# congruence lattice

## Which lattices occur as intervals in subgroup lattices of finite groups? ★★★★

Author(s):

**Conjecture**

There exists a finite lattice that is not an interval in the subgroup lattice of a finite group.

Keywords: congruence lattice; finite groups

## Finite Lattice Representation Problem ★★★★

Author(s):

**Conjecture**

There exists a finite lattice which is not the congruence lattice of a finite algebra.

Keywords: congruence lattice; finite algebra