Is the electron divisible or more broadly do we know if subatomic particles are composed of smaller component particles and if so is there really no smallest particle?

Answer 1

If everything goes to plan, that plan being the Standard Model, the three lepton flavors with their three corresponding neutrinos, the six quark flavors having three colors each, the six force carrier particles, the Higgs boson, and all of their corresponding, if applicable, antiparticles, will be the absolute smallest particles. So far, so good, as there is absolutely no evidence of anything smaller than these, and in fact, we've reached a point of experimental energy amounts where we can safely say that these are the smallest particles out there, assuming we're heading in the right direction with our Standard Model. If the Higgs boson doesn't end up being observed at the LHC, however, we're screwed.

To specifically answer your question, the electron, which is one of the lepton flavors, is one of the indivisible/smallest particles I was talking about.