Cold collapse of a cluster composed of small identical clumps , each of which is in virial equilibrium , is considered .
Since the clumps have no relative motion with respect to each other initially , the cluster collapses by its gravity .
At the first collapse of the cluster , most of the clumps are destroyed , but some survive .
In order to find the condition for the clumps to survive , we made systematic study in two-parameter space : the number of the clumps N _ { c } and the size of the clump r _ { v } .
We obtained the condition , N _ { c } \gg 1 and n _ { k } \geq 1 , where n _ { k } is related to r _ { v } and the initial radius of the cluster R _ { ini } through the relation R _ { ini } / r _ { v } = 2 N _ { c } ^ { ( n _ { k } +5 ) / 6 } .
A simple analytic argument supports the numerical result .
This n _ { k } corresponds to the index of the power spectrum of the density fluctuation in the cosmological hierarchical clustering , and thus our result may suggest that in the systems smaller than 2 / ( \Omega h ^ { 2 } ) Mpc , the first violent collapse is strong enough to sweep away all substructures which exist before the collapse .