In particle physics, an elementary particle or fundamental particle is a particle not known to have any substructure, thus it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made. In the Standard Model of particle physics, the elementary particles include the fundamental fermions (including quarks, leptons, and their antiparticles), and the fundamental bosons (including gauge bosons and the Higgs boson). Although elementary particles are not made up of smaller particles, some of them may change to lighter particles (according to specific rules).
The elementary fermions (matter particles with half integer spin) are:
Quarks: up, down, charm, strange, top, bottom.
Leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino.
The elementary bosons (force carrying particles with integer spin ) are:
Gluon, W and Z, photon.
In what you said, the electron is a fundamental particle but the neutron and proton are not. The proton is composed of two up quarks and one down quark. The neutron has one up quark and two down quarks.
Here are some links that will clear some of the basic questions about quarks (not to write a to long of an answer)