Group #18069527 — subgroups

Subgroups — #18069527

Order 4864.

286 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14565246	C₂	1	1	yes	maximal, characteristic
2	#14563411	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2112	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	C₄	1	2	yes	complemented
5	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic
6	C₂×#10597272	—	2	1	no	—
7	C₄×C₂²⋊Dic₁₉	C₄	1	1	yes	characteristic
8	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
9	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
10	#11926298	—	2	1	no	—
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×M₃₂	—	2	1	no	—
13	C₁₉×C₂²⋊C₁₆	—	2	1	no	—
14	C₁₉×C₂²⋊C₁₆	C₄	1	2	yes	complemented
15	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₉	—	4	2	no	—
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₁₉	C₈	1	2	yes	—
24	C₂×C₄×Dic₁₉	—	2	1	no	—
25	C₂²×C₁₉⋊C₈	—	2	1	no	—
26	C₁₉×M₃₂	—	4	2	no	—
27	C₂×C₁₆×C₁₉	—	2	2	no	—
28	C₁₉⋊#95	—	2	1	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
30	C₂²⋊(C₁₉⋊C₈)	C₈	1	2	yes	—
31	#10597272	—	4	2	no	—
32	#10597269	—	4	2	no	—
33	C₂×C₁₉⋊C₁₆	—	2	2	no	—
34	C₂⁴×C₁₉	C₂×C₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	—	4	1	no	—
36	C₂²×C₄×C₁₉	—	4	1	no	—
37	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	4	1	no	—
48	C₂×C₈×C₁₉	—	4	1	no	—
49	C₂×C₈×C₁₉	—	4	1	no	—
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂²⋊Dic₁₉	—	4	2	no	—
55	C₄×Dic₁₉	—	4	1	no	—
56	C₄×Dic₁₉	—	4	1	no	—
57	C₂×C₁₉⋊C₈	—	2	2	no	—
58	C₂×C₁₉⋊C₈	—	4	1	no	—
59	C₂×C₁₉⋊C₈	—	4	1	no	—
60	C₁₆×C₁₉	—	4	2	no	—
61	C₁₉⋊C₁₆	—	4	2	no	—
62	#7201	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	—	2	2	no	—
64	C₂³×C₁₉	—	4	1	no	—
65	C₂³×C₁₉	—	4	1	no	—
66	C₂³×C₁₉	C₄×C₈	1	1	yes	characteristic
67	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
68	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	4	1	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
79	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
82	C₂×Dic₁₉	—	4	2	no	—
83	C₂×Dic₁₉	—	4	2	no	—
84	C₂×Dic₁₉	—	4	2	no	—
85	C₈×C₁₉	—	2	1	no	—
86	C₈×C₁₉	—	2	1	no	—
87	C₈×C₁₉	—	2	1	no	—
88	C₈×C₁₉	#99	1	2	yes	—
89	C₁₉⋊C₈	—	4	2	no	—
90	#2112	—	19	1	no	—
91	#2112	D₁₉	1	1	yes	characteristic
92	#1752	—	19	1	no	—
93	C₂²×C₁₉	—	2	1	no	—
94	C₂²×C₁₉	—	2	1	no	—
95	C₂²×C₁₉	—	2	1	no	—
96	C₂²×C₁₉	—	2	1	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	—	2	1	no	—
100	C₂²×C₁₉	—	2	1	no	—
101	C₂²×C₁₉	—	4	4	no	—
102	C₂²×C₁₉	#336	1	1	yes	characteristic
103	C₂²×C₁₉	#349	1	2	yes	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	#342	1	1	yes	characteristic
108	C₄×C₁₉	#344	1	1	yes	characteristic
109	Dic₁₉	—	8	2	no	—
110	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×M₃₂	—	2	1	no	—
112	C₂×M₃₂	—	19	2	no	—
113	C₂×C₂²⋊C₈	—	19	1	no	—
114	C₂×#97	—	38	1	no	—
115	C₄×C₂²⋊C₄	—	19	1	no	—
116	C₂²⋊C₁₆	—	2	1	no	—
117	C₂²⋊C₁₆	—	38	1	no	—
118	C₂²⋊C₁₆	—	38	1	no	—
119	C₂²⋊C₁₆	Dic₁₉	1	2	yes	complemented
120	#336	—	38	1	no	—
