Does a normal breast have lumps? a large lump at center of breast, when cupped, is mammary gland tissue or tumor?

See below: A normal breast should not have any clear lump or mass, provided you feel for it by using the flat part of your hand/fingers. Some women have 'lumpy'' breast, often due to fibrocyctic changes which are fairly common in otherwise healthy breasts. If you can feel any lumps in your breast, you must seek a medical examination by a health care professional who can do clinical breast examination for you.