Group #18075491 — subgroups

Subgroups — #18075491

Order 4864.

450 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 113 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×D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14562396	C₂	1	2	yes	maximal, complemented
3	#14561976	C₂	1	1	yes	maximal, characteristic
4	#14561504	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1466	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₁₉⋊C₈	C₄	1	2	yes	—
7	D₄×C₁₉⋊C₈	—	2	2	no	—
8	D₄×C₁₉⋊C₈	—	2	2	no	—
9	#11926601	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926268	—	2	2	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#432	C₂²	1	2	yes	—
18	C₁₉×#323	—	2	2	no	—
19	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₄×D₄×C₁₉	—	2	2	no	—
22	C₄×D₄×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₂²×C₁₉⋊C₈	—	4	4	no	—
29	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
31	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×#97	—	2	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
36	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	#10597260	—	2	2	no	—
40	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
41	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
42	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
43	C₂×D₄×C₁₉	—	2	4	no	—
44	C₂×D₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	4	2	no	—
48	C₂²×C₄×C₁₉	—	4	2	no	—
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂²⋊C₄×C₁₉	—	2	4	no	—
56	C₄²×C₁₉	C₂×D₄	1	2	yes	—
57	C₄²×C₁₉	#41	1	2	yes	—
58	C₂×C₁₉⋊C₈	—	2	2	no	—
59	C₂×C₁₉⋊C₈	—	2	2	no	—
60	C₂×C₁₉⋊C₈	—	4	1	no	—
61	C₂×C₁₉⋊C₈	—	4	4	no	—
62	C₂×C₁₉⋊C₈	—	4	4	no	—
63	C₂×C₁₉⋊C₈	—	4	2	no	—
64	C₂×C₁₉⋊C₈	—	4	2	no	—
65	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
66	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
68	#8622	—	19	1	no	maximal, Sylow
69	C₂³×C₁₉	—	2	2	no	—
70	C₂³×C₁₉	—	2	2	no	—
71	C₂³×C₁₉	—	4	2	no	—
72	C₂³×C₁₉	—	4	2	no	—
73	C₂³×C₁₉	#108	1	4	yes	—
74	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
75	D₄×C₁₉	—	2	8	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	4	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
89	C₈×C₁₉	—	8	2	no	—
90	C₁₉⋊C₈	—	2	1	no	—
91	C₁₉⋊C₈	—	2	2	no	—
92	C₁₉⋊C₈	—	4	2	no	—
93	C₁₉⋊C₈	—	8	2	no	—
94	C₁₉⋊C₈	#100	1	2	yes	—
95	C₂×C₈×D₄	—	19	1	no	—
96	#1568	—	19	2	no	—
97	#1466	—	19	1	no	—
98	#1466	D₁₉	1	1	yes	characteristic
99	#1290	—	19	2	no	—
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	4	no	—
103	C₂²×C₁₉	—	4	4	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	—	4	2	no	—
106	C₂²×C₁₉	—	4	2	no	—
107	C₂²×C₁₉	#380	1	1	yes	characteristic
108	C₂²×C₁₉	C₂×#108	1	2	yes	—
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	4	2	no	—
113	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
114	C₄×C₁₉	#413	1	1	yes	characteristic
115	C₂³×C₈	—	19	2	no	—
116	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
117	C₈×D₄	—	38	2	no	—
118	C₈×D₄	—	38	2	no	—
119	#432	—	19	2	no	—
120	#432	C₂×D₁₉	1	2	yes	—
121	C₂×C₄⋊C₈	—	19	1	no	—
122	C₂×C₂²⋊C₈	—	19	2	no	—
123	C₂×C₄×C₈	—	19	1	no	—
124	#335	—	38	2	no	—
125	#334	—	38	2	no	—
126	#323	—	2	2	no	—
127	#323	—	38	2	no	—
128	C₂×C₁₉	—	2	2	no	—
129	C₂×C₁₉	—	4	4	no	—
130	C₂×C₁₉	#1800	1	1	yes	characteristic
131	C₂×C₁₉	#1810	1	1	yes	characteristic
132	C₂×C₁₉	#1812	1	1	yes	characteristic
133	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
134	C₂³×C₄	C₄×D₁₉	1	2	yes	—
135	C₂²×C₈	—	19	1	no	—
136	C₂²×C₈	—	19	1	no	—
137	C₂²×C₈	—	19	2	no	—
138	C₂²×C₈	—	38	2	no	—
139	C₂²×C₈	—	38	2	no	—
140	C₂²×C₈	—	76	4	no	—
141	C₄×D₄	—	2	2	no	—
142	C₄×D₄	—	2	2	no	—
143	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
144	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
145	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	—	38	2	no	—
149	C₂²⋊C₈	—	2	2	no	—
150	C₂²⋊C₈	—	38	4	no	—
151	C₂²⋊C₈	—	38	2	no	—
152	#97	—	2	2	no	—
153	#97	—	38	2	no	—
154	C₄×C₈	—	19	2	no	—
155	C₄×C₈	—	19	2	no	—
156	C₁₉	#8622	1	1	yes	characteristic, complemented, Sylow
157	C₂⁴	Dic₁₉⋊C₄	1	2	yes	—
158	C₂×D₄	—	2	4	no	—
159	C₂×D₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
165	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	19	1	no	—
170	C₂×C₈	—	19	2	no	—
171	C₂×C₈	—	19	1	no	—
172	C₂×C₈	—	38	2	no	—
173	C₂×C₈	—	38	2	no	—
174	C₂×C₈	—	76	4	no	—
175	C₂×C₈	—	76	1	no	—
176	C₂×C₈	—	76	4	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	—	76	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₂²⋊C₄	—	2	4	no	—
181	C₄²	D₄×D₁₉	1	2	yes	—
182	C₄²	#64543	1	2	yes	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	2	no	—
186	C₂³	—	4	2	no	—
187	C₂³	#10597279	1	4	yes	—
188	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
189	D₄	—	2	8	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#10597323	1	1	yes	characteristic
200	C₂×C₄	#10597324	1	2	yes	—
201	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
202	C₂×C₄	#10597385	1	2	yes	—
203	C₈	—	8	2	no	—
204	C₈	—	19	2	no	—
205	C₈	—	38	1	no	—
206	C₈	—	38	2	no	—
207	C₈	—	76	2	no	—
208	C₈	—	152	2	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	4	no	—
212	C₂²	—	4	4	no	—
213	C₂²	—	4	4	no	—
214	C₂²	—	4	2	no	—
215	C₂²	—	4	2	no	—
216	C₂²	#11926402	1	1	yes	characteristic
217	C₂²	C₂×#10597279	1	2	yes	—
218	C₄	—	2	1	no	—
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	#100×D₁₉	1	1	yes	characteristic
223	C₄	#11926525	1	1	yes	characteristic
224	C₂	—	2	2	no	—
225	C₂	—	4	4	no	—
226	C₂	#14563625	1	1	yes	characteristic
227	C₂	#14563671	1	1	yes	characteristic
228	C₂	#14563679	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#14562396

