A theorem similar to Lagrange’s one for infinite group

Question

My textbook Groups, Matrices, and Vector Spaces - A Group Theoretic Approach to Linear Algebra by James B. Carrell said that

It [Lagrange’s theorem] is undoubtedly the most frequently cited elementary result on finite groups.

I would like to ask if there is a theorem that extends the idea of Lagrange’s theorem to the case of infinite group. Thank you so much for your elaboration!

Answer 1

Here is @Wojowu's comment that answers my question. I post it here to remove this question from unanswered list. All credits are given to @Wojowu.

For any subgroup $H$ of a group $G$ we have $|G| = |H|\cdot|G/H|$, where we are using products of possibly infinite cardinals.