Finite Group Databasebeta

← C₁₉×D₈₅₁ #44568293

Subgroups — C₁₉×D₈₅₁ #44568293

Order 32338.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₂₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₈₅₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×D₃₇	—	23	1	no	maximal, Hall
4	C₁₉×D₂₃	—	37	1	no	maximal, Hall
5	C₂₃×C₃₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×C₃₇	D₂₃	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₂₃	D₃₇	1	1	yes	characteristic, complemented, Hall
8	D₃₇	—	23	1	no	Hall
9	D₂₃	—	37	1	no	Hall
10	C₂×C₁₉	—	851	1	no	Hall
11	C₃₇	C₁₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
12	C₂₃	C₁₉×D₃₇	1	1	yes	characteristic, complemented, Sylow
13	C₁₉	D₈₅₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	851	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₈₅₁
commutator, cosocle, hypocenter	C₂₃×C₃₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₂₃×C₃₇	C₂
LCS	G ▷ C₂₃×C₃₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₂₃×C₃₇	C₂	semidirect
2. D₈₅₁	C₁₉	direct (N × H)
5. C₂₃×C₃₇	C₂×C₁₉	semidirect
6. C₁₉×C₃₇	D₂₃	semidirect
7. C₁₉×C₂₃	D₃₇	semidirect
11. C₃₇	C₁₉×D₂₃	semidirect
12. C₂₃	C₁₉×D₃₇	semidirect
13. C₁₉	D₈₅₁	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×C₂₃×C₃₇	2
D₈₅₁	19
C₁₉×D₃₇	23
C₁₉×D₂₃	37