121	C₂×C₁₉	—	2	2	no	—
122	C₂×C₁₉	—	4	1	no	—
123	C₂×C₁₉	—	4	1	no	—
124	C₂×C₁₉	#1282	1	1	yes	characteristic
125	C₂×C₁₉	#1377	1	1	yes	characteristic
126	C₂×C₁₉	#1378	1	1	yes	characteristic
127	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
128	C₂²×C₈	—	4	2	no	—
129	C₂²×C₈	—	38	1	no	—
130	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
131	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
132	C₂²×C₈	D₇₆	1	1	yes	characteristic
133	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
134	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
135	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
136	C₂×C₂²⋊C₄	—	19	2	no	—
137	C₂×C₄²	—	38	1	no	—
138	M₃₂	—	4	2	no	—
139	M₃₂	—	76	2	no	—
140	C₂×C₁₆	—	2	2	no	—
141	C₂×C₁₆	—	38	2	no	—
142	C₂²⋊C₈	—	19	2	no	—
143	C₂²⋊C₈	—	38	1	no	—
144	#97	—	76	2	no	—
145	#95	—	38	1	no	—
146	C₁₉	#7201	1	1	yes	characteristic, complemented, Sylow
147	C₂⁴	C₈×D₁₉	1	1	yes	characteristic
148	C₂²×C₄	—	4	1	no	—
149	C₂²×C₄	—	4	1	no	—
150	C₂²×C₄	—	38	2	no	—
151	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
152	C₂²×C₄	#64515	1	1	yes	characteristic
153	C₂²×C₄	#64515	1	1	yes	characteristic
154	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
155	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
156	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	1	no	—
161	C₂×C₈	—	4	1	no	—
162	C₂×C₈	—	4	1	no	—
163	C₂×C₈	—	38	2	no	—
164	C₂×C₈	—	76	1	no	—
165	C₂×C₈	—	76	1	no	—
166	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
167	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
168	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
169	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
170	C₂²⋊C₄	—	76	2	no	—
171	C₄²	—	76	1	no	—
172	C₄²	—	76	1	no	—
173	C₁₆	—	4	2	no	—
174	C₁₆	—	76	2	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	4	1	no	—
177	C₂³	—	4	1	no	—
178	C₂³	C₈×Dic₁₉	1	1	yes	characteristic
179	C₂³	Dic₁₉⋊C₈	1	1	yes	characteristic
180	C₂³	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	4	1	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	76	2	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
194	C₂×C₄	#10597272	1	1	yes	characteristic
195	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
196	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
197	C₈	—	2	1	no	—
198	C₈	—	2	1	no	—
199	C₈	—	2	1	no	—
200	C₈	—	76	2	no	—
201	C₈	#10597263	1	2	yes	—
202	C₂²	—	2	1	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	2	1	no	—
205	C₂²	—	2	1	no	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	4	4	no	—
211	C₂²	#11926298	1	1	yes	characteristic
212	C₂²	#11926325	1	2	yes	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	152	2	no	—
217	C₄	#11926310	1	1	yes	characteristic
218	C₄	#11926316	1	1	yes	characteristic
219	C₂	—	2	2	no	—
220	C₂	—	4	1	no	—
221	C₂	—	4	1	no	—
222	C₂	#14561481	1	1	yes	characteristic
223	C₂	#14561718	1	1	yes	characteristic
224	C₂	#14561720	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565246

