Finite Group Databasebeta

← C₂×C₁₉⋊(C₁₇²⋊C₃) #45681978

Subgroups — C₂×C₁₉⋊(C₁₇²⋊C₃) #45681978

Order 32946.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊(C₁₇²⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇²⋊C₃	—	19	1	no	maximal, Hall
5	C₁₇²⋊C₃	—	19	1	no	Hall
6	C₂×C₁₇×C₁₉	—	3	6	no	—
7	C₂×C₁₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
8	C₁₇×C₁₉	—	3	6	no	—
9	C₁₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₉⋊C₃	—	289	1	no	maximal, Hall
11	C₁₉⋊C₃	—	289	1	no	Hall
12	C₂×C₁₉	C₁₇²⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₇	—	3	6	no	—
14	C₁₉	C₂×C₁₇²⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	C₁₇	—	3	6	no	—
16	C₂×C₃	—	5491	1	no	Hall
17	C₃	—	5491	1	no	Sylow
18	C₂	C₁₉⋊(C₁₇²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₁₉⋊(C₁₇²⋊C₃)
commutator, cosocle, hypocenter	C₁₇²×C₁₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₇²×C₁₉	C₃
LCS	G ▷ C₁₇²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊(C₁₇²⋊C₃)	C₂	direct (N × H)
2. C₂×C₁₇²×C₁₉	C₃	semidirect
3. C₁₇²×C₁₉	C₂×C₃	semidirect
7. C₂×C₁₇²	C₁₉⋊C₃	semidirect
9. C₁₇²	C₂×C₁₉⋊C₃	semidirect
12. C₂×C₁₉	C₁₇²⋊C₃	semidirect
14. C₁₉	C₂×C₁₇²⋊C₃	semidirect
18. C₂	C₁₉⋊(C₁₇²⋊C₃)	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⋊(C₁₇²⋊C₃)	2
C₂×C₁₇²×C₁₉	3
C₂×C₁₇²⋊C₃	19
C₂×C₁₉⋊C₃	289