A subalgebra pair of semisimple complex algebras B ⊆ A with inclusion matrix M is depth two iff MM t M ≤ nM for some positive integer n and all corresponding entries. If A and B are the group algebras of finite group-subgroup pair H < G, the induction-restriction table equals M and S = MM t satisfies S 2 ≤ nS iff the subgroup H is depth three in G; similarly depth n > 3 by successive right multiplications of this inequality with alternately M and M t . We show that a Frobenius complement in a Frobenius group is a nontrivial class of examples of depth three subgroups. A tower of Hopf algebras A ⊇ B ⊇ C is shown to be depth-3 if C ⊂ core(B); and this is also a necessary condition if A, B and C are group algebras.