Group #14560937 — subgroups

Subgroups — C₁₉×#3080 #14560937

Order 2432.

384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#479	C₂	1	4	yes	maximal, complemented
4	C₁₉×#478	C₂	1	4	yes	maximal, complemented
5	C₁₉×#428	C₂	1	2	yes	maximal, complemented
6	C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#417	C₂	1	2	yes	maximal
8	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#125	—	2	1	no	—
11	C₁₉×#125	—	2	1	no	—
12	C₁₉×#125	C₂²	1	4	yes	—
13	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
14	C₄×D₄×C₁₉	—	2	2	no	—
15	C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#117	—	2	1	no	—
17	C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₁₉	—	2	1	no	—
21	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#107	C₂²	1	4	yes	—
23	C₁₉×#106	C₂²	1	4	yes	—
24	C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
25	C₁₉×#103	C₂²	1	4	yes	—
26	C₁₉×#102	C₂²	1	4	yes	—
27	#41×C₁₉	—	2	2	no	—
28	#41×C₁₉	Q₈	1	4	yes	—
29	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×D₄×C₁₉	—	2	1	no	—
31	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	D₄	1	2	yes	—
36	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	M₁₆×C₁₉	—	2	4	no	—
38	C₂×C₈×C₁₉	C₂³	1	4	yes	—
39	C₄⋊C₄×C₁₉	—	2	4	no	—
40	C₄⋊C₄×C₁₉	—	2	4	no	—
41	C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₄⋊C₄×C₁₉	—	2	2	no	—
43	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
44	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
45	C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₂²⋊C₄×C₁₉	—	2	2	no	—
47	C₄²×C₁₉	—	2	1	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	D₄	1	1	yes	characteristic
50	C₄²×C₁₉	D₄	1	1	yes	characteristic
51	C₄²×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₁₉	—	2	1	no	—
53	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
54	Q₈×C₁₉	—	2	1	no	—
55	Q₈×C₁₉	C₂×Q₈	1	2	yes	—
56	D₄×C₁₉	—	2	4	no	—
57	D₄×C₁₉	—	2	1	no	—
58	D₄×C₁₉	C₂×Q₈	1	2	yes	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	4	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	4	4	no	—
65	C₂×C₄×C₁₉	—	4	4	no	—
66	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
70	C₂×C₄×C₁₉	#41	1	2	yes	—
71	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
72	C₈×C₁₉	—	2	4	no	—
73	#3080	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂²×C₁₉	—	2	2	no	—
75	C₂²×C₁₉	—	2	2	no	—
76	C₂²×C₁₉	—	4	2	no	—
77	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
78	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
79	C₄×C₁₉	—	2	2	no	—
80	C₄×C₁₉	—	2	2	no	—
81	C₄×C₁₉	—	2	2	no	—
82	C₄×C₁₉	—	4	2	no	—
83	C₄×C₁₉	—	4	4	no	—
84	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
85	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
86	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
87	C₂×#125	C₂×C₁₉	1	1	yes	characteristic, complemented
88	C₄×#41	C₂×C₁₉	1	1	yes	characteristic
89	#479	C₂×C₁₉	1	4	yes	complemented
