How to generate all monoids of order 5?

Let's say that we have the set and we want to generate the 5x5 tables (matrices) of all operations $*:M\times M\to M$ that generates a structure of monoid (i.e. an associative binary operation with an identity element) on M.

More precise the relation must hold for all and there is some with .

How can we implement that efficiently?

I found in this article all 35 monoids of order 4 and I wonder how can matlab generate them and those of order 5 which are exactly 228. (http://oeis.org/A058129). See the article here (look at page 6): https://web.math.pmf.unizg.hr/glasnik/50.2/50(2)-08.pdf