Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic understanding of subgroup's definition, and the inaccurate application of the relevant metarules. For the purposes of this study there has been used the Commognitive Theoretical Framework.