How are finite simple groups similar to prime numbers?

In group theory, finite simple groups are considered the fundamental building blocks of all finite groups, much like prime numbers serve as the multiplicative building blocks for all natural numbers.12

The similarity lies in the concept of decomposition:
* Decomposition: Just as every positive integer greater than 1 can be expressed as a unique product of prime numbers, many groups—specifically all finite groups—can be decomposed into simpler groups in an essentially unique way.12
* Indivisibility: Prime numbers are defined by their inability to be divided further by any positive integer other than 1 and themselves. Similarly, "simple" groups are so named because they cannot be decomposed into smaller, non-trivial normal subgroups, meaning they cannot be broken down further in the context of group structure.21

While these simple groups are the "atoms" of group theory, their internal structure can be quite complex, as demonstrated by the discovery of exotic groups like the "Monster".1