Group #14564728 — subgroups

Subgroups — #14564728

Order 2432.

390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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×#64528	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#64527	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597321	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597267	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597266	C₂	1	1	yes	maximal, characteristic
6	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×#64528	—	2	2	no	—
14	C₂×#64528	—	2	2	no	—
15	C₂×#64528	—	2	2	no	—
16	C₂×#64527	—	2	2	no	—
17	C₂×#64527	—	2	2	no	—
18	C₂×#64527	—	2	2	no	—
19	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
20	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	#10597321	—	2	2	no	—
23	#10597321	—	2	2	no	—
24	C₁₉×#95	—	2	2	no	—
25	#10597267	—	2	2	no	—
26	#10597266	—	2	2	no	—
27	C₂³×D₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	—	2	1	no	—
29	C₂×Q₈×C₁₉	—	2	1	no	—
30	C₂×Q₈×C₁₉	—	2	1	no	—
31	C₂×Q₈×C₁₉	—	2	1	no	—
32	C₂×Q₈×C₁₉	—	2	1	no	—
33	C₂×Q₈×C₁₉	D₄	1	2	yes	—
34	C₂²×C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄×C₁₉	—	2	1	no	—
36	C₂²×C₄×C₁₉	D₄	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×Dic₁₉	—	2	1	no	—
39	C₂×D₇₆	—	2	1	no	—
40	C₂×D₇₆	—	2	1	no	—
41	C₂×D₇₆	—	2	1	no	—
42	C₂×D₇₆	—	2	1	no	—
43	C₂×D₇₆	—	2	1	no	—
44	C₂×D₇₆	D₄	1	2	yes	—
45	C₂×Dic₃₈	—	2	1	no	—
46	C₂×Dic₃₈	—	2	1	no	—
47	C₂×Dic₃₈	—	2	1	no	—
48	C₂×Dic₃₈	—	2	1	no	—
49	C₂×Dic₃₈	—	2	1	no	—
50	C₂×Dic₃₈	D₄	1	2	yes	—
51	C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₄²×C₁₉	—	2	1	no	—
54	C₄²×C₁₉	—	2	1	no	—
55	#64528	—	2	8	no	—
56	#64527	—	2	8	no	—
57	(C₂×D₁₉)⋊C₄	—	2	8	no	—
58	C₂×C₁₉⋊C₈	—	2	1	no	—
59	C₂×C₁₉⋊C₈	—	2	1	no	—
60	C₂×C₁₉⋊C₈	—	2	1	no	—
61	C₂×C₁₉⋊C₈	—	2	1	no	—
62	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
63	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
64	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×D₁₉	—	2	2	no	—
66	C₂²×D₁₉	—	4	1	no	—
67	C₂²×D₁₉	—	4	1	no	—
68	C₂²×D₁₉	—	4	2	no	—
69	C₂²×D₁₉	—	4	2	no	—
70	Q₈×C₁₉	—	2	2	no	—
71	Q₈×C₁₉	—	2	2	no	—
72	Q₈×C₁₉	—	4	1	no	—
73	Q₈×C₁₉	—	4	1	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	4	1	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂×Dic₁₉	—	2	2	no	—
89	C₂×Dic₁₉	—	4	1	no	—
90	C₂×Dic₁₉	—	4	1	no	—
91	D₇₆	—	2	2	no	—
92	D₇₆	—	2	2	no	—
93	D₇₆	—	4	1	no	—
94	D₇₆	—	4	1	no	—
95	Dic₃₈	—	2	2	no	—
96	Dic₃₈	—	2	2	no	—
97	Dic₃₈	—	4	1	no	—
98	Dic₃₈	—	4	1	no	—
99	C₁₉⋊C₈	—	2	2	no	—
100	C₁₉⋊C₈	—	2	2	no	—
101	#2015	—	19	1	no	maximal, Sylow
102	C₂²×C₁₉	#120	1	1	yes	characteristic
103	C₂²×C₁₉	#121	1	1	yes	characteristic
104	C₂²×C₁₉	#127	1	1	yes	characteristic
105	C₂²×C₁₉	#135	1	2	yes	—
106	C₂²×C₁₉	#137	1	2	yes	—
107	C₂×D₁₉	—	4	2	no	—
108	C₂×D₁₉	—	4	4	no	—
109	C₂×D₁₉	—	8	2	no	—
110	C₂×D₁₉	—	8	1	no	—
111	C₂×D₁₉	—	8	1	no	—
112	C₄×C₁₉	—	4	2	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	8	1	no	—
115	C₄×C₁₉	#120	1	1	yes	characteristic
116	C₄×C₁₉	#120	1	1	yes	characteristic
117	C₄×C₁₉	#121	1	1	yes	characteristic
118	C₄×C₁₉	#121	1	1	yes	characteristic
119	Dic₁₉	—	4	2	no	—
120	C₂²×Q₁₆	—	19	1	no	—
121	C₂²×SD₁₆	—	19	1	no	—
122	C₂×#124	—	19	1	no	—
123	C₂×#103	—	19	1	no	—
124	C₂×#102	—	19	1	no	—
125	#391	D₁₉	1	1	yes	characteristic, complemented
126	#336	—	19	1	no	—
