Zassenhaus lemma
In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Zassenhaus, is a technical result on the lattice of subgroups of a group or the lattice of submodules of a module, or more generally for any modular lattice. This can be generalized to the case of a group with operators ( G , Ω ) {\displaystyle (G,\Omega )} with stable subgroups A {\displaystyle A} and C {\displaystyle C} , the above statement being the case of Ω = G {\displaystyle \Omega =G} acting on itself by conjugation.