Minimum sample for what purpose? (I guess minimum sample is zero; do you have a maximum level of uncertainty that you are will to have). Also, are you only interested in that sample of 458? Usually in education you would also be interested in how other similar groups (e.g., the cohort the next year) would perform.
One way would be to:
(1) Define your question
(2) Develop the most appropriate method to answer your research question
(3) Specify the minimum size of the effect/ difference between groups you wish to be able to detect
(4) Determine the level of statistical significance you wish for your test (p < 0.05 is common)
(5) Determine the level of statistical power you wish your test to have (80% or 90% power is normal, less than 60% would be of very little use)
(6) Use all of the above to carry out a power calculation to determine the required minimum sample size to meet all of the above. (There are online statistical power calculators and resources, for example: https://stats.oarc.ucla.edu/other/gpower/)
If you are not too sure what these steps involve I would take each one in turn, and speak to your PhD supervisor and/ or read up on each step.
Or you could plug lots of assumptions into a sample size calculator (many such sample size calculators are online), but you still need to think about all of the above.
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