Confusion in solubility expressions in Henry's Law
Sander (Ref. 1) has compiled a useful review of Henry's law constants in water that includes an introduction showing notation and conversions.
There are two types of Henry's law constants:

Solubility constants convert from pressure to concentration in solution (solubility):

$$c=Hp$$

Volatility constants convert from concentration in solution (solubility) to pressure:

$$p=Kc$$
Usually it is possible to determine which constant is reported by inspecting the units.
References

R. Sander. Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos. Chem. Phys., 15, 4399–4981, 2015.
www.atmos-chem-phys.net/15/4399/2015/doi:10.5194/acp-15-4399-2015