How are materials, textures and material groups associated?

For an object of type mesh how can we fins all the vertexes that materials are associated with and how can we find the textures that are linked to those materials? A different question, how many different groups do we have in Blender? For what i can see we have vertex groups used by animation; material indexes used to associate different materials to a mesh; parent/child groups; and theres a new ‘add to group’ button in the Objects and Links panel. Are there any more kinds of grouping?