Group #18013250 — subgroups

Subgroups — C₁₉×#7291 #18013250

Order 4864.

192 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2162	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1564	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#431	—	2	1	no	—
5	C₁₉×#423	—	2	1	no	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₄⋊C₁₆	—	2	1	no	—
8	C₁₉×C₂²⋊C₁₆	C₄	1	2	yes	—
9	C₄×C₁₆×C₁₉	—	2	1	no	—
10	C₁₉×#335	—	2	1	no	—
11	C₁₉×#335	C₄	1	2	yes	—
12	C₁₉×#335	C₄	1	2	yes	—
13	C₁₉×#334	—	2	1	no	—
14	C₂×M₁₆×C₁₉	—	4	1	no	—
15	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	—	2	2	no	—
19	C₁₉×C₄⋊C₈	—	2	2	no	—
20	C₁₉×C₄⋊C₈	—	2	2	no	—
21	C₁₉×C₄⋊C₈	—	4	1	no	—
22	C₁₉×C₂²⋊C₈	—	4	1	no	—
23	C₄×C₈×C₁₉	—	4	1	no	—
24	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
31	M₁₆×C₁₉	—	8	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	4	1	no	—
34	C₂×C₈×C₁₉	—	4	2	no	—
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₄²×C₁₉	D₈	1	1	yes	characteristic
43	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
44	C₁₆×C₁₉	—	4	2	no	—
45	#7291	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂³×C₁₉	#106	1	1	yes	characteristic
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
58	C₈×C₁₉	—	2	1	no	—
59	C₈×C₁₉	—	2	1	no	—
60	C₈×C₁₉	—	2	1	no	—
61	C₈×C₁₉	—	8	2	no	—
62	C₈×C₁₉	—	8	2	no	—
63	C₈×C₁₉	#108	1	2	yes	—
64	#2162	C₂×C₁₉	1	1	yes	characteristic
65	#1567	C₂×C₁₉	1	1	yes	characteristic
66	#1564	C₂×C₁₉	1	1	yes	characteristic
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	#340	1	1	yes	characteristic
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	#341	1	1	yes	characteristic
75	C₄×C₁₉	#344	1	1	yes	characteristic
76	C₄×C₁₉	#359	1	2	yes	—
77	C₄×C₁₉	#361	1	1	yes	characteristic
78	C₄×C₁₉	#362	1	1	yes	characteristic
79	#431	—	2	1	no	—
80	#423	—	2	1	no	—
81	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
82	C₄⋊C₁₆	—	2	1	no	—
83	C₂²⋊C₁₆	C₄×C₁₉	1	2	yes	—
84	C₄×C₁₆	—	2	1	no	—
85	#335	—	2	1	no	—
86	#335	C₄×C₁₉	1	2	yes	—
87	#335	C₄×C₁₉	1	2	yes	—
88	#334	—	2	1	no	—
89	C₂×C₁₉	—	4	1	no	—
90	C₂×C₁₉	#1301	1	1	yes	characteristic
91	C₂×C₁₉	#1382	1	1	yes	characteristic
92	C₂×C₁₉	#1387	1	1	yes	characteristic
93	C₂×M₁₆	—	4	1	no	—
94	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
95	C₂²×C₈	Q₈×C₁₉	1	1	yes	characteristic
96	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
97	C₂×C₁₆	—	2	2	no	—
98	C₄⋊C₈	—	2	2	no	—
99	C₄⋊C₈	—	2	2	no	—
100	C₄⋊C₈	—	4	1	no	—
101	C₂²⋊C₈	—	4	1	no	—
102	C₄×C₈	—	4	1	no	—
103	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
104	C₄×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
105	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
106	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
107	C₁₉	#7291	1	1	yes	characteristic, direct product factor, Sylow
108	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
109	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
110	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
111	M₁₆	—	8	2	no	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	4	1	no	—
114	C₂×C₈	—	4	2	no	—
115	C₂×C₈	—	4	2	no	—
116	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
117	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
118	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
119	C₂×C₈	C₄⋊C₄×C₁₉	1	1	yes	characteristic
120	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
121	C₄²	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
122	C₄²	D₈×C₁₉	1	1	yes	characteristic
123	C₄²	Q₁₆×C₁₉	1	1	yes	characteristic
124	C₁₆	—	4	2	no	—
125	C₂³	C₁₉×#106	1	1	yes	characteristic
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
132	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
133	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
134	C₂×C₄	C₁₉×#103	1	1	yes	characteristic
135	C₂×C₄	C₁₉×#103	1	1	yes	characteristic
136	C₂×C₄	C₁₉×#107	1	1	yes	characteristic
137	C₈	—	2	1	no	—
138	C₈	—	2	1	no	—
139	C₈	—	2	1	no	—
140	C₈	—	8	2	no	—
141	C₈	—	8	2	no	—
142	C₈	C₁₉×#108	1	2	yes	—
143	C₂²	—	2	1	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	C₁₉×#340	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	C₁₉×#341	1	1	yes	characteristic
151	C₄	C₁₉×#344	1	1	yes	characteristic
152	C₄	C₁₉×#359	1	2	yes	—
153	C₄	C₁₉×#361	1	1	yes	characteristic
154	C₄	C₁₉×#362	1	1	yes	characteristic
155	C₂	—	4	1	no	—
156	C₂	C₁₉×#1301	1	1	yes	characteristic
157	C₂	C₁₉×#1382	1	1	yes	characteristic
158	C₂	C₁₉×#1387	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2162

