By using the GAP

we obtain that S10 contains 1 593 conjugate subgroup classes and 29 594 446 subgroups.The cyclic subgroups consist of 42 conjugate subgroup classes.The solvable subgroups consist of 1 418 conjugate subgroup classes.The nilpotent subgroups have 531 conjugate subgroup classes.The supersolvable subgroups have 923 conjugate subgroup classes.By the table information

we can read off the subgroup number of the specific order and the subgroup number of the particular conjugate subgroup class.