BQNC and Abelian Hidden Subgroup Problem

Question

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?