Finite Group Databasebeta

← C₂×C₂₉×C₁₃₁⋊C₅ #49184337

Subgroups — C₂×C₂₉×C₁₃₁⋊C₅ #49184337

Order 37990.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₉×C₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃₁⋊C₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃₁⋊C₅	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₂₉	—	131	1	no	maximal, Hall
7	C₂×C₁₃₁	C₅×C₂₉	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₉	—	131	1	no	Hall
9	C₁₃₁	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₂₉	C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂₉	C₂×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	131	1	no	Hall
13	C₅	—	131	1	no	Sylow
14	C₂	C₂₉×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₁₃₁⋊C₅	C₂	direct (N × H)
2. C₂×C₂₉×C₁₃₁	C₅	semidirect
3. C₂₉×C₁₃₁	C₂×C₅	semidirect
4. C₂×C₁₃₁⋊C₅	C₂₉	direct (N × H)
5. C₁₃₁⋊C₅	C₂×C₂₉	direct (N × H)
7. C₂×C₁₃₁	C₅×C₂₉	semidirect
9. C₁₃₁	C₂×C₅×C₂₉	semidirect
10. C₂×C₂₉	C₁₃₁⋊C₅	direct (N × H)
11. C₂₉	C₂×C₁₃₁⋊C₅	direct (N × H)
14. C₂	C₂₉×C₁₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×C₁₃₁⋊C₅	2
C₂×C₂₉×C₁₃₁	5
C₂×C₁₃₁⋊C₅	29
C₂×C₅×C₂₉	131