  We revisit moduli stabilization on Calabi-Yau manifolds with a discrete
symmetry. Invariant fluxes allow for a truncation to a symmetric locus in
complex structure moduli space and hence drastically reduce the moduli
stabilization problem in its dimensionality. This makes them an ideal testing
ground for the tadpole conjecture. For a large class of fourfolds, we show that
an invariant flux with non-zero on-shell superpotential on the symmetric locus
necessarily stabilizes at least 60% of the complex structure moduli. In case
this invariant flux induces a relatively small tadpole, it is thus possible to
bypass the bound predicted by the tadpole conjecture at these special loci. As
an example, we discuss a Calabi-Yau hypersurface with $h^{3,1}=3878$ and show
that we can stabilize at least 4932 real moduli with a flux that induces
M2-charge $N_\text{flux} =3$.
