According to the 2010 census, the township has a total area of 37.17 square miles (96.3 km2), of which 37.14 square miles (96.2 km2) (or 99.92%) is land and 0.04 square miles (0.10 km2) (or 0.11%) is water.
- Greenville (the county seat) (west three-quarters)
(This list is based on USGS data and may include former settlements.)
The township contains these nine cemeteries: Hazel Dell, Hazel Dell, Montrose, Mount Auburn, Mount Gilead, Mount Moriah, Old City, Saint Lawrence Catholic and Smith Grove.
- Edw A Utlaut Memorial Heliport
- Greenville Airport
- Greenville Lake
- Greenville Correctional Institution