One of the most impressive early results on the path the the full classification (in terms of being able to understand the statement of the result, if not the 2

One of the most impressive early results on the path the the full classification (in terms of being able to understand the statement of the result, if not the 250 pages of the proof) is that all non-Abelian groups of odd order are not simple. https://en.wikipedia.org/wiki/Feit%E2%80%93Thompson_theorem https://en.wikipedia.org/wiki/Feit%E2%80%93Thompson_theorem