Finite Group Databasebeta

← C₅×C₇×C₁₆₃ #19152913

Subgroups — C₅×C₇×C₁₆₃ #19152913

Order 5705.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₆₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₅×C₁₆₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₆₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
4	C₅×C₇	C₁₆₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇	C₅×C₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₅	C₇×C₁₆₃	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. C₇×C₁₆₃	C₅	direct (N × H)
2. C₅×C₁₆₃	C₇	direct (N × H)
3. C₁₆₃	C₅×C₇	direct (N × H)
4. C₅×C₇	C₁₆₃	direct (N × H)
5. C₇	C₅×C₁₆₃	direct (N × H)
6. C₅	C₇×C₁₆₃	direct (N × H)