It is shown that a stratified group \(\mathbb{M}\) with Lie algebra \({\mathcal M}= W_1\oplus W_2\oplus\cdots\oplus W_l\) is purely \(k\)-unrectifiable if and only if there do not exist \(k\)-dimensional Lie subalgebras contained in the first layer \(W_1\), and for two stratified groups \(\mathbb{M}\) and \(\mathbb{G}\) with Lie algebras \({\mathcal M}\) and \({\mathcal G}\), respectively, \(\mathbb{M}\) is purely \(\mathbb{G}\)-unrectifiable if and only if \({\mathcal M}\) does not contain any Lie subalgebra which is \(G\)-isomorphic to \({\mathcal G}\).