Finite Group Databasebeta

← C₅×C₁₉⋊C₃×C₁₀₇ #44479280

Subgroups — C₅×C₁₉⋊C₃×C₁₀₇ #44479280

Order 30495.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×C₁₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₀₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₁₀₇	—	19	1	no	maximal, Hall
5	C₅×C₁₀₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₀₇	—	19	1	no	Hall
7	C₅×C₁₉⋊C₃	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₀₇	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₉	C₃×C₁₀₇	1	1	yes	characteristic, complemented, Hall
10	C₁₉⋊C₃	C₅×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₉	C₃×C₅×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₅	—	19	1	no	Hall
13	C₅	C₁₉⋊C₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₀₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₅×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₁₀₇	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅×C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₀₇	C₃	semidirect
2. C₁₉⋊C₃×C₁₀₇	C₅	direct (N × H)
3. C₁₉×C₁₀₇	C₃×C₅	semidirect
5. C₅×C₁₀₇	C₁₉⋊C₃	direct (N × H)
7. C₅×C₁₉⋊C₃	C₁₀₇	direct (N × H)
8. C₁₀₇	C₅×C₁₉⋊C₃	direct (N × H)
9. C₅×C₁₉	C₃×C₁₀₇	semidirect
10. C₁₉⋊C₃	C₅×C₁₀₇	direct (N × H)
11. C₁₉	C₃×C₅×C₁₀₇	semidirect
13. C₅	C₁₉⋊C₃×C₁₀₇	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×C₁₀₇	3
C₁₉⋊C₃×C₁₀₇	5
C₃×C₅×C₁₀₇	19
C₅×C₁₉⋊C₃	107