Some 15 years ago I was working on machine recognition of Spanish sentences, and I figured out several patterns of irregular verb conjugations, which I used to reduce the cases I had to test. I do not have the documents so probably I will miss many of the cases.
Some irregularities are just phonetic assimilation and dissimilation such as huir --> huyendo (instead of literal regularity *huiendo). Any verb following the same phonetical pattern will behave the same so this should not be regarded as an irregularity but just as a phonetical rule (the same as c/qu in acercar --> acerque). My code recognized this.
Some irregularities have origin in archaic pronuntiation rules. The most common are the e/ie and o/ue alternations such as querer-->quiere. Disregarding this alternation querer is otherwise a completely regular verb, so in my system I stored with a different symbol (arbitrarily I used ê: quêr-er) and then I used an algorithm to know if it should be ie (when the stress falled in ê) or e (when the stress felt in other syllable).
While not an orthographic-phonetic rule as c/qu or z/c there are a few verbs that have a similar behavior, such as parecer. The final c in the root (pronunced [T] in Spain or [s] in Latin-America) will change into zc before rear vowels. It is an irregularity as it affects both writting and pronunciation, but from a machine point of view it was handled just as an orthographic issue and then the conjugation was regular.
The next analisys where verbs such as tener. (well, after handling the e/ie issue) The have an odd past tense. It is such as the simple indicative past tense (preterito indefinido del indicativo) and some subjunctive tenses used another root (tuv-) and the simple past had different conjugation theme: (tuv-e, -iste, -o, compare with regular am-é, -aste, -ó and com-í, -iste, -ió). That theme is also present in caber and estar, among other. (Their subjunctives use the irregular root with regular theme.) Note, however, that most verbs in this cathegory have further irregularities.
Which leads me to caber. Verb caber has a consistent irregularity when the declination has a rear vowel: the whole root changes from cab- to quep-, so present indicative is quepo, cabes, cabe, cabemos, cabeis, caben; and present subjunctive is quepa, quepas, quepa, quepamos, quepais, quepan. Compare with parecer: parezco, pareces, parece, parecemos, pareceis, parecen and parezca, parezcas, parezca, etc. The same rule to know the c/zc alternace will be used to alternate the whole root. So, caber has three roots: the regular cab-, and the irregular cup- (past thenses) and quep- (present tenses before rear vowels).
Now, there are the complete irregular verbs such as the monosyllabic (ir, ser, estar) and other cases that would be handled with multiple roots, additional conjugation themes, and exceptions.