Finite Group Databasebeta

← C₅×D₂₉×C₁₃₁ #49184339

Subgroups — C₅×D₂₉×C₁₃₁ #49184339

Order 37990.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₉×C₁₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₃₁	—	29	1	no	maximal, Hall
5	C₅×C₁₃₁	D₂₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×D₂₉	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃₁	—	29	1	no	Hall
8	C₅×C₂₉	C₂×C₁₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃₁	C₅×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
10	D₂₉	C₅×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂₉	C₂×C₅×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	29	1	no	Hall
13	C₅	D₂₉×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃₁	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₅×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₅×C₂₉×C₁₃₁	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₅×C₁₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×C₁₃₁	C₂	semidirect
2. D₂₉×C₁₃₁	C₅	direct (N × H)
3. C₂₉×C₁₃₁	C₂×C₅	semidirect
5. C₅×C₁₃₁	D₂₉	direct (N × H)
6. C₅×D₂₉	C₁₃₁	direct (N × H)
8. C₅×C₂₉	C₂×C₁₃₁	semidirect
9. C₁₃₁	C₅×D₂₉	direct (N × H)
10. D₂₉	C₅×C₁₃₁	direct (N × H)
11. C₂₉	C₂×C₅×C₁₃₁	semidirect
13. C₅	D₂₉×C₁₃₁	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×C₁₃₁	2
D₂₉×C₁₃₁	5
C₂×C₅×C₁₃₁	29
C₅×D₂₉	131