Category:Facts about groups of coprime order whose proof requires the assumption that one of them is solvable

This category lists facts whose statement involves a pair of groups of coprime order. The proof requires the assumption that at least one of the groups is solvable. Such facts are true because given two groups of coprime order, one of them is solvable, but the only known proof of this is using the odd-order theorem: any group of odd order is solvable. The odd-order theorem isn't considered elementary because its proof is rather involved, and requires a mix of techniques including character theory.