Inspired by [Witten's Wess-Zumino term arguments](https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CDAQFjAA&url=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2F0550321383900639&ei=nzJLUq6yJJHj4APVw4CgAg&usg=AFQjCNE5s9IxLawM7v6CmiS-NsuR_4Am1w&bvm=bv.53371865,d.dmg), I'm curious to know how one calculates homotopy classes more generally for coset spaces.  In the above example the coset is $G/H=(SU(3)_L\times SU(3)_R)/SU(3)_{\rm diag}\cong SU(3)$ and so the coset space is itself a group, but how does this extend to more general examples like say $G/H=SU(5)/(SU(3)\times SU(2)\times U(1))$?

What about the case where the groups are non-compact, say they're spacetime symmetry groups? For example, $G/H= ISO(4,1)/ISO(3,1)$ or $G/H=SO(4,2)/SO(3,1)$?