You need to make a getCapabilities request (http://localhost:8080/geoserver/ows?service=wms&version=1.3.0&request=GetCapabilities) then look at the xml response. For each layer you will see a list of the available styles.
<Layer queryable="1">
<Name>sf:bugsites</Name>
<Title>Spearfish bug locations</Title>
<Abstract>
Sample data from GRASS, bug sites location, Spearfish, South Dakota, USA
</Abstract>
<KeywordList>
<Keyword>spearfish</Keyword>
<Keyword>sfBugsites</Keyword>
<Keyword>insects</Keyword>
<Keyword>bugsites</Keyword>
<Keyword>tiger_beetles</Keyword>
</KeywordList>
<CRS>EPSG:26713</CRS>
<CRS>CRS:84</CRS>
<EX_GeographicBoundingBox>
<westBoundLongitude>-103.86796131703647</westBoundLongitude>
<eastBoundLongitude>-103.63773523234195</eastBoundLongitude>
<southBoundLatitude>44.373938816704396</southBoundLatitude>
<northBoundLatitude>44.43418821380063</northBoundLatitude>
</EX_GeographicBoundingBox>
<BoundingBox CRS="CRS:84" minx="-103.86796131703647" miny="44.373938816704396" maxx="-103.63773523234195" maxy="44.43418821380063"/>
<BoundingBox CRS="EPSG:26713" minx="590223.4382724703" miny="4914107.882513998" maxx="608462.4604629107" maxy="4920523.89081033"/>
<Style>
<Name>capitals</Name>
<Title>Capital cities</Title>
<Abstract/>
<LegendURL width="20" height="20">
<Format>image/png</Format>
<OnlineResource xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="http://192.168.1.161:8080/ows?service=WMS&request=GetLegendGraphic&format=image%2Fpng&width=20&height=20&layer=bugsites"/>
</LegendURL>
</Style>
<Style>
<Name>burg</Name>
<Title>A small red flag</Title>
<Abstract>A sample of how to use an SVG based symbolizer</Abstract>
<LegendURL width="20" height="20">
<Format>image/png</Format>
<OnlineResource xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="http://192.168.1.161:8080/ows?service=WMS&request=GetLegendGraphic&format=image%2Fpng&width=20&height=20&layer=bugsites&style=burg"/>
</LegendURL>
</Style>
<Style>
<Name>point</Name>
<Title>Default Point</Title>
<Abstract>A sample style that draws a point</Abstract>
<LegendURL width="20" height="20">
<Format>image/png</Format>
<OnlineResource xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="http://192.168.1.161:8080/ows?service=WMS&request=GetLegendGraphic&format=image%2Fpng&width=20&height=20&layer=bugsites&style=point"/>
</LegendURL>
</Style>
</Layer>