Subgroups — C₁₉×#948 #14269700

Order 1824.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#208	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₉×C₃⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₁₉×#131	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₉	C₄	1	1	yes	characteristic
6	C₃×D₄×C₁₉	C₄	1	3	yes	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	3	yes	—
8	C₁₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₃⋊C₈	C₂²	1	3	yes	—
10	#41×C₁₉	D₃	1	1	yes	characteristic
11	M₁₆×C₁₉	—	3	3	no	—
12	C₂×C₈×C₁₉	—	3	3	no	—
13	C₂²×C₃×C₁₉	C₂×C₄	1	3	yes	—
14	C₃×C₄×C₁₉	C₂×C₄	1	3	yes	—
15	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	Q₈×C₁₉	Dic₃	1	1	yes	characteristic
17	D₄×C₁₉	Dic₃	1	3	yes	—
18	C₂×C₄×C₁₉	C₂×D₃	1	3	yes	—
19	C₈×C₁₉	—	3	1	no	—
20	C₈×C₁₉	—	3	3	no	—
21	C₂×C₃×C₁₉	—	2	3	no	—
22	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
23	#948	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₁₉	C₂×Dic₃	1	3	yes	—
25	C₄×C₁₉	C₂×Dic₃	1	3	yes	—
26	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
27	C₃×C₁₉	#131	1	1	yes	characteristic, complemented, Hall
28	C₃×#41	C₂×C₁₉	1	1	yes	characteristic
29	#208	C₂×C₁₉	1	3	yes	complemented
30	C₂×C₃⋊C₈	C₂×C₁₉	1	3	yes	complemented
31	C₂×C₁₉	—	2	3	no	—
32	C₂×C₁₉	C₂²×Dic₃	1	1	yes	characteristic
33	#131	—	3	1	no	Sylow
34	C₃×Q₈	C₄×C₁₉	1	1	yes	characteristic
35	C₃×D₄	C₄×C₁₉	1	3	yes	—
36	C₂×C₃×C₄	C₂²×C₁₉	1	3	yes	—
37	C₃⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
38	C₃⋊C₈	C₂²×C₁₉	1	3	yes	—
39	C₁₉	#948	1	1	yes	characteristic, direct product factor, Sylow
40	#41	D₃×C₁₉	1	1	yes	characteristic
41	M₁₆	—	3	3	no	—
42	C₂×C₈	—	3	3	no	—
43	C₂²×C₃	C₂×C₄×C₁₉	1	3	yes	—
44	C₃×C₄	C₂×C₄×C₁₉	1	3	yes	—
45	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
46	Q₈	Dic₃×C₁₉	1	1	yes	characteristic
47	D₄	Dic₃×C₁₉	1	3	yes	—
48	C₂×C₄	C₂×D₃×C₁₉	1	3	yes	—
49	C₈	—	3	1	no	—
50	C₈	—	3	3	no	—
51	C₂×C₃	—	2	3	no	—
52	C₂×C₃	C₂²×C₄×C₁₉	1	1	yes	characteristic
53	C₂²	C₂×Dic₃×C₁₉	1	3	yes	—
54	C₄	C₂×Dic₃×C₁₉	1	3	yes	—
55	C₄	C₂²×D₃×C₁₉	1	1	yes	characteristic
56	C₃	C₁₉×#131	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	2	3	no	—
58	C₂	C₂²×Dic₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₉	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting, prime radical	C₃×#41×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²×C₄
cosocle	C₃×C₄	C₂³×C₁₉
hypercenter	#41×C₁₉	D₃
hypocenter	C₃	C₁₉×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₉ ◁ #41×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₉×#208	C₂	semidirect
3. C₂×C₁₉×C₃⋊C₈	C₂	semidirect
23. #948	C₁₉	direct (N × H)
27. C₃×C₁₉	#131	semidirect
29. #208	C₂×C₁₉	semidirect
30. C₂×C₃⋊C₈	C₂×C₁₉	semidirect
39. C₁₉	#948	direct (N × H)
56. C₃	C₁₉×#131	semidirect

Maximal subgroups

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

subgroup	index
C₃×#41×C₁₉	2
C₁₉×#208	2
C₂×C₁₉×C₃⋊C₈	2
C₁₉×#131	3
#948	19

Subgroups — C19×#948 #14269700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#948 #14269700