Group #14559326 — subgroups

Subgroups — C₁₉×#1469 #14559326

Order 2432.

256 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 92 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×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#323	C₂	1	4	yes	maximal, complemented
5	C₂²×Q₈×C₁₉	C₄	1	1	yes	characteristic
6	C₂²×D₄×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#124	—	2	1	no	—
8	C₁₉×#124	—	2	1	no	—
9	C₁₉×#124	—	2	1	no	—
10	C₁₉×#124	—	2	1	no	—
11	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
12	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×C₄⋊C₈	—	2	1	no	—
15	C₁₉×C₄⋊C₈	—	2	1	no	—
16	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₁₉×#97	—	2	1	no	—
19	C₄×C₈×C₁₉	—	2	1	no	—
20	C₂⁴×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×Q₈×C₁₉	—	4	2	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	4	2	no	—
27	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₈×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	2	2	no	—
35	C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	—	2	4	no	—
43	C₂³×C₁₉	—	4	2	no	—
44	C₂³×C₁₉	—	4	2	no	—
45	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	Q₈×C₁₉	—	4	2	no	—
47	Q₈×C₁₉	—	4	2	no	—
48	D₄×C₁₉	—	4	2	no	—
49	D₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	2	no	—
55	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₈×C₁₉	—	4	2	no	—
62	C₈×C₁₉	—	4	2	no	—
63	#1469	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	4	2	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	—	8	4	no	—
70	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₁₉	#131	1	2	yes	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	—	2	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	—	4	2	no	—
78	C₄×C₁₉	#100	1	2	yes	—
79	C₂×#124	C₂×C₁₉	1	1	yes	characteristic
80	#432	C₂×C₁₉	1	1	yes	characteristic, complemented
81	#431	C₂×C₁₉	1	1	yes	characteristic, complemented
82	#323	C₂×C₁₉	1	4	yes	complemented
83	C₂×C₁₉	—	2	2	no	—
84	C₂×C₁₉	—	8	2	no	—
85	C₂×C₁₉	#408	1	1	yes	characteristic
86	C₂×C₁₉	#410	1	1	yes	characteristic
87	C₂×C₁₉	C₂×#100	1	1	yes	characteristic
88	C₂²×Q₈	C₄×C₁₉	1	1	yes	characteristic
89	C₂²×D₄	C₄×C₁₉	1	1	yes	characteristic
90	#124	—	2	1	no	—
91	#124	—	2	1	no	—
92	#124	—	2	1	no	—
93	#124	—	2	1	no	—
94	C₂×C₂²⋊C₄	C₄×C₁₉	1	2	yes	—
95	C₂×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
96	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
97	C₄⋊C₈	—	2	1	no	—
98	C₄⋊C₈	—	2	1	no	—
99	C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
100	C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
101	#97	—	2	1	no	—
102	C₄×C₈	—	2	1	no	—
103	C₁₉	#1469	1	1	yes	characteristic, direct product factor, Sylow
104	C₂⁴	C₂×C₄×C₁₉	1	2	yes	—
105	C₂×Q₈	—	2	1	no	—
106	C₂×Q₈	—	2	1	no	—
107	C₂×Q₈	—	4	2	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	—	2	1	no	—
110	C₂×D₄	—	4	2	no	—
111	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
112	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂×C₄×C₁₉	1	2	yes	—
114	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂²⋊C₄	—	2	2	no	—
118	C₂²⋊C₄	—	2	2	no	—
119	C₂²⋊C₄	—	2	2	no	—
120	C₂²⋊C₄	—	2	2	no	—
121	C₄²	D₄×C₁₉	1	1	yes	characteristic
122	C₄²	D₄×C₁₉	1	1	yes	characteristic
123	C₄²	D₄×C₁₉	1	1	yes	characteristic
124	C₄²	D₄×C₁₉	1	1	yes	characteristic
125	C₂³	—	2	2	no	—
126	C₂³	—	2	4	no	—
127	C₂³	—	4	2	no	—
128	C₂³	—	4	2	no	—
129	C₂³	C₂²×C₄×C₁₉	1	1	yes	characteristic
130	Q₈	—	4	2	no	—
131	Q₈	—	4	2	no	—
132	D₄	—	4	2	no	—
133	D₄	—	4	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	4	1	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
141	C₂×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
142	C₂×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
144	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
145	C₈	—	4	2	no	—
146	C₈	—	4	2	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	4	2	no	—
150	C₂²	—	4	2	no	—
151	C₂²	—	4	2	no	—
152	C₂²	—	8	4	no	—
153	C₂²	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
154	C₂²	C₁₉×#131	1	2	yes	—
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	—	2	1	no	—
158	C₄	—	2	1	no	—
159	C₄	—	2	1	no	—
160	C₄	—	4	2	no	—
161	C₄	C₁₉×#100	1	2	yes	—
162	C₂	—	2	2	no	—
163	C₂	—	8	2	no	—
164	C₂	C₁₉×#408	1	1	yes	characteristic
165	C₂	C₁₉×#410	1	1	yes	characteristic
166	C₂	C₂×C₁₉×#100	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#124

