Mathematics
The Concept of a Group and Its Subgroups
Quick fact
The order of a subgroup always divides the order of the group, a result known as Lagrange's theorem—a simple yet powerful constraint on the possible subgroups of any finite group.
Why this is interesting
Imagine a set of symmetries that can be combined, yet within that set there are smaller collections that behave just as nicely. What makes these subsets so special?