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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 (1-50 of 79 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
3600.cv.1.a1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_1$ $1$ ✓
7200.bv.2.d1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ $D_{15}^2:D_4$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
14400.bh.4.f1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ $D_{15}^2:C_4:C_2^2$ $2^{6} \cdot 3^{2} \cdot 5^{2}$ $C_2^2$ $2^{2}$ ✓
14400.bi.4.h1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^2:\OD_{16}:C_2^2$ $2^{6} \cdot 3^{2} \cdot 5^{2}$ $2^{2}$ $-$
14400.bm.4.i1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $F_5^2:S_3^2$ $2^{6} \cdot 3^{2} \cdot 5^{2}$ $2^{2}$ $-$
28800.bb.8.bc1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $(S_3\times F_5)\wr C_2$ $2^{7} \cdot 3^{2} \cdot 5^{2}$ $2^{3}$ $-$
54000.a.15.a1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}:D_5^2.S_3^2$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $3 \cdot 5$ $-$
54000.d.15.a1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}:D_5^2.S_3^2$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $3 \cdot 5$ $-$
54000.q.15.a1.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_3^2:D_5\wr S_3$ $2^{4} \cdot 3^{3} \cdot 5^{3}$ $3 \cdot 5$ $-$
57600.cp.16.g1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ $D_5^2:\POPlus(4,3)$ $2^{8} \cdot 3^{2} \cdot 5^{2}$ $2^{4}$ $-$
115200.cm.32.Z $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^2.S_4\wr C_2$ $2^{9} \cdot 3^{2} \cdot 5^{2}$ $2^{5}$ $-$
129600.n.36.d1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ $A_5^2:S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{2}$ $2^{2} \cdot 3^{2}$ $-$
162000.m.45.b1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3:(C_6^2.S_3^2)$ $2^{4} \cdot 3^{4} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
162000.m.45.c1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3:(C_6^2.S_3^2)$ $2^{4} \cdot 3^{4} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
162000.be.45.a1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_3^3:D_5\wr S_3$ $2^{4} \cdot 3^{4} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
162000.be.45.b1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_3^3:D_5\wr S_3$ $2^{4} \cdot 3^{4} \cdot 5^{3}$ $3^{2} \cdot 5$ $-$
216000.b.60._.Q $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3:(C_{12}^2:D_6)$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.p1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.q1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.s1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.t1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.ci1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.cj1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.cq1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
216000.d.60.cr1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $D_5^3:\He_3.C_2^3$ $2^{6} \cdot 3^{3} \cdot 5^{3}$ $2^{2} \cdot 3 \cdot 5$ $-$
230400.ci.64.O $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $F_5^2.\POPlus(4,3)$ $2^{10} \cdot 3^{2} \cdot 5^{2}$ $2^{6}$ $-$
259200.m.72.d1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $A_5^2:\SOPlus(4,2)$ $2^{7} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 3^{2}$ $-$
259200.n.72.m1 $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $(S_3\times A_5)\wr C_2$ $2^{7} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 3^{2}$ $-$
324000.e.90.D $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_2^4.S_3$ $2^{5} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2} \cdot 5$ $-$
324000.f.90.D $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_2^4.S_3$ $2^{5} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2} \cdot 5$ $-$
324000.m.90.D $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_2^4.S_3$ $2^{5} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2} \cdot 5$ $-$
324000.n.90.D $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_2^4.S_3$ $2^{5} \cdot 3^{4} \cdot 5^{3}$ $2 \cdot 3^{2} \cdot 5$ $-$
518400.n.144._.CF $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $S_5^2.S_3^2$ $2^{8} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3^{2}$ $-$
518400.o.144._.BM $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_3^2.S_5^2:C_2^2$ $2^{8} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3^{2}$ $-$
648000.o.180._.CS $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.o.180._.DZ $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.o.180._.EG $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.o.180._.ES $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.p.180._.O $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.p.180._.BH $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.p.180._.BI $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.p.180._.BQ $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.q.180._.CI $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.q.180._.DZ $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.q.180._.EE $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.q.180._.ES $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_5^3.C_{12}^2.S_3^2$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.r.180._.E $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.r.180._.O $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.r.180._.BI $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
648000.r.180._.BQ $D_5^2:S_3^2$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ $C_{15}^3.C_4^2.D_6$ $2^{6} \cdot 3^{4} \cdot 5^{3}$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
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