Un-orderly refers to anything that is chaotic, untidy, and disorganized. The antonyms for the word "un-orderly" are organized, methodical, and neat. If something is organized, it is arranged in a systematic and logical manner, making it easy to locate and operate. Methodical, on the other hand, refers to anything that is careful, planned, and detailed. It suggests that something has been arranged systematically with a specific purpose in mind. Neat, the third antonym, refers to anything that is tidy and well-groomed. It suggests that something has been cared for and tended to, making it presentable and easy to use. Overall, these three antonyms represent a sense of order and structure that is diametrically opposed to "un-orderly.