Finite Group Databasebeta

← C₅×C₁₉×D₁₆₇ #44540596

Subgroups — C₅×C₁₉×D₁₆₇ #44540596

Order 31730.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₁₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₆₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₆₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₆₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	D₁₆₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₁₉	—	167	1	no	maximal, Hall
8	C₁₆₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₉	D₁₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₉	—	167	1	no	Hall
11	C₁₉	C₅×D₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	167	1	no	Hall
13	C₅	C₁₉×D₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	167	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₁₆₇
commutator, cosocle, hypocenter	C₁₆₇	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₁₆₇	C₂
LCS	G ▷ C₁₆₇
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₆₇	C₂	semidirect
2. C₁₉×D₁₆₇	C₅	direct (N × H)
3. C₁₉×C₁₆₇	C₂×C₅	semidirect
4. C₅×D₁₆₇	C₁₉	direct (N × H)
5. C₅×C₁₆₇	C₂×C₁₉	semidirect
6. D₁₆₇	C₅×C₁₉	direct (N × H)
8. C₁₆₇	C₂×C₅×C₁₉	semidirect
9. C₅×C₁₉	D₁₆₇	direct (N × H)
11. C₁₉	C₅×D₁₆₇	direct (N × H)
13. C₅	C₁₉×D₁₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×C₁₆₇	2
C₁₉×D₁₆₇	5
C₅×D₁₆₇	19
C₂×C₅×C₁₉	167