Is there any software that is designed specifically for algebraic structures, that can do some of the basic constructions in algebra, like
Constructing the congruence lattice of a (finite) algebra, the lattices of sub-algebras, maximal sub-algebras, the sub-algebra generated by a set, quotients, ect.
Testing whether a set of term equations $E$ deduces another set of equations $E'$. Or finding a counter example, ect.
Basic constructions for (finite, commutative) rings, like the Jacobson radical ideal, or the nil-potent radical ideal, or testing whether a subring is integral.
Various constructions on groups, like the Jordon-Holder decomposition, the center, sylow subgroups, ect.