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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H</font> be    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:142"/>
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<a NAME="E2:142"/><b>then </b>
 <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K9">ord</a> <font color="Maroon">H</font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K17" target="_self">index</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:142"/>
 <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="nat_1.html#R1">divides</a>  <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>


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