Finite Group Databasebeta

← C₁₉×D₄₁₃ #30628004

Subgroups — C₁₉×D₄₁₃ #30628004

Order 15694.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₅₉	—	7	1	no	maximal, Hall
3	C₁₉×C₅₉	D₇	1	1	yes	characteristic, complemented, Hall
4	D₄₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₅₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	D₇×C₁₉	—	59	1	no	maximal, Hall
7	C₇×C₁₉	D₅₉	1	1	yes	characteristic, complemented, Hall
8	D₅₉	—	7	1	no	Hall
9	C₅₉	D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₉	—	413	1	no	Hall
11	C₁₉	D₄₁₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₇	—	59	1	no	Hall
13	C₇	C₁₉×D₅₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	413	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₄₁₃
commutator, cosocle, hypocenter	C₇×C₅₉	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₅₉	C₂
LCS	G ▷ C₇×C₅₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₅₉	C₂	semidirect
3. C₁₉×C₅₉	D₇	semidirect
4. D₄₁₃	C₁₉	direct (N × H)
5. C₇×C₅₉	C₂×C₁₉	semidirect
7. C₇×C₁₉	D₅₉	semidirect
9. C₅₉	D₇×C₁₉	semidirect
11. C₁₉	D₄₁₃	direct (N × H)
13. C₇	C₁₉×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₉×C₅₉	2
C₁₉×D₅₉	7
D₄₁₃	19
D₇×C₁₉	59