Group #14564498 — subgroups

Subgroups — #14564498

Order 2432.

384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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	C₂²×#64525	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597264	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597278	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926447	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926445	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
13	C₂×#64525	—	2	2	no	—
14	C₂×#64525	—	2	2	no	—
15	C₂×#64525	C₄	1	4	yes	complemented
16	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₉×#102	—	2	2	no	—
21	#10597278	—	2	2	no	—
22	C₈×Dic₁₉	—	2	2	no	—
23	#10597264	—	2	2	no	—
24	C₂⁴×C₁₉	—	2	1	no	—
25	C₂³×D₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	1	no	—
28	C₂×D₄×C₁₉	—	2	1	no	—
29	C₂×D₄×C₁₉	—	2	1	no	—
30	C₂×D₄×C₁₉	—	2	1	no	—
31	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₉	—	2	1	no	—
35	C₂²×Dic₁₉	D₄	1	2	yes	—
36	C₂×D₇₆	—	2	1	no	—
37	C₂×D₇₆	—	2	1	no	—
38	C₂×D₇₆	—	2	1	no	—
39	C₂×D₇₆	—	2	1	no	—
40	C₂×D₇₆	—	2	1	no	—
41	C₂×D₇₆	C₂×C₄	1	2	yes	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₂×C₈×C₁₉	D₄	1	2	yes	—
45	C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂²⋊Dic₁₉	—	4	4	no	—
48	#64525	—	2	8	no	—
49	(C₂×D₁₉)⋊C₄	—	4	4	no	—
50	C₄⋊Dic₁₉	—	2	1	no	—
51	C₄⋊Dic₁₉	—	2	1	no	—
52	C₄×Dic₁₉	—	2	1	no	—
53	C₄×Dic₁₉	—	2	1	no	—
54	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
55	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
57	C₂³×C₁₉	—	2	2	no	—
58	C₂³×C₁₉	—	4	1	no	—
59	C₂³×C₁₉	—	4	1	no	—
60	C₂³×C₁₉	—	4	2	no	—
61	C₂³×C₁₉	—	4	2	no	—
62	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×D₁₉	—	2	2	no	—
64	C₂²×D₁₉	—	4	1	no	—
65	C₂²×D₁₉	—	4	1	no	—
66	C₂²×D₁₉	—	4	2	no	—
67	C₂²×D₁₉	—	4	2	no	—
68	D₄×C₁₉	—	2	2	no	—
69	D₄×C₁₉	—	2	2	no	—
70	D₄×C₁₉	—	4	1	no	—
71	D₄×C₁₉	—	4	1	no	—
72	C₂×C₄×C₁₉	—	4	1	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
80	C₂×Dic₁₉	—	2	2	no	—
81	C₂×Dic₁₉	—	2	2	no	—
82	C₂×Dic₁₉	—	4	1	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	D₈	1	4	yes	complemented
85	D₇₆	—	2	2	no	—
86	D₇₆	—	2	2	no	—
87	D₇₆	—	4	1	no	—
88	D₇₆	—	4	1	no	—
89	C₈×C₁₉	—	2	2	no	—
90	C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	complemented
91	#1970	—	19	1	no	maximal, Sylow
92	C₂²×C₁₉	—	4	2	no	—
93	C₂²×C₁₉	—	4	4	no	—
94	C₂²×C₁₉	—	8	2	no	—
95	C₂²×C₁₉	—	8	1	no	—
96	C₂²×C₁₉	—	8	1	no	—
97	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
98	C₂²×C₁₉	#121	1	1	yes	characteristic
99	C₂²×C₁₉	#127	1	1	yes	characteristic
100	C₂²×C₁₉	C₂×D₈	1	2	yes	—
101	C₂²×C₁₉	#135	1	2	yes	—
102	C₂×D₁₉	—	4	2	no	—
103	C₂×D₁₉	—	4	4	no	—
104	C₂×D₁₉	—	8	2	no	—
105	C₂×D₁₉	—	8	1	no	—
106	C₂×D₁₉	—	8	1	no	—
107	C₄×C₁₉	—	8	1	no	—
108	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
110	C₄×C₁₉	#121	1	1	yes	characteristic
111	C₄×C₁₉	#124	1	1	yes	characteristic
112	Dic₁₉	—	2	4	no	—
113	Dic₁₉	—	8	1	no	—
114	C₂²×D₈	—	19	1	no	—
115	C₂×#107	—	19	1	no	—
116	C₂×#102	—	19	1	no	—
117	C₂×#102	D₁₉	1	1	yes	characteristic, complemented
118	C₂×C₄×C₈	—	19	1	no	—
119	#390	—	19	1	no	—
120	#390	—	19	1	no	—
121	C₂×C₁₉	—	8	2	no	—
122	C₂×C₁₉	#390	1	1	yes	characteristic
123	C₂×C₁₉	C₄×D₈	1	2	yes	—
124	C₂×C₁₉	#466	1	2	yes	—
