Irregular verbs are eccentrics. They change their vowel but not in a manner we can identify as a pattern. In simple past, there are groups of verbs with the same main vowel.
logen, boten, hoben
The vowel must be stressed.
They look (and sound) as if they are from the same family, but in present tense they have nothing to do with each other.
lügen (to lie), bieten (to offer), heben (to lift)
Verbs in simple past with a stressed a: kamen, baten, stahlen
Present tense: kommen, bitten, stehlen.
Verbs in simple past with a stressed u: trugen, fuhren, einluden.
Present tense: tragen, fahren, einladen.
Some simple past verbs with the stress upon ie stem from present tense verbs with ei as the main vowel.
schrieben, stiegen, blieben
Present tense: schreiben, steigen, bleiben
So, to get to the past, we just need to interchange the letters.
However, other simple past verbs with ie stem from present tense verbs with different vowels.
schliefen, anriefen, hießen
Present tense: schlafen, anrufen (to call on the phone), heißen
When conjugated, they also differ from the verb-ending pattern as we know it. They create their own pattern. Here are two examples (bieten and bleiben).
ich bot blieb
du botest bliebst
er, sie, es bot blieb
ihr botet bliebt
wir, Sie, sie boten blieben
Be aware that this form of the past tense is often used in written language. In spoken language we create the past with the perfect tense combining haben or sein with the participle (gesungen, gegangen etc.)