**Core Concept:**
The core concept of this question is about the anatomy of the femoral sheath and the structures that lie outside of it. The femoral sheath is a bursa that reduces friction between the femur and the structures surrounding it. It is located in the groin region, between the femoral artery and vein, and the common iliac artery.

**Why the Correct Answer is Right:**
The correct answer, **C. Iliopsoas muscle**, lies outside the femoral sheath. The iliopsoas muscle is a paired muscle in the thoracolumbar region, which originates from the iliacus and psoas major muscles. It inserts into the lesser trochanter of the femur and the pubic tubercle, allowing for flexion of the thigh and hip. Due to its origin and insertion sites, the iliopsoas muscle is located outside the femoral sheath, making option C the correct answer.

**Why Each Wrong Option is Incorrect:**
Option **A. Iliacus muscle** is incorrect because it is a part of the iliopsoas muscle complex, originating from the iliacus muscle. Since it is a component of the iliopsoas muscle, it lies within the femoral sheath, not outside.

Option **B. Iliacus muscle**: Similar to option A, the iliacus muscle is a component of the iliopsoas muscle complex and, thus, lies inside the femoral sheath.

Option **D. Common iliac artery**: The common iliac artery is a major blood vessel and is not a muscle or part of a muscle. It is located within the retroperitoneal space and does not belong to the structures located outside the femoral sheath.

**Clinical Pearl:**
Understanding the anatomy of the femoral sheath and the structures that lie within and outside of it is crucial for safe and effective clinical practice, particularly in performing procedures involving the thigh and hip regions, such as femoral nerve blocks or femoral artery punctures.

**Correct Answer Explanation:**
The correct answer is **C. Iliopsoas muscle**. The iliopsoas muscle is a paired muscle that lies outside the femoral sheath due to its origin from the iliacus and psoas major muscles. This muscle is crucial for hip flexion and adduction, and it plays a significant role in the hip joint's stability.