We describe the design and performance of a large magnetic trap for storage and cooling of atomic hydrogen (H). The trap operates in the vacuum space of a dilution refrigerator at a temperature of 1.5 K. Aiming at a large volume of the trap, we implemented the octupole configuration of linear currents (Ioffe bars) for the radial confinement, combined with two axial pinch coils and a 3 T solenoid for the cryogenic H dissociator. The octupole magnet consists of eight race-track segments, which are compressed toward each other with magnetic forces. This provides a mechanically stable and robust construction with a possibility of replacement or repair of each segment. A maximum trap depth of 0.54 K (0.8 T) was reached, corresponding to an effective volume of 0.5 l for hydrogen gas at 50 mK. This is an order of magnitude larger than ever used for trapping atoms.