# Ordered set notation in a simple case

apologies in advance for the noob question. (Really rusty when it comes to order theory notation.)

Suppose I have a set $$\Omega := \{\alpha,\beta_1,...,\beta_n\}$$ (for some fixed $$n\in\mathbb{N}$$). I would like to succinctly express the following:

$$\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad$$ "$$C$$ is a subset of elements from $$\Omega$$ ordered in the following way:
$$\quad\quad\quad\quad\quad \quad\quad\quad\quad\quad\quad$$ 1. If $$\alpha$$ is in $$C$$, then it is placed first.
$$\quad \quad \quad\quad\quad \quad\quad\quad\quad\quad\quad$$ 2. All $$\beta$$'s in $$C$$ are placed in increasing order of their indeces."

I hope this is sufficiently precise; to help illustrate, here are a couple of examples of what I have in mind:
$$\quad \bullet\$$ $$C = (\omega, \beta_1,\beta_3)$$
$$\quad \bullet\$$ $$C = (\beta_2,\beta_3)$$

If there is no succinct, mathematical way to state this, then no worries! Thanks in any case.

The set $$\Omega = \{\alpha, \beta_1, \beta_2, \ldots, \beta_n\}$$ is ordered by $$\leqslant$$ where $$\alpha \leqslant \beta_1 \leqslant \beta_2 \leqslant \ldots \leqslant \beta_n$$.The sequence $$C$$ is a subset of $$\Omega$$ where the elements appear in the order given by $$\leqslant$$. For example $$C = (\alpha, \beta_2)$$ or $$C = (\beta_1, \beta_3, \beta_6)$$.