Spectroscopy in Hydrogen Atom?

This may be a little hard to understand, you might need to have a decent knowledge of spectroscopy and physics to understand this question because im not good at explaining it (not cause your stupid or anything)

A hydrogen atom, which consists of a single electron jumps from one energy level to the next depending on the photon it absorbs.

if the electron is on the first energy level, it can go to 2,3,4,5,6.., this is in the ultraviolet section in the spectra called Lyman; alpha, beta, gamma, delta, epsilon.

If the electron is on the 2nd energy level it can transfer to 3, 4, 5, 6..., This part of the spectra is in the visible section and its called Balmer; aplha, beta, gamma, delta.

If the electron is on the third energy level it can go to 4, 5, 6..., this causes absorption lines in the infrared part of the spectra and its known as Pachen; alpha, beta, gamma.

my question is, is that it? does it end at Pachen or is there more?

please explain.

thank you.