The selling price of a refrigerator, is $583.20. If the markup is 20% of the dealers cost, what is the dealers cost of the refrigerator?

Let the dealer's cost be x.

The markup is 20% of the dealer's cost, which is 0.2x.
The selling price of the refrigerator is the sum of the dealer's cost and the markup, so it is x + 0.2x = 1.2x.
Given that the selling price is $583.20, we have 1.2x = $583.20.
Dividing both sides of the equation by 1.2, we have x = $583.20 / 1.2 = $486.
Therefore, the dealer's cost of the refrigerator is $486. Answer: \boxed{486}.