125	C₂×C₁₉	#493	1	1	yes	characteristic
126	C₂×C₁₉	#495	1	1	yes	characteristic
127	D₁₉	—	8	2	no	—
128	C₂²×D₄	—	19	1	no	—
129	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
130	C₂×D₈	—	19	4	no	—
131	C₂×D₈	—	38	2	no	—
132	C₂×D₈	—	38	2	no	—
133	C₂²×C₈	—	19	1	no	—
134	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
135	C₂×C₄⋊C₄	—	19	1	no	—
136	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
137	C₂×C₂²⋊C₄	—	38	2	no	—
138	C₂×C₂²⋊C₄	—	38	2	no	—
139	C₂×C₄²	—	19	1	no	—
140	#107	—	38	2	no	—
141	#102	—	2	2	no	—
142	#102	—	38	2	no	—
143	C₄×C₈	—	38	2	no	—
144	C₁₉	#1970	1	1	yes	characteristic, complemented, Sylow
145	C₂⁴	—	2	1	no	—
146	C₂⁴	—	38	1	no	—
147	C₂×D₄	—	2	1	no	—
148	C₂×D₄	—	2	1	no	—
149	C₂×D₄	—	2	1	no	—
150	C₂×D₄	—	2	1	no	—
151	C₂×D₄	—	2	1	no	—
152	C₂×D₄	—	19	2	no	—
153	C₂×D₄	—	38	1	no	—
154	C₂×D₄	—	38	1	no	—
155	C₂×D₄	—	38	1	no	—
156	C₂×D₄	—	38	1	no	—
157	C₂×D₄	—	38	1	no	—
158	C₂×D₄	C₄×D₁₉	1	2	yes	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	19	2	no	—
161	C₂²×C₄	—	38	1	no	—
162	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
163	D₈	—	38	8	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	19	2	no	—
167	C₂×C₈	—	19	2	no	—
168	C₂×C₈	—	19	2	no	—
169	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	1	no	—
172	C₄⋊C₄	—	38	1	no	—
173	C₄⋊C₄	—	38	1	no	—
174	C₂²⋊C₄	—	76	4	no	—
175	C₂²⋊C₄	—	76	4	no	—
176	C₄²	—	38	1	no	—
177	C₄²	—	38	1	no	—
178	C₂³	—	2	2	no	—
179	C₂³	—	4	1	no	—
180	C₂³	—	4	1	no	—
181	C₂³	—	4	2	no	—
182	C₂³	—	4	2	no	—
183	C₂³	—	38	2	no	—
184	C₂³	—	76	1	no	—
185	C₂³	—	76	1	no	—
186	C₂³	—	76	2	no	—
187	C₂³	—	76	2	no	—
188	C₂³	D₄×D₁₉	1	1	yes	characteristic
189	D₄	—	2	2	no	—
190	D₄	—	2	2	no	—
191	D₄	—	4	1	no	—
192	D₄	—	4	1	no	—
193	D₄	—	38	2	no	—
194	D₄	—	38	2	no	—
195	D₄	—	76	1	no	—
196	D₄	—	76	1	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	19	4	no	—
200	C₂×C₄	—	38	2	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	—	76	2	no	—
204	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
205	C₂×C₄	#64541	1	1	yes	characteristic
206	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
207	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
208	C₂×C₄	#64543	1	1	yes	characteristic
209	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
210	C₈	—	2	2	no	—
211	C₈	—	19	4	no	—
212	C₂²	—	4	4	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	8	1	no	—
215	C₂²	—	8	1	no	—
216	C₂²	—	8	2	no	—
217	C₂²	—	76	4	no	—
218	C₂²	—	76	2	no	—
219	C₂²	—	152	1	no	—
220	C₂²	—	152	1	no	—
221	C₂²	—	152	2	no	—
222	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
223	C₂²	#10597330	1	1	yes	characteristic
224	C₂²	D₈×D₁₉	1	2	yes	—
225	C₂²	#10597362	1	2	yes	—
226	C₂²	#10597386	1	1	yes	characteristic
227	C₄	—	8	1	no	—
228	C₄	—	38	4	no	—
229	C₄	—	152	1	no	—
230	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
231	C₄	#10597331	1	1	yes	characteristic
232	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
233	C₄	#10597385	1	1	yes	characteristic
234	C₂	—	8	2	no	—
235	C₂	—	152	2	no	—
236	C₂	#11926444	1	1	yes	characteristic
237	C₂	#11926624	1	2	yes	—
238	C₂	#11926779	1	2	yes	—
239	C₂	#11926919	1	1	yes	characteristic
240	C₂	#11926925	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64525

