Let $(G_i)_{i\in I}$ be a family of groups. A subgroup $H$ of the direct product $\prod_{i\in I}G_i$ is said to be a subdirect product (or subcartesian product) of $(G_i)_{i\in I}$ if $\pi_i(H)=G_i$ for each $i\in I$ where $\pi_i\colon\prod_{i\in I}G_i\to G_i$ is the $i$ th projection map.