C₂

yes

maximal, complemented

#14561976

C₂

yes

maximal, characteristic

#14561504

C₂

yes

maximal, complemented

C₁₉×#1466

C₂

yes

maximal, characteristic

C₂³×C₁₉⋊C₈

C₄

yes

—

D₄×C₁₉⋊C₈

—

D₄×C₁₉⋊C₈

—

#11926601

C₂²

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#432

C₂²

yes

—

C₁₉×#323

—

C₂²×D₄×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8622

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#108

yes

—

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

D₄×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×C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#100

yes

—

C₂×C₈×D₄

—

#1568

—

#1466

—

#1466

D₁₉

yes

characteristic

#1290

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

#380

yes

characteristic

108

C₂²×C₁₉

C₂×#108

yes

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

C₂×#100

yes

characteristic

114

C₄×C₁₉

#413

yes

characteristic

115

C₂³×C₈

—

116

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

117

C₈×D₄

—

118

C₈×D₄

—

119

#432

—

120

#432

C₂×D₁₉

yes

—

121

C₂×C₄⋊C₈

—

122

C₂×C₂²⋊C₈

—

123

C₂×C₄×C₈

—

124

#335

—

125

#334

—

126

#323

—

127

#323

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#1800

yes

characteristic

131

C₂×C₁₉

#1810

yes

characteristic

132

C₂×C₁₉

#1812

yes

characteristic

133

C₂²×D₄

Dic₃₈

yes

characteristic

134

C₂³×C₄

C₄×D₁₉

yes

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₄×D₄

—

142

C₄×D₄

—

143

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

144

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

145

C₂×C₄²

C₂²×D₁₉

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₂²⋊C₈

—

150

C₂²⋊C₈

—

151

C₂²⋊C₈

—

152

#97

—

153

#97

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₁₉

#8622

yes

characteristic, complemented, Sylow

157

C₂⁴

Dic₁₉⋊C₄

yes

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

Dic₁₉⋊C₄

yes

—

165

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

166

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

167

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₄⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

D₄×D₁₉

yes

—

182

C₄²

#64543

yes

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

#10597279

yes

—

188

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

189

D₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#10597323

yes

characteristic

200

C₂×C₄

#10597324

yes

—

201

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

202

C₂×C₄

#10597385

yes

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

208

C₈

—

152

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

#11926402

yes

characteristic

217

C₂²

C₂×#10597279

yes

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#100×D₁₉

yes

characteristic

223

C₄

#11926525

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#14563625

yes

characteristic

227

C₂

#14563671

yes

characteristic

228

C₂

#14563679

yes

characteristic

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1466	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂²×D₄×C₁₉	Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1466	D₁₉
hypocenter	C₁₉	#8622
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1466

subgroup

G/H

center

C₂²

#11926402

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1466

C₂

socle

C₂²×C₁₉

#380

prime radical

C₂²×D₄×C₁₉

Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1466

N	H ≅ G/N	type
2. #14562396	C₂	semidirect
4. #14561504	C₂	semidirect
156. C₁₉	#8622	semidirect

H ≅ G/N

type

2. #14562396

C₂

semidirect

4. #14561504

C₂

semidirect

156. C₁₉

#8622

semidirect

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

subgroup	index
C₂×D₄×C₁₉⋊C₈	2
#14562396	2
#14561976	2
#14561504	2
C₁₉×#1466	2
#8622	19

subgroup

index

C₂×D₄×C₁₉⋊C₈

C₁₉×#1466

Subgroups — #18075491

Conjugacy classes of subgroups

Complements

Maximal subgroups