Classification of finite minimal simple groups

Statement
Here is a list of all the finite minimal simple groups (up to isomorphism):


 * 1) The projective special linear group $$PSL(2,2^p)$$, where $$p$$ is a prime number.
 * 2) The projective special linear group $$PSL(2,3^p)$$, where $$p$$ is an odd prime.
 * 3) The projective special linear group $$PSL(2,p)$$, where $$p > 3$$ is a prime such that $$5 | p^2 + 1$$.
 * 4) The Suzuki group $$Sz(2^p) = {}^2B_2(2^p)$$, where $$p$$ is an odd prime.
 * 5) The projective special linear group $$PSL(3,3)$$.

Related facts

 * Classification of finite N-groups
 * Classification of finite simple groups