Science and Education Publishing American Journal of Mathematical Analysis 2333-8431 3 2 2015 06 23 On the Construction of Families of type П1 Subfactors Each Containing a Middle Subfactors 44 46 EN Bahman Mashood Former lecturer at university of Saskatchewan, San Francisco/California Mahmood Khoshkam AJMA2015324 10.12691/ajma-3-2-4 2015 01 09 2015 04 07 2015 06 23 In this article we are going to construct a family of type П1 subfactors each containing a middle subfactor. As a result of the above construction we show that the set of the indices of hyperfinite irreducible subfactors contains the interval [37.0037,).