Officers have circulated their photographs and descriptions in a bid to track down the men and women, who are wanted for offences including theft and fraud.
It is believed they may hold vital information about the crimes.
Two are convicted criminals who have absconded from prison.
Anyone with information on their whereabouts should call Derbyshire Constabulary on 101 or Crimestoppers on 0800 555111.
1. Prison absconder
Leroy Deriggs failed to return to Sudbury open prison after a period of day release on Thursday, December 26. The 43-year-old was serving a 27-month sentence for robbery, imposed in London, when he vanished. Photo: JPI Media
2. Prison absconder
Daniel Russell, 28, absonded from Sudbury open prison on Wednesday, December18. He was convicted at Bristol Crown Court in October 2014 and sentenced to 13 years and 10 months for robbery and aggravated burglary. He has the word 'Dan' tattooed on his left arm. Photo: JPI Media
3. Theft
This man is wanted for questioning over the use of a lost cash card for a number of transactions in Buxton on January 18. Photo: JPI Media
4. Theft
This woman is one of two women wanted over the theft of items from a shop on Chatsworth Road, Chesterfield, on November 29, 2019. Photo: JPI Media