Not very much actually. Finite simple groups are kind of like prime numbers: any finite group can be broken down into simple subgroups similar to how any natura

Not very much actually. Finite simple groups are kind of like prime numbers: any finite group can be broken down into simple subgroups similar to how any natural number can be broken down into a multiset of prime number factors. That's why the classification of finite simple groups is so important, it's essentially a classification of all finite groups. https://en.wikipedia.org/wiki/Composition_series#Uniqueness:_Jordan–Hölder_theorem https://en.wikipedia.org/wiki/Composition_series#Uniqueness:...