Patterns for present tense verb conjugation

Question

This question also has an answer here (in Ukrainian):
Простий спосіб визначення дієвідміни: -уть (-ють) проти -ать (-ять)

I'm aware that there are four sets of present tense endings, each named by their third person plural. They are separated into two sets of iotified pairs. first conjugation (-уть, -ють) and second conjugation (-ать, -ять).

Are there any rules or generalizations about which verbs take first conjugation and which verbs take second conjugation? I understand that the non-iotified ending is used after a consonant and the iotified one after a vowel.

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Мені відомо, що існує чотири закінчення теперішнього часу, кожне з яких назване за третьою особою множини. Вони розділені на два набори йотованих пар: першої дієвідміни (-уть, -ють) та другої дієвідміни (-ать, -ять).

Чи існує яке-небудь правило або узагальнення, які дієслова відносять до першої дієвідміни і які дієслова відносять до другої дієвідміни? Я розумію, що нейотоване закінчення використовується після приголосного, а йотоване після голосної.

Answer 1

Are there any rules or generalizations about which verbs take first conjugation and which verbs take second conjugation?

Yes, but you need more than just an infinitive.

Caveat, your question specifically calls 1st and 2nd conjugation groups by its endings -уть/-ють and -ать/-ять, respectively. I believe this is how it is called in your textbook.
This answer also relies on observation about how the verbs conjugate in 3rd person plural.
I admit this looks like a dead loop, but I believe this is the most academic way how we define these conjugation groups. Also, this answer is useful if you know what form a verb takes in 1st person singular.

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This article has a great writeup, let me formalize it in most succinct manner:

Most verbs belong to the 1st conjugation group.

A verb belongs to the 2nd group if any of below is true:

1. its root ends with -и-, -і-, -ї- and also -жа-, -ча-, -ша-
   • and the end vowel drops in 1st person singular or 3rd person plural
2. verbs ending with -отіти
3. several verbs not belonging to rules listed above:
   • стоя-ти {to stand} (root ends with -я)
   • боя-тися {to be scared} (root ends with -я)
   • спа-ти {to sleep} (root ends with -а-, but not after ж/ч/ш)
   • біг-ти {to run} (root ends with consonant)

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Several examples to explain vowel drop in 1st person singular and 3rd person plural; I marked with underscore (_) the place where the vowel dropped:

• ба́чи-ти / ба́ч_-у / ба́ч_-ать — root ends with -и-, and it drops → 2nd group {to see}
• жи́-ти / жив-у́ / жив-у́ть — root ends with -и-, and it does not drop → 1st group {to live}
• сиді́-ти / сид_ж-у́ / сид_-я́ть — root ends with -і-, and it drops → 2nd group {to sit}
• білі́-ти / білі́-ю / білі́-ють — root ends with -і-, and it does not drop → 1st group {to whiten}
• крича́-ти / крич_-у́ / крич_-а́ть — root ends with -ча-, and -а- drops → 2nd group {to scream}
• постача́-ти / постача́-ю / постача́-ють — root ends with -ча-, and -а- does not drop → 1st group {to deliver}

This verb is tricky; it has two forms, one for 1st conjugation group and one for the 2nd. Note, they both have exactly equivalent meaning {to bubble}:

• бульк-оті́-ти / булькоч-у́ / бульк-отя́ть — root ends with -оті- → 2nd group
• бульк-ота́-ти / булькоч-у́ / булько́ч-уть — root ends with -ота- → 1nd group