There are so many variables in this question that it's hard to respond.
{240.21(B)(1)}If you have a conductor to a subpanel less than 10'long, that conductor does not have to be protected at its ampacity. It can be 1/10 of the ampacity of the OCPD that feeds it.
{408.16}The subpanel, however cannot be protected by a larger OCPD than its rating, so it would have to be protected by a main breaker or a OCPD in the main panel if the sub's rated at less than the main panel's OCPD.