C₂

yes

maximal, characteristic

C₁₉×#432

C₂

yes

maximal, characteristic, complemented

C₁₉×#431

C₂

yes

maximal, characteristic, complemented

C₁₉×#323

C₂

yes

maximal, complemented

C₂²×Q₈×C₁₉

C₄

yes

characteristic

C₂²×D₄×C₁₉

C₄

yes

characteristic

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#124

—

C₂×C₂²⋊C₄×C₁₉

C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂⁴×C₁₉

C₂×C₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

#1469

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#131

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#100

yes

—

C₂×#124

C₂×C₁₉

yes

characteristic

#432

C₂×C₁₉

yes

characteristic, complemented

#431

C₂×C₁₉

yes

characteristic, complemented

#323

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₄×C₁₉

yes

characteristic

C₂²×D₄

C₄×C₁₉

yes

—

—

—

—

C₂×C₂²⋊C₄

C₄×C₁₉

yes

—

C₂×C₂²⋊C₄

C₂²×C₁₉

yes

—

C₂×C₄²

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

C₂²×C₁₉

yes

—

100

C₂²⋊C₈

C₂²×C₁₉

yes

—

101

#97

—

102

C₄×C₈

—

103

C₁₉

#1469

yes

characteristic, direct product factor, Sylow

104

C₂⁴

C₂×C₄×C₁₉

yes

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂²×C₄

C₂×C₄×C₁₉

yes

characteristic

112

C₂²×C₄

C₂×C₄×C₁₉

yes

characteristic

113

C₂²×C₄

C₂×C₄×C₁₉

yes

—

114

C₂²×C₄

C₂³×C₁₉

yes

characteristic

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂²⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

D₄×C₁₉

yes

characteristic

122

C₄²

D₄×C₁₉

yes

characteristic

123

C₄²

D₄×C₁₉

yes

characteristic

124

C₄²

D₄×C₁₉

yes

characteristic

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

C₂²×C₄×C₁₉

yes

characteristic

130

Q₈

—

131

Q₈

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

140

C₂×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

141

C₂×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

142

C₂×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

143

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

144

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

154

C₂²

C₁₉×#131

yes

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

C₁₉×#100

yes

—

162

C₂

—

163

C₂

—

164

C₂

C₁₉×#408

yes

characteristic

165

C₂

C₁₉×#410

yes

characteristic

166

C₂

C₂×C₁₉×#100

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₄×C₁₉

Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

prime radical

C₂²×D₄×C₁₉

C₄

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#432	C₂	semidirect
3. C₁₉×#431	C₂	semidirect
4. C₁₉×#323	C₂	semidirect
63. #1469	C₁₉	direct (N × H)
80. #432	C₂×C₁₉	semidirect
81. #431	C₂×C₁₉	semidirect
82. #323	C₂×C₁₉	semidirect
103. C₁₉	#1469	direct (N × H)

H ≅ G/N

type

2. C₁₉×#432

C₂

semidirect

3. C₁₉×#431

C₂

semidirect

4. C₁₉×#323

C₂

semidirect

63. #1469

C₁₉

direct (N × H)

80. #432

C₂×C₁₉

semidirect

81. #431

C₂×C₁₉

semidirect

82. #323

C₂×C₁₉

semidirect

103. C₁₉

#1469

direct (N × H)

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

subgroup	index
C₂×C₁₉×#124	2
C₁₉×#432	2
C₁₉×#431	2
C₁₉×#323	2
#1469	19

subgroup

index

C₂×C₁₉×#124

C₁₉×#432

C₁₉×#431

C₁₉×#323

#1469

Subgroups — C₁₉×#1469 #14559326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1469 #14559326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1469 #14559326