Finite Group Databasebeta

← C₅×D₃₁₆₁ #44539199

Subgroups — C₅×D₃₁₆₁ #44539199

Order 31610.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₁₀₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₀₉	—	29	1	no	maximal, Hall
5	C₅×C₁₀₉	D₂₉	1	1	yes	characteristic, complemented, Hall
6	C₅×D₂₉	—	109	1	no	maximal, Hall
7	D₁₀₉	—	29	1	no	Hall
8	C₅×C₂₉	D₁₀₉	1	1	yes	characteristic, complemented, Hall
9	C₁₀₉	C₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
10	D₂₉	—	109	1	no	Hall
11	C₂₉	C₅×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3161	1	no	Hall
13	C₅	D₃₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	3161	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₁₆₁
commutator, cosocle, hypocenter	C₂₉×C₁₀₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₂₉×C₁₀₉	C₂
LCS	G ▷ C₂₉×C₁₀₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×C₁₀₉	C₂	semidirect
2. D₃₁₆₁	C₅	direct (N × H)
3. C₂₉×C₁₀₉	C₂×C₅	semidirect
5. C₅×C₁₀₉	D₂₉	semidirect
8. C₅×C₂₉	D₁₀₉	semidirect
9. C₁₀₉	C₅×D₂₉	semidirect
11. C₂₉	C₅×D₁₀₉	semidirect
13. C₅	D₃₁₆₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₂₉×C₁₀₉	2
D₃₁₆₁	5
C₅×D₁₀₉	29
C₅×D₂₉	109