Finite Group Databasebeta

← C₂×C₅₃×C₁₀₁ #24924177

Subgroups — C₂×C₅₃×C₁₀₁ #24924177

Order 10706.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₁₀₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₀₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅₃	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₀₁	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₅₃	C₂×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	C₅₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×C₁₀₁	C₂	direct (N × H)
2. C₂×C₁₀₁	C₅₃	direct (N × H)
3. C₂×C₅₃	C₁₀₁	direct (N × H)
4. C₁₀₁	C₂×C₅₃	direct (N × H)
5. C₅₃	C₂×C₁₀₁	direct (N × H)
6. C₂	C₅₃×C₁₀₁	direct (N × H)