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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 (1-50 of 63 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
100.2.50.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{100}$ $2^{2} \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
100.5.50.a1.a1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{50}$ $2^{2} \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
100.5.50.a1.b1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{50}$ $2^{2} \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
100.5.50.a1.c1 $C_2$ $2$ ✓ ✓ ✓ $C_2\times C_{50}$ $2^{2} \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
150.1.50.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ $S_3\times C_{25}$ $2 \cdot 3 \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
150.4.50.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{150}$ $2 \cdot 3 \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.2.50.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_{250}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.4.50.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $D_5\times C_{25}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.9.50.a1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{50}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.9.50.a1.b1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{50}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.9.50.a1.c1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{50}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.9.50.a1.d1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{50}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
250.9.50.a1.e1 $C_5$ $5$ ✓ ✓ ✓ $C_5\times C_{50}$ $2 \cdot 5^{3}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
350.2.50.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $D_7\times C_{25}$ $2 \cdot 5^{2} \cdot 7$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
350.4.50.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ ✓ $C_{350}$ $2 \cdot 5^{2} \cdot 7$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
550.1.50.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{11}:C_{50}$ $2 \cdot 5^{2} \cdot 11$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
550.2.50.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $C_{11}:C_{50}$ $2 \cdot 5^{2} \cdot 11$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
550.4.50.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ $D_{11}\times C_{25}$ $2 \cdot 5^{2} \cdot 11$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
550.6.50.a1.a1 $C_{11}$ $11$ $11$ ✓ ✓ ✓ ✓ $C_{550}$ $2 \cdot 5^{2} \cdot 11$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
650.2.50.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ $C_{25}\times D_{13}$ $2 \cdot 5^{2} \cdot 13$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
650.4.50.a1.a1 $C_{13}$ $13$ $13$ ✓ ✓ ✓ ✓ $C_{650}$ $2 \cdot 5^{2} \cdot 13$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
800.384.50.a1 $C_2^4$ $2^{4}$ ✓ ✓ ✓ $C_2^4:C_{50}$ $2^{5} \cdot 5^{2}$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
850.2.50.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ $C_{25}\times D_{17}$ $2 \cdot 5^{2} \cdot 17$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
850.4.50.a1.a1 $C_{17}$ $17$ $17$ ✓ ✓ ✓ ✓ $C_{850}$ $2 \cdot 5^{2} \cdot 17$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
950.2.50.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ $C_{25}\times D_{19}$ $2 \cdot 5^{2} \cdot 19$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
950.4.50.a1.a1 $C_{19}$ $19$ $19$ ✓ ✓ ✓ ✓ $C_{950}$ $2 \cdot 5^{2} \cdot 19$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1150.2.50.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ $C_{25}\times D_{23}$ $2 \cdot 5^{2} \cdot 23$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1150.4.50.a1.a1 $C_{23}$ $23$ $23$ ✓ ✓ ✓ ✓ $C_{1150}$ $2 \cdot 5^{2} \cdot 23$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1450.2.50.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ $C_{25}\times D_{29}$ $2 \cdot 5^{2} \cdot 29$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1450.4.50.a1.a1 $C_{29}$ $29$ $29$ ✓ ✓ ✓ ✓ $C_{1450}$ $2 \cdot 5^{2} \cdot 29$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1550.1.50.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{31}:C_{50}$ $2 \cdot 5^{2} \cdot 31$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1550.2.50.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{31}:C_{50}$ $2 \cdot 5^{2} \cdot 31$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1550.4.50.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ $C_{25}\times D_{31}$ $2 \cdot 5^{2} \cdot 31$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1550.6.50.a1.a1 $C_{31}$ $31$ $31$ ✓ ✓ ✓ ✓ $C_{1550}$ $2 \cdot 5^{2} \cdot 31$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1850.2.50.a1.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ $C_{25}\times D_{37}$ $2 \cdot 5^{2} \cdot 37$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
1850.4.50.a1.a1 $C_{37}$ $37$ $37$ ✓ ✓ ✓ ✓ $C_{1850}$ $2 \cdot 5^{2} \cdot 37$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
3350.a.50.a1.a1 $C_{67}$ $67$ $67$ ✓ ✓ ✓ ✓ $C_{3350}$ $2 \cdot 5^{2} \cdot 67$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
3350.b.50.a1.a1 $C_{67}$ $67$ $67$ ✓ ✓ ✓ $C_{25}\times D_{67}$ $2 \cdot 5^{2} \cdot 67$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
4150.a.50.a1.a1 $C_{83}$ $83$ $83$ ✓ ✓ ✓ ✓ $C_{4150}$ $2 \cdot 5^{2} \cdot 83$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
5050.a.50.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ ✓ $C_{5050}$ $2 \cdot 5^{2} \cdot 101$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
5050.b.50.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ $C_{101}:C_{50}$ $2 \cdot 5^{2} \cdot 101$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
5050.c.50.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ $C_{101}:C_{50}$ $2 \cdot 5^{2} \cdot 101$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
5050.d.50.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ $C_{25}\times D_{101}$ $2 \cdot 5^{2} \cdot 101$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
5050.f.50.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ $C_{101}:C_{50}$ $2 \cdot 5^{2} \cdot 101$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
5050.g.50.a1.a1 $C_{101}$ $101$ $101$ ✓ ✓ ✓ $C_{101}:C_{50}$ $2 \cdot 5^{2} \cdot 101$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
7550.a.50.a1.a1 $C_{151}$ $151$ $151$ ✓ ✓ ✓ ✓ $C_{7550}$ $2 \cdot 5^{2} \cdot 151$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
7550.b.50.a1.a1 $C_{151}$ $151$ $151$ ✓ ✓ ✓ $C_{151}:C_{50}$ $2 \cdot 5^{2} \cdot 151$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
7550.c.50.a1.a1 $C_{151}$ $151$ $151$ ✓ ✓ ✓ $C_{151}:C_{50}$ $2 \cdot 5^{2} \cdot 151$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
7550.d.50.a1.a1 $C_{151}$ $151$ $151$ ✓ ✓ ✓ $C_{25}\times D_{151}$ $2 \cdot 5^{2} \cdot 151$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
7550.f.50.a1.a1 $C_{151}$ $151$ $151$ ✓ ✓ ✓ $C_{151}:C_{50}$ $2 \cdot 5^{2} \cdot 151$ $C_{50}$ $2 \cdot 5^{2}$ ✓ ✓
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