Finite Group Databasebeta

← C₁₇×C₃₇×D₁₉ #37560752

Subgroups — C₁₇×C₃₇×D₁₉ #37560752

Order 23902.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₇×C₃₇	—	19	1	no	maximal, Hall
4	C₁₉×C₃₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
5	C₁₇×D₁₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₃₇	D₁₉	1	1	yes	characteristic, direct product factor, Hall
7	C₁₇×C₁₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃₇	—	19	1	no	Hall
9	D₁₉	C₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃₇	C₁₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₇	—	19	1	no	Hall
12	C₁₉	C₂×C₁₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
13	C₁₇	C₃₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₃₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₁₇×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₁₉×C₃₇	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₁₇×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₁₉×C₃₇	C₂	semidirect
2. C₃₇×D₁₉	C₁₇	direct (N × H)
4. C₁₉×C₃₇	C₂×C₁₇	semidirect
5. C₁₇×D₁₉	C₃₇	direct (N × H)
6. C₁₇×C₃₇	D₁₉	direct (N × H)
7. C₁₇×C₁₉	C₂×C₃₇	semidirect
9. D₁₉	C₁₇×C₃₇	direct (N × H)
10. C₃₇	C₁₇×D₁₉	direct (N × H)
12. C₁₉	C₂×C₁₇×C₃₇	semidirect
13. C₁₇	C₃₇×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₁₉×C₃₇	2
C₃₇×D₁₉	17
C₂×C₁₇×C₃₇	19
C₁₇×D₁₉	37