..."verbs that behave like бить"...
... вить лить пить шить and prefixed forms ...and verbs that behave like мыть (выть крыть ныть рыть) and prefixed forms. Пасть => красть класть.

More of the 'а' verbs that mutate throughout the present tense: писать искать резать шептать махать.

искать махать have third type of mutation, velar (first two above are dental and labial).

г => ж
к => ч
х => ш
ск => щ

This mutation is rare compared to the dental and labial mutation. Also, the velar mutation is different than the following change, but it is easy to confuse the different types of changes:
ке => че
ге => же