C₂

yes

maximal, characteristic

C₁₉×#1567

C₂

yes

maximal, characteristic

C₁₉×#1564

C₂

yes

maximal, characteristic

C₁₉×#431

—

C₁₉×#423

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

C₄

yes

—

C₄×C₁₆×C₁₉

—

C₁₉×#335

—

C₁₉×#335

C₄

yes

—

C₁₉×#335

C₄

yes

—

C₁₉×#334

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₁₆×C₁₉

—

#7291

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#106

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#108

yes

—

#2162

C₂×C₁₉

yes

characteristic

#1567

C₂×C₁₉

yes

characteristic

#1564

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

C₄×C₁₉

yes

—

C₄×C₁₆

—

#335

—

#335

C₄×C₁₉

yes

—

#335

C₄×C₁₉

yes

—

#334

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₈

Q₈×C₁₉

yes

characteristic

C₂×C₄²

D₄×C₁₉

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₂²⋊C₈

—

102

C₄×C₈

—

103

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

104

C₄×C₈

C₂×C₄×C₁₉

yes

characteristic

105

C₄×C₈

D₄×C₁₉

yes

characteristic

106

C₄×C₈

D₄×C₁₉

yes

characteristic

107

C₁₉

#7291

yes

characteristic, direct product factor, Sylow

108

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

109

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

110

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₄²×C₁₉

yes

characteristic

117

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

118

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

119

C₂×C₈

C₄⋊C₄×C₁₉

yes

characteristic

120

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

121

C₄²

C₂²⋊C₄×C₁₉

yes

characteristic

122

C₄²

D₈×C₁₉

yes

characteristic

123

C₄²

Q₁₆×C₁₉

yes

characteristic

124

C₁₆

—

125

C₂³

C₁₉×#106

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₁₉×#95

yes

characteristic

132

C₂×C₄

C₁₉×#102

yes

characteristic

133

C₂×C₄

C₁₉×#102

yes

characteristic

134

C₂×C₄

C₁₉×#103

yes

characteristic

135

C₂×C₄

C₁₉×#103

yes

characteristic

136

C₂×C₄

C₁₉×#107

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

C₁₉×#108

yes

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₁₉×#340

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

C₁₉×#341

yes

characteristic

151

C₄

C₁₉×#344

yes

characteristic

152

C₄

C₁₉×#359

yes

—

153

C₄

C₁₉×#361

yes

characteristic

154

C₄

C₁₉×#362

yes

characteristic

155

C₂

—

156

C₂

C₁₉×#1301

yes

characteristic

157

C₂

C₁₉×#1382

yes

characteristic

158

C₂

C₁₉×#1387

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#102
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#340
prime radical	C₂³×C₁₉	#106
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

#102

commutator

C₂×C₈

C₄²×C₁₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₁₉

C₂²×C₁₉

C₂³×C₁₉

G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
45. #7291	C₁₉	direct (N × H)
107. C₁₉	#7291	direct (N × H)

H ≅ G/N

type

45. #7291

C₁₉

direct (N × H)

107. C₁₉

#7291

direct (N × H)

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

subgroup	index
C₁₉×#2162	2
C₁₉×#1567	2
C₁₉×#1564	2
#7291	19

subgroup

index

C₁₉×#2162

C₁₉×#1567

C₁₉×#1564

#7291

Subgroups — C₁₉×#7291 #18013250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7291 #18013250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7291 #18013250