127	C₂×C₁₉	#392	1	1	yes	characteristic
128	C₂×C₁₉	#452	1	2	yes	—
129	C₂×C₁₉	#464	1	2	yes	—
130	C₂×C₁₉	#495	1	1	yes	characteristic
131	C₂×C₁₉	#497	1	1	yes	characteristic
132	D₁₉	—	8	2	no	—
133	C₂²×Q₈	—	19	1	no	—
134	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
135	C₂²×D₄	—	19	1	no	—
136	C₂×Q₁₆	—	38	2	no	—
137	C₂×Q₁₆	—	38	2	no	—
138	C₂×Q₁₆	—	38	2	no	—
139	C₂×SD₁₆	—	38	2	no	—
140	C₂×SD₁₆	—	38	2	no	—
141	C₂×SD₁₆	—	38	2	no	—
142	C₂²×C₈	—	19	1	no	—
143	C₂²×C₈	—	19	1	no	—
144	#124	—	38	2	no	—
145	#124	—	38	2	no	—
146	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
147	C₂×C₂²⋊C₄	—	38	2	no	—
148	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
149	#103	—	38	2	no	—
150	#102	—	38	2	no	—
151	#95	—	2	2	no	—
152	C₁₉	#2015	1	1	yes	characteristic, complemented, Sylow
153	C₂⁴	—	38	1	no	—
154	C₂×Q₈	—	2	1	no	—
155	C₂×Q₈	—	2	1	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	19	2	no	—
160	C₂×Q₈	—	38	1	no	—
161	C₂×Q₈	—	38	1	no	—
162	C₂×Q₈	—	38	1	no	—
163	C₂×Q₈	—	38	1	no	—
164	C₂×Q₈	—	38	1	no	—
165	C₂×Q₈	D₇₆	1	2	yes	—
166	C₂×D₄	—	19	2	no	—
167	C₂×D₄	—	38	1	no	—
168	C₂×D₄	—	38	1	no	—
169	C₂×D₄	—	38	1	no	—
170	C₂×D₄	—	38	1	no	—
171	C₂×D₄	—	38	1	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	38	1	no	—
175	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
176	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
177	Q₁₆	—	38	8	no	—
178	SD₁₆	—	38	8	no	—
179	C₂×C₈	—	19	2	no	—
180	C₂×C₈	—	19	2	no	—
181	C₂×C₈	—	38	1	no	—
182	C₂×C₈	—	38	1	no	—
183	C₂×C₈	—	38	1	no	—
184	C₂×C₈	—	38	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	2	1	no	—
187	C₂²⋊C₄	—	38	8	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	1	no	—
190	C₂³	—	38	2	no	—
191	C₂³	—	76	1	no	—
192	C₂³	—	76	1	no	—
193	C₂³	—	76	2	no	—
194	C₂³	—	76	2	no	—
195	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
196	Q₈	—	2	2	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	4	1	no	—
199	Q₈	—	4	1	no	—
200	Q₈	—	38	2	no	—
201	Q₈	—	38	2	no	—
202	Q₈	—	76	1	no	—
203	Q₈	—	76	1	no	—
204	D₄	—	38	2	no	—
205	D₄	—	38	2	no	—
206	D₄	—	76	1	no	—
207	D₄	—	76	1	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	38	2	no	—
217	C₂×C₄	—	76	1	no	—
218	C₂×C₄	—	76	1	no	—
219	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
220	C₂×C₄	#64541	1	1	yes	characteristic
221	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
222	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
223	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
224	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₈	—	38	2	no	—
226	C₈	—	38	2	no	—
227	C₂²	—	76	4	no	—
228	C₂²	—	76	2	no	—
229	C₂²	—	152	1	no	—
230	C₂²	—	152	1	no	—
231	C₂²	—	152	2	no	—
232	C₂²	#10597376	1	1	yes	characteristic
233	C₂²	#10597383	1	1	yes	characteristic
234	C₂²	#10597386	1	1	yes	characteristic
235	C₂²	#10597388	1	2	yes	—
236	C₂²	#10597396	1	2	yes	—
237	C₄	—	4	2	no	—
238	C₄	—	4	2	no	—
239	C₄	—	8	1	no	—
240	C₄	—	76	2	no	—
241	C₄	#10597328	1	1	yes	characteristic
242	C₄	#10597328	1	1	yes	characteristic
243	C₄	#10597330	1	1	yes	characteristic
244	C₄	#10597330	1	1	yes	characteristic
245	C₂	—	152	2	no	—
246	C₂	#11926453	1	1	yes	characteristic
247	C₂	#11926704	1	2	yes	—
248	C₂	#11926766	1	2	yes	—
249	C₂	#11926926	1	1	yes	characteristic
250	C₂	#11926936	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal, characteristic, complemented

