Subgroups — C₁₉×#11744634 #30685555

Order 17100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#1044	—	3	1	no	maximal
3	C₁₉×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
5	C₁₉×#1044	—	9	1	no	Hall
6	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic
7	C₁₉×ΓL(1,𝔽₁₆)	—	15	2	no	—
8	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic
9	#11744634	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₉×Dic₉	—	25	1	no	maximal, Hall
11	C₃×D₅×C₁₉	—	15	2	no	—
12	C₅²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
13	(C₅⋊D₅)⋊C₉	C₂×C₁₉	1	1	yes	characteristic
14	C₁₉×AGL(1,𝔽₅)	—	45	2	no	—
15	C₂×C₉×C₁₉	—	25	1	no	—
16	C₃⋊#1044	—	3	1	no	—
17	C₃×C₅×C₁₉	—	3	2	no	—
18	Dic₃×C₁₉	—	75	1	no	—
19	C₅²⋊C₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
20	D₅×C₁₉	—	15	2	no	—
21	C₉×C₁₉	—	25	1	no	Hall
22	C₃×C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic
23	C₂×C₃×C₁₉	—	25	1	no	—
24	#1044	—	9	1	no	Hall
25	C₅×C₁₉	—	3	2	no	—
26	C₄×C₁₉	—	225	1	no	Hall
27	C₃×C₅²	Dic₃×C₁₉	1	1	yes	characteristic
28	ΓL(1,𝔽₁₆)	—	15	2	no	—
29	C₃×C₁₉	#64480	1	1	yes	characteristic
30	C₅⋊D₅	D₉×C₁₉	1	1	yes	characteristic
31	C₂×C₁₉	—	25	1	no	—
32	Dic₉	—	25	1	no	Hall
33	C₃×D₅	—	15	2	no	—
34	C₅²	C₁₉×Dic₉	1	1	yes	characteristic, complemented, Sylow
35	AGL(1,𝔽₅)	—	45	2	no	—
36	C₁₉	#11744634	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₉	—	25	1	no	—
38	C₃×C₅	—	3	2	no	—
39	Dic₃	—	75	1	no	—
40	D₅	—	15	2	no	—
41	C₉	—	25	1	no	Sylow
42	C₂×C₃	—	25	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	225	1	no	Sylow
45	C₃	C₁₉×#64480	1	1	yes	characteristic
46	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#11744634
commutator, hypocenter	C₅²⋊C₉	C₄×C₁₉
Frattini	C₃	C₁₉×#64480
Fitting, socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₅⋊D₅	D₃
cosocle	(C₅⋊D₅)⋊C₉	C₂×C₁₉
LCS	G ▷ C₅²⋊C₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
3. C₁₉×C₅²⋊C₉	C₄	semidirect
9. #11744634	C₁₉	direct (N × H)
12. C₅²×C₁₉	Dic₉	semidirect
19. C₅²⋊C₉	C₄×C₁₉	semidirect
34. C₅²	C₁₉×Dic₉	semidirect
36. C₁₉	#11744634	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×(C₅⋊D₅)⋊C₉	2
C₁₉×C₃⋊#1044	3
#11744634	19
C₁₉×Dic₉	25

Subgroups — C19×#11744634 #30685555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11744634 #30685555