Context :

Aims : If the concordance \Lambda CDM model is a true description of the universe , it should also properly predict the properties and structure of dark matter haloes , where galaxies are born .
Using N-body simulations with a broad scale of mass and spatial resolution , we study the structure of dark matter haloes , the distribution of masses and the spatial distribution of subhaloes within the main haloes .

Methods : We carry out three \Lambda CDM simulations with different resolutions using the AMIGA code .
Dark matter haloes are identified using an algorithm that is based on the adaptive grid structure of the simulation code .
The haloes we find encompass the mass scales from 10 ^ { 8 } \mathrm { M } _ { \sun } to 10 ^ { 15 } \mathrm { M } _ { \sun } .

Results : We find that if we have to study the halo structure ( search for subhaloes ) , the haloes have to contain at least 10 ^ { 4 } particles .
For such haloes , where we can resolve substructure , we determined the subhalo mass function and found that it is close to a power law with the slope -0.9 ( at present time ) , consistent with previous studies .
This slope depends slightly on the redshift and it is approximately the same for main haloes .
The subhalo mass fraction ( M _ { \mbox { \scriptsize subH } } / M _ { \mbox { \scriptsize MH } } ) is between 0.08 and 0.2 , increasing slightly with redshift and with the mass of the main halo .
Its distribution is approximated using the Weibull distribution at different epochs .
The mean values of subhalo mass are independent of the main halo mass .
The spatial density of subhaloes , scaled to the virial radius of the main halo ( r _ { \mbox { \scriptsize vir } } ) , is independent of redshift and follows the r ^ { 1 / 3 } rule .

Conclusions :