Finite Group Databasebeta

Subgroups — #44531139

Order 31310.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30627800	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁×C₁₀₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	D₁₀₁⋊C₅	—	31	1	no	maximal, Hall
5	C₁₀₁⋊C₅	—	31	1	no	Hall
6	D₃₁⋊C₅	—	101	1	no	maximal, Hall
7	D₁₀₁	—	31	1	no	Hall
8	ΓL(1,𝔽₃₂)	—	101	1	no	Hall
9	C₁₀₁	D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
10	D₃₁	—	101	1	no	Hall
11	C₃₁	D₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3131	1	no	Hall
13	C₅	—	3131	1	no	Sylow
14	C₂	—	3131	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁×C₁₀₁	C₂×C₅
LCS	G ▷ C₃₁×C₁₀₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #30627800	C₂	semidirect
2. D₃₁₃₁	C₅	semidirect
3. C₃₁×C₁₀₁	C₂×C₅	semidirect
9. C₁₀₁	D₃₁⋊C₅	semidirect
11. C₃₁	D₁₀₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
#30627800	2
D₃₁₃₁	5
D₁₀₁⋊C₅	31
D₃₁⋊C₅	101