  For integers $k,t \geq 2$, and $1\leq r \leq t$ let $D_k^\times(r,t;n)$ be
the number of parts among all $k$-indivisible partitions of $n$ (i.e.,
partitions where all parts are not divisible by $k$) of $n$ that are congruent
to $r$ modulo $t$. Using Wright's circle method, we derive an asymptotic for
$D_k^\times(r,t;n)$ as $n \to \infty$ when $k,t$ are coprime. The main term of
this asymptotic does not depend on $r$, and so, in a weak asymptotic sense, the
parts are equidistributed among congruence classes. However, inspection of the
lower order terms indicates a bias towards different congruence classes modulo
$t$. This induces an ordering on the congruence classes modulo $t$, which we
call the $k$-indivisible ordering. We prove that for $k \geq
\frac{6(t^2-1)}{\pi^2}$ the $k$-indivisible ordering matches the natural
ordering. We also explore the properties of these orderings when $k <
\frac{6(t^2-1)}{\pi^2}$.
