We construct a large halo K-giant sample by combining the positions, distances, radial velocities, and metallicities of over 13000 LAMOST DR5 halo K giants with the Gaia DR2 proper motions, which covers a Galactocentric distance range of 5-120kpc. Using a position-velocity clustering estimator (the 6Distance), we statistically quantify the presence of position-velocity substructure at high significance: K giants have more close pairs in position-velocity space than a smooth stellar halo. We find that the amount of substructure in the halo increases with increasing distance and metallicity. With a percolation algorithm named friends-of-friends to identify groups, we identify members belonging to Sagittarius (Sgr) Streams, Monoceros Ring, Virgo Overdensity, Hercules-Aquila Cloud, Orphan Streams, and other unknown substructures and find that the Sgr streams account for a large part of grouped stars beyond 20kpc and enhance the increase of substructure with distance and metallicity. For the first time, we identify spectroscopic members of Monoceros Ring in the southern and northern Galactic hemispheres, which presents a rotation of about 185km/s and a mean metallicity of -0.66dex.

Cone search capability for table J/ApJ/880/65/groups (Known (Table 3) and unknown (Table 4) substructures)

Cone search capability for table J/ApJ/880/65/table5 (Group member catalog in groups with five or more members)