An engine system, comprising: a cylinder block and a cylinder head configured to form a cylinder; a piston reciprocatably accommodated in the cylinder; a main combustion chamber defined by the cylinder block, the cylinder head, and the piston; a subchamber that is separated from the main combustion chamber by a partition, and configured to communicate with the main combustion chamber through a communicating hole formed in the partition; an injector configured to inject fuel into the main combustion chamber; a main spark plug configured to perform main ignition for igniting a mixture gas inside the main combustion chamber; a subspark plug configured to perform subignition for igniting the mixture gas inside the subchamber; and a controller that is electrically connected to, and configured to output an electric signal for control to, the injector, the main spark plug, and the subspark plug, wherein in a low-load range (A2H) where an engine load is below a given reference load (Tqs) or when an engine load is below a given reference load (Tqs), the controller is configured to: control the main spark plug and the subspark plug so that the subignition is performed after the main ignition; and in a high-speed range where an engine speed is above a given reference engine speed, retard the timing of the subignition compared with a low-speed range where the engine speed is below the reference engine speed, or if an engine speed is above a given reference engine speed, retard the timing of the subignition compared with the timing of the subignition when the engine speed is below the reference engine speed, wherein the controller is configured to suspend the main ignition and subignition in a low-speed low-load range where the engine speed is below a second given reference engine speed below the reference engine speed and the engine load is below a second given reference load higher than the reference load (Tqs), or when the engine speed is below a second given reference engine speed below the reference engine speed and the engine load is below a second given reference load higher than the reference load (Tqs). a cylinder block and a cylinder head configured to form a cylinder; a piston reciprocatably accommodated in the cylinder; a main combustion chamber defined by the cylinder block, the cylinder head, and the piston; a subchamber that is separated from the main combustion chamber by a partition, and configured to communicate with the main combustion chamber through a communicating hole formed in the partition; an injector configured to inject fuel into the main combustion chamber; a main spark plug configured to perform main ignition for igniting a mixture gas inside the main combustion chamber; a subspark plug configured to perform subignition for igniting the mixture gas inside the subchamber; and a controller that is electrically connected to, and configured to output an electric signal for control to, the injector, the main spark plug, and the subspark plug, wherein in a low-load range (A2H) where an engine load is below a given reference load (Tqs) or when an engine load is below a given reference load (Tqs), the controller is configured to: control the main spark plug and the subspark plug so that the subignition is performed after the main ignition; and in a high-speed range where an engine speed is above a given reference engine speed, retard the timing of the subignition compared with a low-speed range where the engine speed is below the reference engine speed, or if an engine speed is above a given reference engine speed, retard the timing of the subignition compared with the timing of the subignition when the engine speed is below the reference engine speed, wherein control the main spark plug and the subspark plug so that the subignition is performed after the main ignition; and in a high-speed range where an engine speed is above a given reference engine speed, retard the timing of the subignition compared with a low-speed range where the engine speed is below the reference engine speed, or if an engine speed is above a given reference engine speed, retard the timing of the subignition compared with the timing of the subignition when the engine speed is below the reference engine speed, wherein the controller is configured to suspend the main ignition and subignition in a low-speed low-load range where the engine speed is below a second given reference engine speed below the reference engine speed and the engine load is below a second given reference load higher than the reference load (Tqs), or when the engine speed is below a second given reference engine speed below the reference engine speed and the engine load is below a second given reference load higher than the reference load (Tqs).