Question: How to generate a polynomial corresponding to a solvable Galois group of order 60?

Of course, we know the A5 of 60 order is an unsolvable group, but as the wiki here, There are also some solvable groups in the same 60 order. Similarly, although map(IsSolubleNumber, [60, 120, 168, 180]) will give false, there are some solvable groups in orders 60, 120, order 168, and order 180. But how to find these corresponding solvable polynomials by maple? I tried to generate them using random polynomials like this:

    do poly := randpoly(x, degree = rand(6 .. 8)()); until irreduc(poly);
    G := GaloisGroup(poly, x);
until IsSoluble(G) and is(GroupOrder(G) in {60, 120, 168, 180});
galois(poly, x);

But I didn't get any result even after one night..

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