Finite Group Databasebeta

← C₅×#20261879 #44526953

Subgroups — C₅×#20261879 #44526953

Order 31065.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#20261879	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₀₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₀₉⋊C₃	—	19	1	no	maximal, Hall
5	C₅×C₁₀₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
6	C₁₀₉⋊C₃	—	19	1	no	Hall
7	C₅×C₁₉⋊C₃	—	109	1	no	maximal, Hall
8	C₁₀₉	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₉	C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₁₉⋊C₃	—	109	1	no	Hall
11	C₁₉	C₅×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₅	—	2071	1	no	Hall
13	C₅	#20261879	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	2071	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#20261879
commutator, cosocle, hypocenter	C₁₉×C₁₀₉	C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₁₀₉	C₃
LCS	G ▷ C₁₉×C₁₀₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₀₉	C₃	semidirect
2. #20261879	C₅	direct (N × H)
3. C₁₉×C₁₀₉	C₃×C₅	semidirect
5. C₅×C₁₀₉	C₁₉⋊C₃	semidirect
8. C₁₀₉	C₅×C₁₉⋊C₃	semidirect
9. C₅×C₁₉	C₁₀₉⋊C₃	semidirect
11. C₁₉	C₅×C₁₀₉⋊C₃	semidirect
13. C₅	#20261879	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×C₁₉×C₁₀₉	3
#20261879	5
C₅×C₁₀₉⋊C₃	19
C₅×C₁₉⋊C₃	109