Classification of groups of order four times a prime congruent to 1 modulo 4

Statement
Suppose $$p$$ is an odd prime that is congruent to 1 modulo 4, i.e., 4 divides $$p - 1$$.

Then, there are five isomorphism classes of groups of order $$4p$$, as detailed below:

General version

 * Classification of groups of order a product of a prime-square and another prime

Similar classifications

 * Classification of groups of order four times a prime congruent to 3 modulo four
 * Classification of groups of order 12
 * Classification of groups of prime-square order
 * Classification of groups of prime-cube order