Old exam problems on Sylow theory

The following problems from previous years use Sylow theory, which we have not covered, so these problems can be ignored if you use these old exams for revision/exam practice.

2022: 1a
2020: 3
2018: 2a
2017: 2b
2014: 3c
2013: 3
2012: 1b, 1c, 1d
2011: 2b, 2c
2010: 2
2009: 1b, 1c
2006: 1c, 4
2004: 1