Finite Group Databasebeta

← C₁₉×D₈₃₁ #44539059

Subgroups — C₁₉×D₈₃₁ #44539059

Order 31578.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₂₇₇	—	3	1	no	maximal, Hall
3	C₁₉×C₂₇₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₈₃₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₂₇₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	D₂₇₇	—	3	1	no	Hall
7	C₂₇₇	D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
8	D₃×C₁₉	—	277	1	no	maximal, Hall
9	C₃×C₁₉	D₂₇₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉	—	831	1	no	Hall
11	C₁₉	D₈₃₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	—	277	1	no	Hall
13	C₃	C₁₉×D₂₇₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	831	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₈₃₁
commutator, cosocle, hypocenter	C₃×C₂₇₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₂₇₇	C₂
LCS	G ▷ C₃×C₂₇₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₂₇₇	C₂	semidirect
3. C₁₉×C₂₇₇	D₃	semidirect
4. D₈₃₁	C₁₉	direct (N × H)
5. C₃×C₂₇₇	C₂×C₁₉	semidirect
7. C₂₇₇	D₃×C₁₉	semidirect
9. C₃×C₁₉	D₂₇₇	semidirect
11. C₁₉	D₈₃₁	direct (N × H)
13. C₃	C₁₉×D₂₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×C₂₇₇	2
C₁₉×D₂₇₇	3
D₈₃₁	19
D₃×C₁₉	277