Conjugate subgroups · Qual Corpus

Let \(G\) be a group. Two subgroups \(H, K \leq G\) are conjugate if there exists \(g\in G\) such that \(gHg^{-1} = K\).

Conjugate subgroups have the same cardinality: if \(gHg^{-1} = K\), then \(h\mapsto ghg^{-1}\) is a bijection \(H\to K\).