Rule of thumb: Minimum population size to calculate sample size for data that needs to be disaggregated

As a rule of thumb, what should be the minimum population size required to calculate a reliable sample size for a survey, given that the survey responses need to be disaggregated by various demographic groups (race, gender, age, zip codes, etc.)? Also, does the minimum size of a specific demographic group within the population matter when calculating the sample size, assuming the overall population size is above the threshold?

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