admits a non-discrete metrizable group topology $\tau_0$, then in the group $G$, there are:
– Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are incomparable;
– Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are comparable.