Group #14560070 — subgroups

Subgroups — C₁₉×#2213 #14560070

Order 2432.

170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#509	C₂	1	2	yes	maximal, complemented
2	C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#361	C₂	1	2	yes	maximal, complemented
6	C₁₉×#135	C₂²	1	1	yes	characteristic
7	C₂×D₈×C₁₉	—	2	1	no	—
8	C₂×D₈×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#131	—	2	1	no	—
10	C₁₉×#127	—	2	1	no	—
11	C₁₉×SD₃₂	—	2	2	no	—
12	C₁₉×D₁₆	—	2	2	no	—
13	C₁₉×M₃₂	C₂²	1	2	yes	—
14	C₁₉×#108	C₂²	1	1	yes	characteristic
15	C₁₉×#104	—	2	1	no	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	#41×C₁₉	—	2	1	no	—
18	C₂×D₄×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	—	4	2	no	—
20	Q₁₆×C₁₉	D₄	1	1	yes	characteristic, complemented
21	SD₁₆×C₁₉	—	2	1	no	—
22	D₈×C₁₉	—	2	2	no	—
23	D₈×C₁₉	—	2	2	no	—
24	D₈×C₁₉	—	4	1	no	—
25	D₈×C₁₉	—	4	1	no	—
26	D₈×C₁₉	D₄	1	1	yes	characteristic, complemented
27	M₁₆×C₁₉	—	2	1	no	—
28	M₁₆×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₁₆×C₁₉	—	2	2	no	—
34	C₂³×C₁₉	—	4	2	no	—
35	Q₈×C₁₉	—	2	1	no	—
36	D₄×C₁₉	—	2	1	no	—
37	D₄×C₁₉	—	4	1	no	—
38	D₄×C₁₉	—	4	2	no	—
39	D₄×C₁₉	—	4	2	no	—
40	D₄×C₁₉	—	8	4	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₁₉	—	4	1	no	—
45	C₈×C₁₉	D₈	1	1	yes	characteristic
46	C₈×C₁₉	D₈	1	1	yes	characteristic
47	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₈×C₁₉	#41	1	1	yes	characteristic
49	#2213	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₁₉	—	4	1	no	—
51	C₂²×C₁₉	—	8	4	no	—
52	C₂²×C₁₉	—	8	2	no	—
53	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	—	4	1	no	—
56	C₄×C₁₉	#121	1	1	yes	characteristic
57	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
58	#509	C₂×C₁₉	1	2	yes	complemented
59	#493	C₂×C₁₉	1	1	yes	characteristic, complemented
60	#443	C₂×C₁₉	1	1	yes	characteristic, complemented
61	#364	C₂×C₁₉	1	1	yes	characteristic, complemented
62	#361	C₂×C₁₉	1	2	yes	complemented
63	C₂×C₁₉	—	2	1	no	—
64	C₂×C₁₉	—	8	1	no	—
65	C₂×C₁₉	—	16	2	no	—
66	C₂×C₁₉	#459	1	1	yes	characteristic
67	#135	C₂²×C₁₉	1	1	yes	characteristic
68	C₂×D₈	—	2	1	no	—
69	C₂×D₈	C₂²×C₁₉	1	2	yes	—
70	#131	—	2	1	no	—
71	#127	—	2	1	no	—
72	SD₃₂	—	2	2	no	—
73	D₁₆	—	2	2	no	—
74	M₃₂	C₂²×C₁₉	1	2	yes	—
75	#108	C₂²×C₁₉	1	1	yes	characteristic
76	#104	—	2	1	no	—
77	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
78	C₁₉	#2213	1	1	yes	characteristic, direct product factor, Sylow
79	#41	—	2	1	no	—
80	C₂×D₄	—	2	2	no	—
81	C₂×D₄	—	4	2	no	—
82	Q₁₆	D₄×C₁₉	1	1	yes	characteristic, complemented
83	SD₁₆	—	2	1	no	—
84	D₈	—	2	2	no	—
85	D₈	—	2	2	no	—
86	D₈	—	4	1	no	—
87	D₈	—	4	1	no	—
88	D₈	D₄×C₁₉	1	1	yes	characteristic, complemented
89	M₁₆	—	2	1	no	—
90	M₁₆	—	4	1	no	—
91	C₂×C₈	—	4	1	no	—
92	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
93	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
94	C₄²	D₄×C₁₉	1	1	yes	characteristic
95	C₁₆	—	2	2	no	—
96	C₂³	—	4	2	no	—
97	Q₈	—	2	1	no	—
98	D₄	—	2	1	no	—
99	D₄	—	4	1	no	—
100	D₄	—	4	2	no	—
101	D₄	—	4	2	no	—
102	D₄	—	8	4	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
106	C₈	—	4	1	no	—
107	C₈	D₈×C₁₉	1	1	yes	characteristic
108	C₈	D₈×C₁₉	1	1	yes	characteristic
109	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
110	C₈	#41×C₁₉	1	1	yes	characteristic
111	C₂²	—	4	1	no	—
112	C₂²	—	8	4	no	—
113	C₂²	—	8	2	no	—
114	C₂²	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	4	1	no	—
117	C₄	C₁₉×#121	1	1	yes	characteristic
118	C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	8	1	no	—
121	C₂	—	16	2	no	—
122	C₂	C₁₉×#459	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#509