90	#478	C₂×C₁₉	1	4	yes	complemented
91	#428	C₂×C₁₉	1	2	yes	complemented
92	#423	C₂×C₁₉	1	1	yes	characteristic, complemented
93	#417	C₂×C₁₉	1	2	yes	—
94	C₂×C₁₉	—	2	2	no	—
95	C₂×C₁₉	—	4	2	no	—
96	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₁₉	#575	1	2	yes	—
98	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
99	C₂×M₁₆	C₂²×C₁₉	1	2	yes	—
100	#125	—	2	1	no	—
101	#125	—	2	1	no	—
102	#125	C₂²×C₁₉	1	4	yes	—
103	C₄×Q₈	C₂²×C₁₉	1	2	yes	—
104	C₄×D₄	—	2	2	no	—
105	C₄×D₄	C₂²×C₁₉	1	2	yes	—
106	#117	—	2	1	no	—
107	#117	C₂²×C₁₉	1	1	yes	characteristic
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
110	C₂×C₄²	—	2	1	no	—
111	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
112	#107	C₂²×C₁₉	1	4	yes	—
113	#106	C₂²×C₁₉	1	4	yes	—
114	C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
115	#103	C₂²×C₁₉	1	4	yes	—
116	#102	C₂²×C₁₉	1	4	yes	—
117	C₁₉	#3080	1	1	yes	characteristic, direct product factor, Sylow
118	#41	—	2	2	no	—
119	#41	Q₈×C₁₉	1	4	yes	—
120	C₂×Q₈	C₂³×C₁₉	1	1	yes	characteristic
121	C₂×D₄	—	2	1	no	—
122	C₂×D₄	C₂³×C₁₉	1	1	yes	characteristic
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	—	2	2	no	—
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	D₄×C₁₉	1	2	yes	—
127	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
128	M₁₆	—	2	4	no	—
129	C₂×C₈	C₂³×C₁₉	1	4	yes	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	2	2	no	—
134	C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
135	C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
136	C₂²⋊C₄	—	2	1	no	—
137	C₂²⋊C₄	—	2	2	no	—
138	C₄²	—	2	1	no	—
139	C₄²	—	2	2	no	—
140	C₄²	D₄×C₁₉	1	1	yes	characteristic
141	C₄²	D₄×C₁₉	1	1	yes	characteristic
142	C₄²	C₂³×C₁₉	1	2	yes	—
143	C₂³	—	2	1	no	—
144	C₂³	C₂×D₄×C₁₉	1	1	yes	characteristic
145	Q₈	—	2	1	no	—
146	Q₈	C₂×Q₈×C₁₉	1	2	yes	—
147	D₄	—	2	4	no	—
148	D₄	—	2	1	no	—
149	D₄	C₂×Q₈×C₁₉	1	2	yes	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	4	2	no	—
155	C₂×C₄	—	4	4	no	—
156	C₂×C₄	—	4	4	no	—
157	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
158	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
159	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
160	C₂×C₄	C₂×Q₈×C₁₉	1	2	yes	—
161	C₂×C₄	#41×C₁₉	1	2	yes	—
162	C₂×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
163	C₈	—	2	4	no	—
164	C₂²	—	2	2	no	—
165	C₂²	—	2	2	no	—
166	C₂²	—	4	2	no	—
167	C₂²	C₁₉×C₂²⋊Q₈	1	2	yes	—
168	C₂²	C₂²×D₄×C₁₉	1	1	yes	characteristic
169	C₄	—	2	2	no	—
170	C₄	—	2	2	no	—
171	C₄	—	2	2	no	—
172	C₄	—	4	2	no	—
173	C₄	—	4	4	no	—
174	C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
175	C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
176	C₄	C₂×#41×C₁₉	1	1	yes	characteristic
177	C₂	—	2	2	no	—
178	C₂	—	4	2	no	—
179	C₂	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
180	C₂	C₁₉×#575	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#125

