1. Carbonates: These minerals contain the carbonate anion (CO3)2-. Common examples include calcite (CaCO3), dolomite (CaMg(CO3)2), and siderite (FeCO3).

2. Sulfates: These minerals contain the sulfate anion (SO4)2-. Common examples include gypsum (CaSO4·2H2O), anhydrite (CaSO4), and barite (BaSO4).

3. Halides: These minerals contain a halide anion (F-, Cl-, Br-, or I-). Common examples include halite (NaCl), fluorite (CaF2), and sylvite (KCl).

It's important to note that this is a simplification. There are many other important groups of non-silicate minerals, such as oxides, sulfides, and phosphates. However, the carbonates, sulfates, and halides are among the most common and important groups.