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The Beretta M9A1 (which is the current military issued pistol) is used by US Navy personnel, notably by CAPT Tom Chandler.
Beretta M9A3
In "Bread and Circuses" (S4E03), Tom uses a pistol that resembles the Beretta M9A3.
Colt Mustang
In "Bread and Circuses" (S4E03), Lucia (Sibylla Deen) is armed with a pistol that resembles the Colt Mustang. Tom later handles the pistol.
Heckler & Koch P30
Kara Green (Marissa Neitling) continues to use a Heckler & Koch P30 as her sidearm, including in Season 4's premiere "In Medias Res" (S4E01).
Rifles/Carbines
M4A1
The M4A1 carbine continues to be the primary weapon carried by the sailors aboard the USS Nathan James. The M4A1 also appears to be carried by CPO Wolf "Wolf-Man" Taylor (Bren Foster) in Season 4.
Members of the Nathan James' Vulture team are armed what appears to be the factory Daniel Defense DDM4 MK18 rifle while searching for Slattery in "Nostos" (S4E04).
AKMSU
An AKMSU rifle is seen in the hands of enemy fighters.
AKM
Severak enemy fighters appear to be armed with the AKM.
AKMS
AKMS rifles are also seen used by enemy fighters.
Sniper Rifles
SVD Dragunov
An SVD Dragunov is seen used by an enemy fighter in "In Media Res" (S4E01).
Submachine Guns
Steyr SPP
The bodyguards carry Steyr SPP machine pistols in "Bread and Circuses" (S4E03).
Machine Guns
Browning M2
The Browning M2HB is one of the weapons on the Nathan James and military Humvees.
M60D
An M60D machine gun is seen mounted on the US Navy UH-1 Huey. The machine gun is operated by PO3 Kathleen Nolan (Jade Chynoweth).
M240B
The M240B is on Navy RHIBs as well as military Humvees.
Nathan James Weapons
5" Mark 45 Mod 2
The 5" Mark 45 Mod 2 artillery gun is the main defensive weapon of the Nathan James.
Phalanx CIWS
A Phalanx CIWS is seen as one of the defensive weapons of the Navy Destroyer USS Nathan James.