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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 52 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
4200.o.1.a1.a1 $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_1$ $1$ ✓
4200.o.2.a1.a1 $C_5\times C_{420}$ $2^{2} \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_2$ $2$ ✓
4200.o.3.a1.a1 $C_{35}:C_{40}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_3$ $3$ ✓
4200.o.4.a1.a1 $C_5\times C_{210}$ $2 \cdot 3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_4$ $2^{2}$ ✓
4200.o.5.a1.a1 $C_{105}:C_8$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5$ $5$ ✓
4200.o.6.a1.a1 $C_5\times C_{140}$ $2^{2} \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_6$ $2 \cdot 3$ ✓
4200.o.8.a1.a1 $C_5\times C_{105}$ $3 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_8$ $2^{3}$ ✓
4200.o.10.a1.a1 $C_{420}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $D_5$ $2 \cdot 5$
4200.o.10.b1.a1 $C_{420}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{10}$ $2 \cdot 5$ ✓
4200.o.12.a1.a1 $C_5\times C_{70}$ $2 \cdot 5^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{12}$ $2^{2} \cdot 3$ ✓
4200.o.14.a1.a1 $C_5\times C_{60}$ $2^{2} \cdot 3 \cdot 5^{2}$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $D_7$ $2 \cdot 7$
4200.o.15.a1.a1 $C_{35}:C_8$ $2^{3} \cdot 5 \cdot 7$ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{15}$ $3 \cdot 5$ ✓
4200.o.20.a1.a1 $C_{210}$ $2 \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_4$ $2^{2} \cdot 5$
4200.o.20.b1.a1 $C_{210}$ $2 \cdot 3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{20}$ $2^{2} \cdot 5$ ✓
4200.o.24.a1.a1 $C_5\times C_{35}$ $5^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{24}$ $2^{3} \cdot 3$ ✓
4200.o.28.a1.a1 $C_5\times C_{30}$ $2 \cdot 3 \cdot 5^{2}$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_4$ $2^{2} \cdot 7$
4200.o.30.a1.a1 $C_{140}$ $2^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_3\times D_5$ $2 \cdot 3 \cdot 5$
4200.o.30.b1.a1 $C_{140}$ $2^{2} \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{30}$ $2 \cdot 3 \cdot 5$ ✓
4200.o.40.a1.a1 $C_{105}$ $3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_8$ $2^{3} \cdot 5$
4200.o.40.b1.a1 $C_{105}$ $3 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{40}$ $2^{3} \cdot 5$ ✓
4200.o.42.a1.a1 $C_5\times C_{20}$ $2^{2} \cdot 5^{2}$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_3\times D_7$ $2 \cdot 3 \cdot 7$
4200.o.50.a1.a1 $C_{84}$ $2^{2} \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5\times D_5$ $2 \cdot 5^{2}$
4200.o.56.a1.a1 $C_5\times C_{15}$ $3 \cdot 5^{2}$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_8$ $2^{3} \cdot 7$
4200.o.60.a1.a1 $C_{70}$ $2 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_{12}$ $2^{2} \cdot 3 \cdot 5$
4200.o.60.b1.a1 $C_{70}$ $2 \cdot 5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓
4200.o.70.a1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $D_{35}$ $2 \cdot 5 \cdot 7$
4200.o.70.b1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5\times D_7$ $2 \cdot 5 \cdot 7$
4200.o.84.a1.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_{12}$ $2^{2} \cdot 3 \cdot 7$
4200.o.100.a1.a1 $C_{42}$ $2 \cdot 3 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_{20}$ $2^{2} \cdot 5^{2}$
4200.o.120.a1.a1 $C_{35}$ $5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_{24}$ $2^{3} \cdot 3 \cdot 5$
4200.o.120.b1.a1 $C_{35}$ $5 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{120}$ $2^{3} \cdot 3 \cdot 5$ ✓
4200.o.140.a1.a1 $C_{30}$ $2 \cdot 3 \cdot 5$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{35}:C_4$ $2^{2} \cdot 5 \cdot 7$
4200.o.140.b1.a1 $C_{30}$ $2 \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_{20}$ $2^{2} \cdot 5 \cdot 7$
4200.o.150.a1.a1 $C_{28}$ $2^{2} \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $D_5\times C_{15}$ $2 \cdot 3 \cdot 5^{2}$
4200.o.168.a1.a1 $C_5^2$ $5^{2}$ $5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_{24}$ $2^{3} \cdot 3 \cdot 7$
4200.o.200.a1.a1 $C_{21}$ $3 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_{40}$ $2^{3} \cdot 5^{2}$
4200.o.210.a1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_3\times D_{35}$ $2 \cdot 3 \cdot 5 \cdot 7$
4200.o.210.b1.a1 $C_{20}$ $2^{2} \cdot 5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $D_7\times C_{15}$ $2 \cdot 3 \cdot 5 \cdot 7$
4200.o.280.a1.a1 $C_{15}$ $3 \cdot 5$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{35}:C_8$ $2^{3} \cdot 5 \cdot 7$
4200.o.280.b1.a1 $C_{15}$ $3 \cdot 5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_{40}$ $2^{3} \cdot 5 \cdot 7$
4200.o.300.a1.a1 $C_{14}$ $2 \cdot 7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_{60}$ $2^{2} \cdot 3 \cdot 5^{2}$
4200.o.350.a1.a1 $C_{12}$ $2^{2} \cdot 3$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5\times D_{35}$ $2 \cdot 5^{2} \cdot 7$
4200.o.420.a1.a1 $C_{10}$ $2 \cdot 5$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{105}:C_4$ $2^{2} \cdot 3 \cdot 5 \cdot 7$
4200.o.420.b1.a1 $C_{10}$ $2 \cdot 5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_{60}$ $2^{2} \cdot 3 \cdot 5 \cdot 7$
4200.o.600.a1.a1 $C_7$ $7$ $7$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_5:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2}$ ✓
4200.o.700.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{35}:C_{20}$ $2^{2} \cdot 5^{2} \cdot 7$
4200.o.840.a1.a1 $C_5$ $5$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{105}:C_8$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓
4200.o.840.b1.a1 $C_5$ $5$ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_7:C_{120}$ $2^{3} \cdot 3 \cdot 5 \cdot 7$ ✓
4200.o.1050.a1.a1 $C_4$ $2^{2}$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{15}\times D_{35}$ $2 \cdot 3 \cdot 5^{2} \cdot 7$
4200.o.1400.a1.a1 $C_3$ $3$ $3$ ✓ ✓ ✓ ✓ $C_{35}:C_{120}$ $2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ $C_{35}:C_{40}$ $2^{3} \cdot 5^{2} \cdot 7$ ✓
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