It must be answered in a form of example..
subsidiarity- fastfood chain like jollibee and mang inasal, their mother company is Jollibee Foods Corp.(JFC) and mang inasal is only a subsidiary/under to JFC.
Solidarity - Is like 2 company merge for their common interest. like, Green Bank and EastWest bank.
it is only my opinion..free to correct me..thanks!