Finite Group Databasebeta

← C₂×#23780044 #35207463

Subgroups — C₂×#23780044 #35207463

Order 20634.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23780044	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×C₁₈₁⋊C₃	—	19	1	no	maximal, Hall
5	C₁₈₁⋊C₃	—	19	1	no	Hall
6	C₂×C₁₈₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
7	C₁₈₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₁₉⋊C₃	—	181	1	no	maximal, Hall
9	C₁₉⋊C₃	—	181	1	no	Hall
10	C₂×C₁₉	C₁₈₁⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₁₉	C₂×C₁₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	3439	1	no	Hall
13	C₃	—	3439	1	no	Sylow
14	C₂	#23780044	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	#23780044
commutator, cosocle, hypocenter	C₁₉×C₁₈₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₈₁	C₃
LCS	G ▷ C₁₉×C₁₈₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. #23780044	C₂	direct (N × H)
2. C₂×C₁₉×C₁₈₁	C₃	semidirect
3. C₁₉×C₁₈₁	C₂×C₃	semidirect
6. C₂×C₁₈₁	C₁₉⋊C₃	semidirect
7. C₁₈₁	C₂×C₁₉⋊C₃	semidirect
10. C₂×C₁₉	C₁₈₁⋊C₃	semidirect
11. C₁₉	C₂×C₁₈₁⋊C₃	semidirect
14. C₂	#23780044	direct (N × H)

Maximal subgroups

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

subgroup	index
#23780044	2
C₂×C₁₉×C₁₈₁	3
C₂×C₁₈₁⋊C₃	19
C₂×C₁₉⋊C₃	181