C₂

yes

maximal, complemented

C₁₉×#493

C₂

yes

maximal, characteristic, complemented

C₁₉×#443

C₂

yes

maximal, characteristic, complemented

C₁₉×#364

C₂

yes

maximal, characteristic, complemented

C₁₉×#361

C₂

yes

maximal, complemented

C₁₉×#135

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

—

C₁₉×#131

—

C₁₉×#127

—

C₁₉×SD₃₂

—

C₁₉×D₁₆

—

C₁₉×M₃₂

C₂²

yes

—

C₁₉×#108

C₂²

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#41×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

D₄

yes

characteristic, complemented

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

D₄

yes

characteristic, complemented

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

#509

C₂×C₁₉

yes

complemented

#493

C₂×C₁₉

yes

characteristic, complemented

#443

C₂×C₁₉

yes

characteristic, complemented

#364

C₂×C₁₉

yes

characteristic, complemented

#361

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

#135

C₂²×C₁₉

yes

characteristic

C₂×D₈

—

C₂×D₈

C₂²×C₁₉

yes

—

#131

—

#127

—

SD₃₂

—

D₁₆

—

M₃₂

C₂²×C₁₉

yes

—

#108

C₂²×C₁₉

yes

characteristic

#104

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2213

yes

characteristic, direct product factor, Sylow

#41

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

D₄×C₁₉

yes

characteristic, complemented

SD₁₆

—

D₈

—

D₈

—

D₈

—

D₈

—

D₈

D₄×C₁₉

yes

characteristic, complemented

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

D₄

—

D₄

—

100

D₄

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

106

C₈

—

107

C₈

D₈×C₁₉

yes

characteristic

108

C₈

D₈×C₁₉

yes

characteristic

109

C₈

C₂×D₄×C₁₉

yes

characteristic

110

C₈

#41×C₁₉

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₁₉×AGL(1,ℤ/8)

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

C₁₉×#121

yes

characteristic

118

C₄

C₂×D₈×C₁₉

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

122

C₂

C₁₉×#459

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#459

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₁₉×#509	C₂	semidirect
2. C₁₉×#493	C₂	semidirect
3. C₁₉×#443	C₂	semidirect
4. C₁₉×#364	C₂	semidirect
5. C₁₉×#361	C₂	semidirect
20. Q₁₆×C₁₉	D₄	semidirect
26. D₈×C₁₉	D₄	semidirect
49. #2213	C₁₉	direct (N × H)
58. #509	C₂×C₁₉	semidirect
59. #493	C₂×C₁₉	semidirect
60. #443	C₂×C₁₉	semidirect
61. #364	C₂×C₁₉	semidirect
62. #361	C₂×C₁₉	semidirect
78. C₁₉	#2213	direct (N × H)
82. Q₁₆	D₄×C₁₉	semidirect
88. D₈	D₄×C₁₉	semidirect

H ≅ G/N

type

1. C₁₉×#509

C₂

semidirect

2. C₁₉×#493

C₂

semidirect

3. C₁₉×#443

C₂

semidirect

4. C₁₉×#364

C₂

semidirect

5. C₁₉×#361

C₂

semidirect

20. Q₁₆×C₁₉

D₄

semidirect

26. D₈×C₁₉

D₄

semidirect

49. #2213

C₁₉

direct (N × H)

58. #509

C₂×C₁₉

semidirect

59. #493

C₂×C₁₉

semidirect

60. #443

C₂×C₁₉

semidirect

61. #364

C₂×C₁₉

semidirect

62. #361

C₂×C₁₉

semidirect

78. C₁₉

#2213

direct (N × H)

82. Q₁₆

D₄×C₁₉

semidirect

88. D₈

D₄×C₁₉

semidirect

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

subgroup	index
C₁₉×#509	2
C₁₉×#493	2
C₁₉×#443	2
C₁₉×#364	2
C₁₉×#361	2
#2213	19

subgroup

index

C₁₉×#509

C₁₉×#493

C₁₉×#443

C₁₉×#364

C₁₉×#361

#2213

Subgroups — C₁₉×#2213 #14560070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2213 #14560070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2213 #14560070