Finite Group Databasebeta

← C₁₉×Dic₆ #90709

Subgroups — C₁₉×Dic₆ #90709

Order 456.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₉	C₂	1	2	yes	maximal
3	Q₈×C₁₉	—	3	1	no	maximal, Hall
4	C₂×C₃×C₁₉	C₂²	1	1	yes	characteristic
5	C₄×C₁₉	—	3	2	no	—
6	C₄×C₁₉	D₃	1	1	yes	characteristic
7	C₃×C₁₉	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₉	C₂×D₃	1	1	yes	characteristic
9	Dic₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉	Dic₆	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×C₄	C₂×C₁₉	1	1	yes	characteristic
12	Dic₃	C₂×C₁₉	1	2	yes	—
13	Q₈	—	3	1	no	Sylow
14	C₂×C₃	C₂²×C₁₉	1	1	yes	characteristic
15	C₄	—	3	2	no	—
16	C₄	D₃×C₁₉	1	1	yes	characteristic
17	C₃	Q₈×C₁₉	1	1	yes	characteristic, complemented, Sylow
18	C₂	C₂×D₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₉	C₂×D₃
commutator, cosocle	C₂×C₃	C₂²×C₁₉
Frattini	C₂	C₂×D₃×C₁₉
Fitting	C₃×C₄×C₁₉	C₂
socle, prime radical	C₂×C₃×C₁₉	C₂²
hypercenter	C₄×C₁₉	D₃
hypocenter	C₃	Q₈×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉

Complements

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

N	H ≅ G/N	type
7. C₃×C₁₉	Q₈	semidirect
9. Dic₆	C₁₉	direct (N × H)
10. C₁₉	Dic₆	direct (N × H)
17. C₃	Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₁₉	2
Dic₃×C₁₉	2
Q₈×C₁₉	3
Dic₆	19