Some understanding about how matter is put together came with the discovery of the electron, proton, and neutron - - three subatomic particles that make up all matter of everyday perception.  In the early 1900s, a particle outside the atom, the photon, was verified by experimental evidence.  Two other particles were verified in the 1930s, the neutrino (“little neutral one”) and the positron (a positively charged electron, later realized to be the antiparticle of the electron).  By the mid-1930s a total of six such particles were known.  Since that time, high-energy accelerator experiments have made it possible to collide particles with great violence, probing the inner parts of atoms and how they are put together.  A multitude of subatomic particles is now known to exist.

Is there a way to organize or categorize all of these subatomic particles, similiar to the way the periodic table organizes the elements to help explain the structure of matter?

Yes.

All of matter consists of two types of fundamental particles, leptons and quarks. The word "fundamental" is key here. By fundamental particles we mean particles that are simple and structureless - - not having any internal components.

Leptons are a group of six fundamental particles that exist independently. The group includes the familiar electron, the muon (an overweight relative of the electron), and the tau (an even more massive version of the electron). In addition, there are three distinct neutrinos - - one associated with each of the charged leptons. For each lepton there is a corresponding antiparticle, or antilepton, with the same mass but opposite electric charge. One example of where leptons play a role is in radioactive neutron decay, where an electron (beta particle) is emitted along with an anti-electron neutrino.

The quarks constitute the second group of fundamental particles. Again there are six; each fancifully identified by its flavor.  They are called up, down,  charm,  strange, top, bottom.  Each flavor carries a fractional charge that is either – 1/3 or + 2/3 of the charge on the proton.  Antiquarks have equal but opposite charges. The quarks are the true building blocks of matter since they make up the hadrons.

Hadrons are a group of composite particles with an internal structure, so they are not fundamental particles.  There are two subgroups of hadrons: (1) the mesons and (2) the baryons.  Hundreds of short-lived hadrons have been identified that exist briefly after high-energy collisions.  Among the more stable are the baryons named protons and neutrons.

In order to explain how identical quarks could combine as observed,  each flavor was assigned three quantum states that are called color.  Each flavor can carry a charge of red, green, or blue.  Antiquarks carry a corresponding anticolor, for example, a red quark has an antiquark of the color cyan, a green quark has an antiquark of the color magenta, and a blue quark has an antiquark of the color yellow.  The idea of quark color was designed to follow the allowable combinations of quarks and antiquarks according to the exclusion principle.  Hadrons do not have a color charge, so the sum of the quark colors making up the hadron must result in a white hadron.  Baryons are made up of three quarks, so a combination of a red, a green and a blue quark would be acceptable, since this would result in a white baryon.  Mesons are made up of a quark and an antiquark so a combination of a blue quark and a yellow antiquark would be acceptable since this would result in a white meson.

The quark model holds that all matter is made from combinations of six quarks, six leptons, and their antiparticles.   The story of subnuclear elementary particles is by no means complete.  For example there are reports of the discovery of a pentaquark - - a combination of a baryon and a meson. This is permissible in terms of the color theory above since the pentaquark would be "white".

In addition, there is no explanation for why quarks and leptons even exist. Nor is there an explanation for why they have the masses they possess. Finally, do the quarks and leptons themselves have a sub-structure?

Answers to these and more questions await further research.

Suggested further resources

The Standard Model of FUNDAMENTAL PARTICLES AND INTERACTIONS       [teaching chart], 1988-1999, THE Contemporary Physics Education Project,    distributed by Science Kit and Boreal Laboratories, www.sciencekit.com

See also: http://www.cpepweb.org/

http://particleadventure.org/particleadventure/

R. M. Barnett et al, The Charm of the Strange Quarks, 1st ed. (Springer-Verlag        New York, Inc, New York 2000)

"Evidence for 'Pentaquark' Particle Sets Theorists Re-joyce-ing,"
Science,Vol 301, p 153 (July 11, 2003).