Finite Group Databasebeta

← C₁₃×Dic₃₈ #14520344

Subgroups — C₁₃×Dic₃₈ #14520344

Order 1976.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₁₉	C₂	1	2	yes	maximal
3	C₂×C₁₃×C₁₉	C₂²	1	1	yes	characteristic
4	C₁₃×C₁₉	Q₈	1	1	yes	characteristic, complemented, Hall
5	Dic₃₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	Q₈×C₁₃	—	19	1	no	maximal, Hall
7	C₄×C₁₉	C₂×C₁₃	1	1	yes	characteristic
8	Dic₁₉	C₂×C₁₃	1	2	yes	—
9	C₄×C₁₃	—	19	2	no	—
10	C₄×C₁₃	D₁₉	1	1	yes	characteristic
11	C₂×C₁₉	C₂²×C₁₃	1	1	yes	characteristic
12	C₂×C₁₃	C₂×D₁₉	1	1	yes	characteristic
13	C₁₉	Q₈×C₁₃	1	1	yes	characteristic, complemented, Sylow
14	C₁₃	Dic₃₈	1	1	yes	characteristic, direct product factor, Sylow
15	Q₈	—	19	1	no	Sylow
16	C₄	—	19	2	no	—
17	C₄	C₁₃×D₁₉	1	1	yes	characteristic
18	C₂	C₂×C₁₃×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₃	C₂×D₁₉
commutator, cosocle	C₂×C₁₉	C₂²×C₁₃
Frattini	C₂	C₂×C₁₃×D₁₉
Fitting	C₄×C₁₃×C₁₉	C₂
socle, prime radical	C₂×C₁₃×C₁₉	C₂²
hypercenter	C₄×C₁₃	D₁₉
hypocenter	C₁₉	Q₈×C₁₃
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃

Complements

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

N	H ≅ G/N	type
4. C₁₃×C₁₉	Q₈	semidirect
5. Dic₃₈	C₁₃	direct (N × H)
13. C₁₉	Q₈×C₁₃	semidirect
14. C₁₃	Dic₃₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×C₁₉	2
C₁₃×Dic₁₉	2
Dic₃₈	13
Q₈×C₁₃	19