C₂

yes

maximal, characteristic

#14563411

C₂

yes

maximal, characteristic

C₁₉×#2112

C₂

yes

maximal, characteristic

C₂×#10597269

C₄

yes

complemented

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

characteristic

C₂×#10597272

—

C₄×C₂²⋊Dic₁₉

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926298

—

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×M₃₂

—

C₁₉×C₂²⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

C₄

yes

complemented

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₂²⋊Dic₁₉

C₈

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₈

yes

—

#10597272

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7201

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄×C₈

yes

characteristic

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

C₂³×C₁₉

C₄⋊C₈

yes

characteristic

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

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#99

yes

—

C₁₉⋊C₈

—

#2112

—

#2112

D₁₉

yes

characteristic

#1752

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

#336

yes

characteristic

103

C₂²×C₁₉

#349

yes

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

#342

yes

characteristic

108

C₄×C₁₉

#344

yes

characteristic

109

Dic₁₉

—

110

C₂³×C₈

C₂×D₁₉

yes

characteristic

111

C₂×M₃₂

—

112

C₂×M₃₂

—

113

C₂×C₂²⋊C₈

—

114

C₂×#97

—

115

C₄×C₂²⋊C₄

—

116

C₂²⋊C₁₆

—

117

C₂²⋊C₁₆

—

118

C₂²⋊C₁₆

—

119

C₂²⋊C₁₆

Dic₁₉

yes

complemented

120

#336

—

121

C₂×C₁₉

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

#1282

yes

characteristic

125

C₂×C₁₉

#1377

yes

characteristic

126

C₂×C₁₉

#1378

yes

characteristic

127

C₂³×C₄

C₄×D₁₉

yes

characteristic

128

C₂²×C₈

—

129

C₂²×C₈

—

130

C₂²×C₈

Dic₃₈

yes

characteristic

131

C₂²×C₈

C₄×D₁₉

yes

characteristic

132

C₂²×C₈

D₇₆

yes

characteristic

133

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

134

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

135

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

—

138

M₃₂

—

139

M₃₂

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

C₂²⋊C₈

—

143

C₂²⋊C₈

—

144

#97

—

145

#95

—

146

C₁₉

#7201

yes

characteristic, complemented, Sylow

147

C₂⁴

C₈×D₁₉

yes

characteristic

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

C₈×D₁₉

yes

characteristic

152

C₂²×C₄

#64515

yes

characteristic

153

C₂²×C₄

#64515

yes

characteristic

154

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

155

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

156

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

167

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

168

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

169

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

170

C₂²⋊C₄

—

171

C₄²

—

172

C₄²

—

173

C₁₆

—

174

C₁₆

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

C₈×Dic₁₉

yes

characteristic

179

C₂³

Dic₁₉⋊C₈

yes

characteristic

180

C₂³

(C₂×D₁₉)⋊C₈

yes

characteristic

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

Dic₁₉⋊C₈

yes

characteristic

194

C₂×C₄

#10597272

yes

characteristic

195

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

196

C₂×C₄

C₁₉⋊#95

yes

characteristic

197

C₈

—

198

C₈

—

199

C₈

—

200

C₈

—

201

C₈

#10597263

yes

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

#11926298

yes

characteristic

212

C₂²

#11926325

yes

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

152

—

217

C₄

#11926310

yes

characteristic

218

C₄

#11926316

yes

characteristic

219

C₂

—

220

C₂

—

221

C₂

—

222

C₂

#14561481

yes

characteristic

223

C₂

#14561718

yes

characteristic

224

C₂

#14561720

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₁₉⋊#95
commutator	C₂³×C₁₉	C₄×C₈
Frattini	C₂³×C₈	C₂×D₁₉
Fitting	C₁₉×#2112	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂⁴×C₁₉	C₂×C₈
cosocle	C₂³×C₈×C₁₉	C₂²
hypercenter	#2112	D₁₉
hypocenter	C₁₉	#7201
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂×C₄

C₁₉⋊#95

commutator

C₂³×C₁₉

C₄×C₈

Frattini

C₂³×C₈

C₂×D₁₉

Fitting

C₁₉×#2112

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂⁴×C₁₉

C₂×C₈

cosocle

C₂³×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
4. C₂×#10597269	C₄	semidirect
14. C₁₉×C₂²⋊C₁₆	C₄	semidirect
119. C₂²⋊C₁₆	Dic₁₉	semidirect
146. C₁₉	#7201	semidirect

H ≅ G/N

type

4. C₂×#10597269

C₄

semidirect

14. C₁₉×C₂²⋊C₁₆

C₄

semidirect

119. C₂²⋊C₁₆

Dic₁₉

semidirect

146. C₁₉

#7201

semidirect

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

subgroup	index
#14565246	2
#14563411	2
C₁₉×#2112	2
#7201	19

subgroup

index

#14565246

#14563411

C₁₉×#2112

#7201

Subgroups — #18069527

Conjugacy classes of subgroups

Complements

Maximal subgroups