Finite Group Databasebeta

← C₂×C₁₉⋊C₃×C₁₈₁ #35207461

Subgroups — C₂×C₁₉⋊C₃×C₁₈₁ #35207461

Order 20634.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×C₁₈₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₉×C₁₈₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₁₈₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₈₁	—	19	1	no	maximal, Hall
5	C₃×C₁₈₁	—	19	1	no	Hall
6	C₂×C₁₈₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₁₈₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₁₉⋊C₃	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₉⋊C₃	C₂×C₁₈₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₉	C₃×C₁₈₁	1	1	yes	characteristic, complemented, Hall
11	C₁₉	C₂×C₃×C₁₈₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	19	1	no	Hall
13	C₃	—	19	1	no	Sylow
14	C₂	C₁₉⋊C₃×C₁₈₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₈₁	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₁₈₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₈₁	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₈₁

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₃×C₁₈₁	C₂	direct (N × H)
2. C₂×C₁₉×C₁₈₁	C₃	semidirect
3. C₁₉×C₁₈₁	C₂×C₃	semidirect
6. C₂×C₁₈₁	C₁₉⋊C₃	direct (N × H)
7. C₁₈₁	C₂×C₁₉⋊C₃	direct (N × H)
8. C₂×C₁₉⋊C₃	C₁₈₁	direct (N × H)
9. C₁₉⋊C₃	C₂×C₁₈₁	direct (N × H)
10. C₂×C₁₉	C₃×C₁₈₁	semidirect
11. C₁₉	C₂×C₃×C₁₈₁	semidirect
14. C₂	C₁₉⋊C₃×C₁₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉⋊C₃×C₁₈₁	2
C₂×C₁₉×C₁₈₁	3
C₂×C₃×C₁₈₁	19
C₂×C₁₉⋊C₃	181