A paratopological group G is saturated if the in- verse U−1 of each non-empty set U ½ G has non-empty interior. It is shown that a [first-countable] paratopological group H is a closed subgroup of a saturated (totally bounded) [abelian] paratopological group if and only if H admits a continuous bijective homomorphism onto a (totally bounded) [abelian] topological group G [such that for each neighborhood U ½ H of the unit e there is a closed subset F ½ G with e 2 h−1(F) ½ U]. As an application we construct a paratopological group whose character exceeds its ¼-weight as well as the character of its group reflexion. Also we present several ex- amples of (para)topological groups which are subgroups of totally bounded paratopological groups but fail to be subgroups of regular totally bounded paratopological groups.