C₂

yes

maximal, characteristic, complemented

C₄×#41×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#479

C₂

yes

maximal, complemented

C₁₉×#478

C₂

yes

maximal, complemented

C₁₉×#428

C₂

yes

maximal, complemented

C₁₉×#423

C₂

yes

maximal, characteristic, complemented

C₁₉×#417

C₂

yes

maximal

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₂²

yes

—

C₁₉×#117

—

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

—

C₁₉×#106

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#103

C₂²

yes

—

C₁₉×#102

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

Q₈

yes

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

C₂×Q₈

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₈×C₁₉

—

#3080

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

C₂×#125

C₂×C₁₉

yes

characteristic, complemented

C₄×#41

C₂×C₁₉

yes

characteristic

#479

C₂×C₁₉

yes

complemented

#478

C₂×C₁₉

yes

complemented

#428

C₂×C₁₉

yes

complemented

#423

C₂×C₁₉

yes

characteristic, complemented

#417

C₂×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

C₂×C₁₉

#575

yes

—

C₂×#41

C₂²×C₁₉

yes

characteristic

C₂×M₁₆

C₂²×C₁₉

yes

—

100

#125

—

101

#125

—

102

#125

C₂²×C₁₉

yes

—

103

C₄×Q₈

C₂²×C₁₉

yes

—

104

C₄×D₄

—

105

C₄×D₄

C₂²×C₁₉

yes

—

106

#117

—

107

#117

C₂²×C₁₉

yes

characteristic

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

110

C₂×C₄²

—

111

C₂×C₄²

C₂²×C₁₉

yes

characteristic

112

#107

C₂²×C₁₉

yes

—

113

#106

C₂²×C₁₉

yes

—

114

C₄⋊C₈

C₂²×C₁₉

yes

—

115

#103

C₂²×C₁₉

yes

—

116

#102

C₂²×C₁₉

yes

—

117

C₁₉

#3080

yes

characteristic, direct product factor, Sylow

118

#41

—

119

#41

Q₈×C₁₉

yes

—

120

C₂×Q₈

C₂³×C₁₉

yes

characteristic

121

C₂×D₄

—

122

C₂×D₄

C₂³×C₁₉

yes

characteristic

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

D₄×C₁₉

yes

—

127

C₂²×C₄

C₂³×C₁₉

yes

characteristic

128

M₁₆

—

129

C₂×C₈

C₂³×C₁₉

yes

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

C₂³×C₁₉

yes

—

135

C₄⋊C₄

C₂³×C₁₉

yes

—

136

C₂²⋊C₄

—

137

C₂²⋊C₄

—

138

C₄²

—

139

C₄²

—

140

C₄²

D₄×C₁₉

yes

characteristic

141

C₄²

D₄×C₁₉

yes

characteristic

142

C₄²

C₂³×C₁₉

yes

—

143

C₂³

—

144

C₂³

C₂×D₄×C₁₉

yes

characteristic

145

Q₈

—

146

Q₈

C₂×Q₈×C₁₉

yes

—

147

D₄

—

148

D₄

—

149

D₄

C₂×Q₈×C₁₉

yes

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×D₄×C₁₉

yes

—

158

C₂×C₄

C₂×D₄×C₁₉

yes

—

159

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

160

C₂×C₄

C₂×Q₈×C₁₉

yes

—

161

C₂×C₄

#41×C₁₉

yes

—

162

C₂×C₄

C₂⁴×C₁₉

yes

characteristic

163

C₈

—

164

C₂²

—

165

C₂²

—

166

C₂²

—

167

C₂²

C₁₉×C₂²⋊Q₈

yes

—

168

C₂²

C₂²×D₄×C₁₉

yes

characteristic

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

C₁₉×C₂²⋊Q₈

yes

—

175

C₄

C₂²×Q₈×C₁₉

yes

characteristic

176

C₄

C₂×#41×C₁₉

yes

characteristic

177

C₂

—

178

C₂

—

179

C₂

C₂×C₁₉×C₂²⋊Q₈

yes

characteristic

180

C₂

C₁₉×#575

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂²×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₁₉

prime radical

C₂×#41×C₁₉

C₂²

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×#125	C₂	semidirect
3. C₁₉×#479	C₂	semidirect
4. C₁₉×#478	C₂	semidirect
5. C₁₉×#428	C₂	semidirect
6. C₁₉×#423	C₂	semidirect
73. #3080	C₁₉	direct (N × H)
87. C₂×#125	C₂×C₁₉	semidirect
89. #479	C₂×C₁₉	semidirect
90. #478	C₂×C₁₉	semidirect
91. #428	C₂×C₁₉	semidirect
92. #423	C₂×C₁₉	semidirect
117. C₁₉	#3080	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×#125

C₂

semidirect

3. C₁₉×#479

C₂

semidirect

4. C₁₉×#478

C₂

semidirect

5. C₁₉×#428

C₂

semidirect

6. C₁₉×#423

C₂

semidirect

73. #3080

C₁₉

direct (N × H)

87. C₂×#125

C₂×C₁₉

semidirect

89. #479

C₂×C₁₉

semidirect

90. #478

C₂×C₁₉

semidirect

91. #428

C₂×C₁₉

semidirect

92. #423

C₂×C₁₉

semidirect

117. C₁₉

#3080

direct (N × H)

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

subgroup	index
C₂×C₁₉×#125	2
C₄×#41×C₁₉	2
C₁₉×#479	2
C₁₉×#478	2
C₁₉×#428	2
C₁₉×#423	2
C₁₉×#417	2
#3080	19

subgroup

index

C₂×C₁₉×#125

C₄×#41×C₁₉

C₁₉×#479

C₁₉×#478

C₁₉×#428

C₁₉×#423

C₁₉×#417

#3080

Subgroups — C₁₉×#3080 #14560937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#3080 #14560937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#3080 #14560937