Torus package on a torus

Let $ G $ to be a nilpotent Lie group and $ H <J $ to be two closed subgroups such as
$$ G / H to G / J $$ is a bundle of fibers with fibers $ J / H $.

Assume that $ G / J = (S ^ 1) ^ m $ and $ J / H = (S ^ 1) ^ m $. Is the package trivial?