Finite Group Databasebeta

← D₅×C₃₁×C₁₀₇ #45684262

Subgroups — D₅×C₃₁×C₁₀₇ #45684262

Order 33170.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₁×C₁₀₇	—	5	1	no	maximal, Hall
3	C₃₁×C₁₀₇	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₀₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₀₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
6	D₅×C₃₁	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₀₇	—	5	1	no	Hall
8	C₅×C₃₁	C₂×C₁₀₇	1	1	yes	characteristic, complemented, Hall
9	C₁₀₇	D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃₁	—	5	1	no	Hall
11	C₃₁	D₅×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₃₁×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₃₁×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁×C₁₀₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃₁×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₁₀₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃₁×C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₁₀₇	C₂	semidirect
3. C₃₁×C₁₀₇	D₅	direct (N × H)
4. D₅×C₁₀₇	C₃₁	direct (N × H)
5. C₅×C₁₀₇	C₂×C₃₁	semidirect
6. D₅×C₃₁	C₁₀₇	direct (N × H)
8. C₅×C₃₁	C₂×C₁₀₇	semidirect
9. C₁₀₇	D₅×C₃₁	direct (N × H)
11. C₃₁	D₅×C₁₀₇	direct (N × H)
12. D₅	C₃₁×C₁₀₇	direct (N × H)
13. C₅	C₂×C₃₁×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₃₁×C₁₀₇	2
C₂×C₃₁×C₁₀₇	5
D₅×C₁₀₇	31
D₅×C₃₁	107