Let \(G\) be a Lie group acting smoothly on a manifold \(M\), and let \(\mathfrak g\) denote the corresponding Lie algebra of infinitesimal generators. The symmetry group of a closed submanifold \(S\subset M\) is the subgroup \(G_s=\{g\in S\mid g\cdot S=S\}\). A submanifold \(S\) is nonsingular if \(G_s\) acts freely on \(S\). A nonsingular submanifold is maximally symmetric if \(\dim G_s=\dim S\) and hence coincides with an orbit of its symmetry group \(S=G_s\cdot z_0\) for some \(z_i\in M\). According to É. Cartan a nonsingular submanifold is maximally symmetric iff all its differential invariants are constant. The aim of this article is to develop effective formulae for computation the values of the differential invariants of such a maximally symmetric orbit \(G_s\cdot z_0\) directly from the infinitesimal generators of its symmetry group, namely the symmetry subalgebra \(\mathfrak g_s\subset \mathfrak g\).