Following \textit{I. M. Gelfand} and \textit{V. A. Ponomarev} [Colloq. Math. Soc. János Bolyai 5, 163-237 (1972; Zbl 0294.15002)] a system \(S=(V;E_ 1,...,E_ r)\) of a finite-dimensional vector space V and of subspaces \(E_ 1,...,E_ r\) has defect \(\rho(S)=\sum \dim E_ i-2 \dim V.\) A system S is said to be decomposable if there exist subspaces \(P_ 1,...,P_ n\) such that V is the direct sum of the \(P_ i's\) and every \(E_ i\) is the direct sum of \(E_ i\cap P_ 1,...,E_ i\cap P_ n.\) An indecomposable system S with \(\rho(S)=0\) is called regular. Eventually, a subspace W of V, where V appears in a regular system S, is called invariant if the subsystem \(S_ W=(W;E_ 1\cap W,...,E_ r\cap W)\) has defect \(\rho(S_ W)=0.\) The author investigates modular lattices L which can be represented in the lattice of all subspaces of some vector space V. More precisely, if \(x_ 1,...,x_ r\) are generators of L, then L is considered to have a representation in a system S such that every \(x_ i\) is represented by the corresponding \(E_ i\). An element \(x\in L\) is said to be invariant if every representation into a regular system assigns to x an invariant subspace. Results: (1) Invariant elements form a sublattice of L. (2) If y and \(x\vee z\) are invariant and x,z are generators, then \((y\wedge x)\vee(y\wedge z)\) is also invariant. (3) There is a construction of the sublattice of invariant elements for the free modular lattice \(L=FM(4).\)