What did the Feit-Thompson theorem prove about finite simple groups?

The Feit-Thompson theorem, published in 1963 by mathematicians Walter Feit and John Griggs Thompson, proved a long-standing conjecture by William Burnside: every non-abelian (or noncommutative) finite simple group has an even number of elements.123

Because finite groups are composed of simple groups acting as "building blocks," this result provided a critical structural insight into the nature of all finite groups. By establishing that these groups must contain elements of order two (elements $x$ such that $x^2=1$), the theorem allowed mathematicians to analyze the structure of these groups more effectively.13

The proof was famously complex, spanning over 250 pages, and served as a major catalyst for the ambitious, decades-long collaborative effort to achieve a full classification of all finite simple groups. This landmark achievement reinforced the mathematical community's belief that such a classification was possible, eventually leading to the completion of the "Enormous Theorem" in the early 1980s.123