Finite Group Databasebeta

← C₅×D₃₃₁₇ #45684261

Subgroups — C₅×D₃₃₁₇ #45684261

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	D₃₃₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₁₀₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₀₇	—	31	1	no	maximal, Hall
5	C₅×C₁₀₇	D₃₁	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃₁	—	107	1	no	maximal, Hall
7	D₁₀₇	—	31	1	no	Hall
8	C₅×C₃₁	D₁₀₇	1	1	yes	characteristic, complemented, Hall
9	C₁₀₇	C₅×D₃₁	1	1	yes	characteristic, complemented, Sylow
10	D₃₁	—	107	1	no	Hall
11	C₃₁	C₅×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3317	1	no	Hall
13	C₅	D₃₃₁₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	3317	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₃₁₇
commutator, cosocle, hypocenter	C₃₁×C₁₀₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₃₁×C₁₀₇	C₂
LCS	G ▷ C₃₁×C₁₀₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃₁×C₁₀₇	C₂	semidirect
2. D₃₃₁₇	C₅	direct (N × H)
3. C₃₁×C₁₀₇	C₂×C₅	semidirect
5. C₅×C₁₀₇	D₃₁	semidirect
8. C₅×C₃₁	D₁₀₇	semidirect
9. C₁₀₇	C₅×D₃₁	semidirect
11. C₃₁	C₅×D₁₀₇	semidirect
13. C₅	D₃₃₁₇	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×C₃₁×C₁₀₇	2
D₃₃₁₇	5
C₅×D₁₀₇	31
C₅×D₃₁	107