Emergency services were called to the incident near to the exit for the B600 at Somercotes on Saturday, April 23.
One of three people who died in the crash has now been named as Kudakwashe Mdianyama, who was a passenger in the silver Ford Focus when it left the road and collided with a tree at around 2.15am.
The 23-year-old, who was from Coventry, died at the scene of the single-car collision.
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Two other women, both aged 21, have not been formerly identified, however, their families are aware and are being supported by specially trained officers, Derbyshire police said.
A second man remains in a serious but stable condition at hospital following the incident, while a third woman injured in the crash has now left hospital and is recovering at home.
Officers continue to make enquiries into the circumstances of the collision and remain keen to hear from anyone who may have witnessed the crash or noticed the vehicle travelling on the M1 southbound shortly before the incident.
Police are also appealing to for anyone with dashcam or CCTV footage which could help their enquiries to get in touch.
If you have any information which you think could help, please contact Derbyshire Constabulary quoting reference 22*0229425.
You can also anonymously contact the independent charity Crimestoppers, on 0800 555 111, or by visiting the CrimeStoppers website.