Group #18013120 — subgroups

Subgroups — C₁₉×#7161 #18013120

Order 4864.

202 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 126 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	C₂×C₁₉×#364	C₂	1	2	yes	maximal
2	C₂×C₁₉×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×M₃₂	—	2	2	no	—
4	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#364	—	2	2	no	—
8	C₁₉×#364	C₄	1	4	yes	—
9	C₁₉×#346	—	2	2	no	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
13	C₁₉×M₃₂	—	2	4	no	—
14	C₁₉×M₃₂	—	4	2	no	—
15	C₂×C₁₆×C₁₉	—	2	1	no	—
16	C₂×C₁₆×C₁₉	—	2	1	no	—
17	C₂×C₁₆×C₁₉	—	2	1	no	—
18	C₂×C₁₆×C₁₉	—	2	1	no	—
19	C₂×C₁₆×C₁₉	—	4	2	no	—
20	C₂×C₁₆×C₁₉	C₈	1	2	yes	—
21	C₂×C₁₆×C₁₉	C₈	1	2	yes	—
22	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₉	D₄	1	2	yes	—
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
27	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
29	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
33	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
34	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
35	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
36	C₄²×C₁₉	—	2	1	no	—
37	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
38	C₁₆×C₁₉	—	2	2	no	—
39	C₁₆×C₁₉	—	2	2	no	—
40	C₁₆×C₁₉	—	4	4	no	—
41	#7161	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂³×C₁₉	#108	1	1	yes	characteristic
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
51	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
52	C₈×C₁₉	#97	1	1	yes	characteristic
53	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
54	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
55	C₈×C₁₉	#102	1	2	yes	—
56	C₈×C₁₉	#103	1	2	yes	—
57	C₂×#364	C₂×C₁₉	1	2	yes	—
58	C₂×#346	C₂×C₁₉	1	1	yes	characteristic
59	C₂²×C₁₉	—	2	2	no	—
60	C₂²×C₁₉	#334	1	1	yes	characteristic
61	C₂²×C₁₉	#335	1	1	yes	characteristic
62	C₂²×C₁₉	#341	1	1	yes	characteristic
63	C₄×C₁₉	—	4	2	no	—
64	C₄×C₁₉	#334	1	1	yes	characteristic
65	C₄×C₁₉	#335	1	1	yes	characteristic
66	C₄×C₁₉	#336	1	1	yes	characteristic
67	C₄×C₁₉	#340	1	1	yes	characteristic
68	C₂×M₃₂	—	2	2	no	—
69	C₂²×C₁₆	C₄×C₁₉	1	1	yes	characteristic
70	C₂²×C₁₆	C₄×C₁₉	1	1	yes	characteristic
71	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
72	#364	—	2	2	no	—
73	#364	C₄×C₁₉	1	4	yes	—
74	#346	—	2	2	no	—
75	C₂×C₁₉	—	2	1	no	—
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	#1277	1	1	yes	characteristic
78	C₂×C₁₉	#1369	1	2	yes	—
79	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
80	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
81	C₂×C₄²	Q₈×C₁₉	1	1	yes	characteristic
82	M₃₂	—	2	4	no	—
83	M₃₂	—	4	2	no	—
84	C₂×C₁₆	—	2	1	no	—
85	C₂×C₁₆	—	2	1	no	—
86	C₂×C₁₆	—	2	1	no	—
87	C₂×C₁₆	—	2	1	no	—
88	C₂×C₁₆	—	4	2	no	—
89	C₂×C₁₆	C₈×C₁₉	1	2	yes	—
90	C₂×C₁₆	C₈×C₁₉	1	2	yes	—
91	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
92	C₄×C₈	D₄×C₁₉	1	2	yes	—
93	C₁₉	#7161	1	1	yes	characteristic, direct product factor, Sylow
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
96	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
97	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
98	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
99	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
100	C₂×C₈	C₂×C₈×C₁₉	1	1	yes	characteristic
101	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
102	C₂×C₈	M₁₆×C₁₉	1	1	yes	characteristic
103	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
104	C₂×C₈	SD₁₆×C₁₉	1	2	yes	—
105	C₂×C₈	Q₁₆×C₁₉	1	1	yes	characteristic
106	C₄²	—	2	1	no	—
107	C₄²	C₄⋊C₄×C₁₉	1	2	yes	—
108	C₁₆	—	2	2	no	—
109	C₁₆	—	2	2	no	—
110	C₁₆	—	4	4	no	—
111	C₂³	C₁₉×#108	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
115	C₂×C₄	C₁₉×C₄⋊C₈	1	1	yes	characteristic
116	C₂×C₄	C₁₉×C₄⋊C₈	1	1	yes	characteristic
117	C₂×C₄	C₁₉×#106	1	1	yes	characteristic
118	C₂×C₄	C₁₉×#107	1	1	yes	characteristic
119	C₂×C₄	C₁₉×#108	1	1	yes	characteristic
120	C₈	C₄×C₈×C₁₉	1	1	yes	characteristic
121	C₈	C₁₉×#97	1	1	yes	characteristic
122	C₈	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
123	C₈	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
124	C₈	C₁₉×#102	1	2	yes	—
125	C₈	C₁₉×#103	1	2	yes	—
126	C₂²	—	2	2	no	—
127	C₂²	C₁₉×#334	1	1	yes	characteristic
128	C₂²	C₁₉×#335	1	1	yes	characteristic
129	C₂²	C₁₉×#341	1	1	yes	characteristic
130	C₄	—	4	2	no	—
131	C₄	C₁₉×#334	1	1	yes	characteristic
132	C₄	C₁₉×#335	1	1	yes	characteristic
133	C₄	C₁₉×#336	1	1	yes	characteristic
134	C₄	C₁₉×#340	1	1	yes	characteristic
135	C₂	—	2	1	no	—
136	C₂	—	2	1	no	—
137	C₂	C₁₉×#1277	1	1	yes	characteristic
138	C₂	C₁₉×#1369	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#364

