  The tadpole conjecture proposes that complex structure moduli stabilisation
by fluxes that have low tadpole charge can be realised only at special points
in moduli space, leading generically to (large) gauge symmetries. Here we
provide an exhaustive survey of the gauge symmetries arising in F-theory flux
compactifications on products of attractive $\mbox{K3}$ surfaces, with complex
structure moduli fully stabilised. We compute the minimal rank of the left-over
non-abelian gauge group for all flux configurations within the tadpole bound,
finding that it is always non-zero. It decreases in a roughly linear fashion
with the tadpole charge, reaching zero at charge 30. By working out possible
gauge algebras for different values of the tadpole, we find that all simple ADE
Lie algebras of rank $\le 18$ appear.
