On the theoretical side, particle physics is quantum field theory. Relativistic quantum mechanics helps, which then needs special relativity and nonrelativistic quantum mechanics. Electrodynamics is probably useful to understand special relativity better. Nonrelativistic quantum mechanics relies on concepts introduced in classical mechanics (in particular, Hamilton/Lagrange formalism) and algebra and analysis.
On the experimental side, special relativity is absolutely necessary, if you want to understand the detectors some solid-state physics is necessary, electrodynamics for sure, maybe electronics depending on the level of detail.
I'm sure I forgot some points.