C₂

yes

maximal

C₂×C₁₉×#346

C₂

yes

maximal, characteristic

C₂×C₁₉×M₃₂

—

C₂²×C₁₆×C₁₉

C₄

yes

characteristic

C₂²×C₁₆×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#364

—

C₁₉×#364

C₄

yes

—

C₁₉×#346

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₈

yes

—

C₂×C₁₆×C₁₉

C₈

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₄⋊C₄

yes

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7161

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#108

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

#102

yes

—

C₈×C₁₉

#103

yes

—

C₂×#364

C₂×C₁₉

yes

—

C₂×#346

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

—

C₂²×C₁₆

C₄×C₁₉

yes

characteristic

C₂²×C₁₆

C₄×C₁₉

yes

characteristic

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

#364

—

#364

C₄×C₁₉

yes

—

#346

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1277

yes

characteristic

C₂×C₁₉

#1369

yes

—

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₈

D₄×C₁₉

yes

characteristic

C₂×C₄²

Q₈×C₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₈×C₁₉

yes

—

C₂×C₁₆

C₈×C₁₉

yes

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

D₄×C₁₉

yes

—

C₁₉

#7161

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄²×C₁₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₉

yes

—

C₂×C₈

C₂×C₈×C₁₉

yes

characteristic

100

C₂×C₈

C₂×C₈×C₁₉

yes

characteristic

101

C₂×C₈

M₁₆×C₁₉

yes

characteristic

102

C₂×C₈

M₁₆×C₁₉

yes

characteristic

103

C₂×C₈

D₈×C₁₉

yes

characteristic

104

C₂×C₈

SD₁₆×C₁₉

yes

—

105

C₂×C₈

Q₁₆×C₁₉

yes

characteristic

106

C₄²

—

107

C₄²

C₄⋊C₄×C₁₉

yes

—

108

C₁₆

—

109

C₁₆

—

110

C₁₆

—

111

C₂³

C₁₉×#108

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₁₉×#95

yes

characteristic

115

C₂×C₄

C₁₉×C₄⋊C₈

yes

characteristic

116

C₂×C₄

C₁₉×C₄⋊C₈

yes

characteristic

117

C₂×C₄

C₁₉×#106

yes

characteristic

118

C₂×C₄

C₁₉×#107

yes

characteristic

119

C₂×C₄

C₁₉×#108

yes

characteristic

120

C₈

C₄×C₈×C₁₉

yes

characteristic

121

C₈

C₁₉×#97

yes

characteristic

122

C₈

C₁₉×C₂²⋊C₈

yes

characteristic

123

C₈

C₁₉×C₂²⋊C₈

yes

characteristic

124

C₈

C₁₉×#102

yes

—

125

C₈

C₁₉×#103

yes

—

126

C₂²

—

127

C₂²

C₁₉×#334

yes

characteristic

128

C₂²

C₁₉×#335

yes

characteristic

129

C₂²

C₁₉×#341

yes

characteristic

130

C₄

—

131

C₄

C₁₉×#334

yes

characteristic

132

C₄

C₁₉×#335

yes

characteristic

133

C₄

C₁₉×#336

yes

characteristic

134

C₄

C₁₉×#340

yes

characteristic

135

C₂

—

136

C₂

—

137

C₂

C₁₉×#1277

yes

characteristic

138

C₂

C₁₉×#1369

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₉	#106
commutator	C₈	C₄×C₈×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#334
prime radical	C₂³×C₁₉	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#106

commutator

C₈

C₄×C₈×C₁₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₁₉

C₂²×C₁₉

C₂³×C₁₉

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
41. #7161	C₁₉	direct (N × H)
93. C₁₉	#7161	direct (N × H)

H ≅ G/N

type

41. #7161

C₁₉

direct (N × H)

93. C₁₉

#7161

direct (N × H)

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

subgroup	index
C₂×C₁₉×#364	2
C₂×C₁₉×#346	2
#7161	19

subgroup

index

C₂×C₁₉×#364

C₂×C₁₉×#346

#7161

Subgroups — C₁₉×#7161 #18013120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7161 #18013120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7161 #18013120