C₂

yes

maximal, characteristic

C₂×#10597264

C₂

yes

maximal, characteristic, complemented

C₂×#10597278

C₂

yes

maximal, characteristic, complemented

C₂×C₈×Dic₁₉

C₂

yes

maximal, characteristic, complemented

#11926447

C₂

yes

maximal, characteristic, complemented

#11926445

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#102

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×#64525

—

C₂×#64525

—

C₂×#64525

C₄

yes

complemented

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#102

—

#10597278

—

C₈×Dic₁₉

—

#10597264

—

C₂⁴×C₁₉

—

C₂³×D₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

#64525

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

complemented

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

C₂²⋊C₄

yes

complemented

#1970

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

100

C₂²×C₁₉

C₂×D₈

yes

—

101

C₂²×C₁₉

#135

yes

—

102

C₂×D₁₉

—

103

C₂×D₁₉

—

104

C₂×D₁₉

—

105

C₂×D₁₉

—

106

C₂×D₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

109

C₄×C₁₉

C₄×D₄

yes

characteristic

110

C₄×C₁₉

#121

yes

characteristic

111

C₄×C₁₉

#124

yes

characteristic

112

Dic₁₉

—

113

Dic₁₉

—

114

C₂²×D₈

—

115

C₂×#107

—

116

C₂×#102

—

117

C₂×#102

D₁₉

yes

characteristic, complemented

118

C₂×C₄×C₈

—

119

#390

—

120

#390

—

121

C₂×C₁₉

—

122

C₂×C₁₉

#390

yes

characteristic

123

C₂×C₁₉

C₄×D₈

yes

—

124

C₂×C₁₉

#466

yes

—

125

C₂×C₁₉

#493

yes

characteristic

126

C₂×C₁₉

#495

yes

characteristic

127

D₁₉

—

128

C₂²×D₄

—

129

C₂²×D₄

C₂×D₁₉

yes

characteristic

130

C₂×D₈

—

131

C₂×D₈

—

132

C₂×D₈

—

133

C₂²×C₈

—

134

C₂²×C₈

C₂×D₁₉

yes

characteristic

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

137

C₂×C₂²⋊C₄

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₄²

—

140

#107

—

141

#102

—

142

#102

—

143

C₄×C₈

—

144

C₁₉

#1970

yes

characteristic, complemented, Sylow

145

C₂⁴

—

146

C₂⁴

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

C₄×D₁₉

yes

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂²×D₁₉

yes

characteristic

163

D₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

C₂²⋊D₁₉

yes

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₂²⋊C₄

—

175

C₂²⋊C₄

—

176

C₄²

—

177

C₄²

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

D₄×D₁₉

yes

characteristic

189

D₄

—

190

D₄

—

191

D₄

—

192

D₄

—

193

D₄

—

194

D₄

—

195

D₄

—

196

D₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

205

C₂×C₄

#64541

yes

characteristic

206

C₂×C₄

D₄×D₁₉

yes

characteristic

207

C₂×C₄

D₄×D₁₉

yes

characteristic

208

C₂×C₄

#64543

yes

characteristic

209

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

210

C₈

—

211

C₈

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

152

—

220

C₂²

—

152

—

221

C₂²

—

152

—

222

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

223

C₂²

#10597330

yes

characteristic

224

C₂²

D₈×D₁₉

yes

—

225

C₂²

#10597362

yes

—

226

C₂²

#10597386

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

152

—

230

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

231

C₄

#10597331

yes

characteristic

232

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

233

C₄

#10597385

yes

characteristic

234

C₂

—

235

C₂

—

152

—

236

C₂

#11926444

yes

characteristic

237

C₂

#11926624

yes

—

238

C₂

#11926779

yes

—

239

C₂

#11926919

yes

characteristic

240

C₂

#11926925

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#102	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×#64525	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#102	D₁₉
hypocenter	C₁₉	#1970
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#102

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×#64525

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#102

N	H ≅ G/N	type
2. C₂×#10597264	C₂	semidirect
3. C₂×#10597278	C₂	semidirect
4. C₂×C₈×Dic₁₉	C₂	semidirect
5. #11926447	C₂	semidirect
6. #11926445	C₂	semidirect
7. C₂×C₁₉×#102	C₂	semidirect
15. C₂×#64525	C₄	semidirect
84. C₂×Dic₁₉	D₈	semidirect
90. C₁₉⋊C₈	C₂²⋊C₄	semidirect
117. C₂×#102	D₁₉	semidirect
144. C₁₉	#1970	semidirect

H ≅ G/N

type

2. C₂×#10597264

C₂

semidirect

3. C₂×#10597278

C₂

semidirect

4. C₂×C₈×Dic₁₉

C₂

semidirect

5. #11926447

C₂

semidirect

6. #11926445

C₂

semidirect

7. C₂×C₁₉×#102

C₂

semidirect

15. C₂×#64525

C₄

semidirect

84. C₂×Dic₁₉

D₈

semidirect

90. C₁₉⋊C₈

C₂²⋊C₄

semidirect

117. C₂×#102

D₁₉

semidirect

144. C₁₉

#1970

semidirect

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

subgroup	index
C₂²×#64525	2
C₂×#10597264	2
C₂×#10597278	2
C₂×C₈×Dic₁₉	2
#11926447	2
#11926445	2
C₂×C₁₉×#102	2
#1970	19

subgroup

index

C₂²×#64525

C₂×C₈×Dic₁₉

C₂×C₁₉×#102

Subgroups — #14564498

Conjugacy classes of subgroups

Complements

Maximal subgroups