C₂²×#64527

C₂

yes

maximal, characteristic

C₂×#10597321

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal, characteristic, complemented

C₂×#10597266

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#391

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

—

—

—

—

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597321

—

#10597321

—

C₁₉×#95

—

#10597267

—

#10597266

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#64528

—

#64527

—

(C₂×D₁₉)⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

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×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

—

101

#2015

—

maximal, Sylow

102

C₂²×C₁₉

#120

yes

characteristic

103

C₂²×C₁₉

#121

yes

characteristic

104

C₂²×C₁₉

#127

yes

characteristic

105

C₂²×C₁₉

#135

yes

—

106

C₂²×C₁₉

#137

yes

—

107

C₂×D₁₉

—

108

C₂×D₁₉

—

109

C₂×D₁₉

—

110

C₂×D₁₉

—

111

C₂×D₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#120

yes

characteristic

116

C₄×C₁₉

#120

yes

characteristic

117

C₄×C₁₉

#121

yes

characteristic

118

C₄×C₁₉

#121

yes

characteristic

119

Dic₁₉

—

120

C₂²×Q₁₆

—

121

C₂²×SD₁₆

—

122

C₂×#124

—

123

C₂×#103

—

124

C₂×#102

—

125

#391

D₁₉

yes

characteristic, complemented

126

#336

—

127

C₂×C₁₉

#392

yes

characteristic

128

C₂×C₁₉

#452

yes

—

129

C₂×C₁₉

#464

yes

—

130

C₂×C₁₉

#495

yes

characteristic

131

C₂×C₁₉

#497

yes

characteristic

132

D₁₉

—

133

C₂²×Q₈

—

134

C₂²×Q₈

C₂×D₁₉

yes

characteristic

135

C₂²×D₄

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

#124

—

145

#124

—

146

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

147

C₂×C₂²⋊C₄

—

148

C₂×C₄²

C₂×D₁₉

yes

characteristic

149

#103

—

150

#102

—

151

#95

—

152

C₁₉

#2015

yes

characteristic, complemented, Sylow

153

C₂⁴

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

D₇₆

yes

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊D₁₉

yes

—

176

C₂²×C₄

C₂²×D₁₉

yes

characteristic

177

Q₁₆

—

178

SD₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

D₄

—

205

D₄

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

C₂×D₇₆

yes

characteristic

220

C₂×C₄

#64541

yes

characteristic

221

C₂×C₄

D₄×D₁₉

yes

characteristic

222

C₂×C₄

D₄×D₁₉

yes

characteristic

223

C₂×C₄

D₄×D₁₉

yes

characteristic

224

C₂×C₄

D₄×D₁₉

yes

characteristic

225

C₈

—

226

C₈

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

152

—

230

C₂²

—

152

—

231

C₂²

—

152

—

232

C₂²

#10597376

yes

characteristic

233

C₂²

#10597383

yes

characteristic

234

C₂²

#10597386

yes

characteristic

235

C₂²

#10597388

yes

—

236

C₂²

#10597396

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

#10597328

yes

characteristic

242

C₄

#10597328

yes

characteristic

243

C₄

#10597330

yes

characteristic

244

C₄

#10597330

yes

characteristic

245

C₂

—

152

—

246

C₂

#11926453

yes

characteristic

247

C₂

#11926704

yes

—

248

C₂

#11926766

yes

—

249

C₂

#11926926

yes

characteristic

250

C₂

#11926936

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₇₆	C₂²
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2015
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
1. C₂²×#64528	C₂	semidirect
4. C₂×#10597267	C₂	semidirect
6. #11926299	C₂	semidirect
7. C₁₉×#391	C₂	semidirect
125. #391	D₁₉	semidirect
152. C₁₉	#2015	semidirect

H ≅ G/N

type

1. C₂²×#64528

C₂

semidirect

4. C₂×#10597267

C₂

semidirect

6. #11926299

C₂

semidirect

7. C₁₉×#391

C₂

semidirect

125. #391

D₁₉

semidirect

152. C₁₉

#2015

semidirect

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

subgroup	index
C₂²×#64528	2
C₂²×#64527	2
C₂×#10597321	2
C₂×#10597267	2
C₂×#10597266	2
#11926299	2
C₁₉×#391	2
#2015	19

subgroup

index

C₂²×#64528

C₂²×#64527

C₁₉×#391

Subgroups — #14564728

Conjugacy classes of subgroups

Complements

Maximal subgroups