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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (displaying both matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
249000.a.2._.B $C_{249}\times D_{250}$ $2^{2} \cdot 3 \cdot 5^{3} \cdot 83$ ✓ ✓ $C_{249}\times D_{500}$ $2^{3} \cdot 3 \cdot 5^{3} \cdot 83$ $C_2$ $2$ ✓
249000.a.2._.C $C_{249}\times D_{250}$ $2^{2} \cdot 3 \cdot 5^{3} \cdot 83$ ✓ ✓ $C_{249}\times D_{500}$ $2^{3} \cdot 3 \cdot 5^{3} \cdot 83$ $C_2$ $2$ ✓
  displayed columns for results