The crash occurred close to the Roscoe Boulevard exit, near the side of the freeway at about 3:21 a.m.
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Witnesses told the California Highway Patrol the driver might have been racing, but authorities have not yet determined the cause of the collision.
Crews worked to clear the scene after the vehicle had gone down an embankment.
The driver has been identified as 39-year-old Arutyun Darakchyan.
Another person injured in the crash was transported to an area hospital in unknown condition.
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The far right lane and the southbound on-ramp to the 405 were closed but have since reopened. Traffic on the busy thoroughfare was snarled more than usual during the morning rush hour commute, with bumper-to-bumper traffic beginning around the 118 Freeway interchange.
An investigation is ongoing.