1. -ften, -sten and -stle. Common word spellings that (almost) always produce a silent < t >.
2. Fricative + < t > + consonant. There are other spellings where the < t > is not necessarily silent but can be silent in fast, connected speech. This can occur both within a word and between words.
Within a word: lastly, postman, coastguard, wristband
Between words: blurriest photos, aircraft problems, robust theory, weirdest coincidence
3. French loanwords. In some French loanwords, we try to keep something of the original pronunciation, and this includes keeping the original silent < t >: ballet, gourmet, rapport, ricochet, penchant.
4. 3 consonant sounds at the end of a word = middle 't' is silent: acts, ducts, students.