BQNC and Abelian Hidden Subgroup Problem

We know integer factorization is in $$BPP^{BQNC}$$ from Cleve and Watrous.

1. Is Abelian Hidden Subgroup Problem also in $$BPP^{BQNC}$$?

2. In particular is Discrete Logarithm in $$BQNC$$ or at least in $$BPP^{BQNC}$$ and is there any reference which explicitly relates Discrete Logarithm and $$BQNC$$?

If not what is it that makes integer factorization special?