Group #18082440 — subgroups

Subgroups — #18082440

Order 4864.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14564613	C₂	1	2	yes	maximal
2	#14563380	C₂	1	1	yes	maximal, characteristic
3	#14562394	C₂	1	1	yes	maximal, characteristic
4	#14562090	C₂	1	2	yes	maximal
5	C₁₉×#3170	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
9	#11926303	—	2	4	no	—
10	#11926298	—	2	2	no	—
11	#11926297	—	2	2	no	—
12	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
13	C₁₉×#533	C₂²	1	2	yes	—
14	C₁₉×#500	C₄	1	1	yes	characteristic, complemented
15	C₁₉×#494	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#487	C₄	1	2	yes	complemented
17	C₁₉×#467	—	2	2	no	—
18	C₄×Q₁₆×C₁₉	—	2	2	no	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₁₉	—	2	2	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
24	C₁₉×#125	—	2	2	no	—
25	C₁₉×C₂²⋊Q₈	—	2	2	no	—
26	C₁₉×C₂²⋊Q₈	—	2	2	no	—
27	C₄×Q₈×C₁₉	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₁₉×#117	—	2	2	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₄×Dic₁₉	—	2	1	no	—
32	C₂×C₄×Dic₁₉	—	2	1	no	—
33	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
34	C₂×#64520	—	2	2	no	—
35	C₂²×C₁₉⋊C₈	—	2	1	no	—
36	C₁₉×#107	—	2	2	no	—
37	C₁₉×#103	—	2	4	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	1	no	—
44	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	2	no	—
51	Q₁₆×C₁₉	—	4	4	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₄×Dic₁₉	—	2	2	no	—
68	C₄×Dic₁₉	—	4	2	no	—
69	C₄×Dic₁₉	—	4	2	no	—
70	C₄×Dic₁₉	Q₁₆	1	4	yes	complemented
71	#64520	—	4	4	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	#9848	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	#121	1	1	yes	characteristic
77	Q₈×C₁₉	—	4	4	no	—
78	Q₈×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₂×Dic₁₉	—	2	4	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₈×C₁₉	—	2	2	no	—
95	C₈×C₁₉	—	2	2	no	—
96	C₁₉⋊C₈	—	4	2	no	—
97	C₁₉⋊C₈	—	8	2	no	—
98	#3170	D₁₉	1	1	yes	characteristic
99	#1994	—	19	2	no	—
100	#1744	—	19	1	no	—
101	#1567	—	19	1	no	—
102	#1493	—	19	2	no	—
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	—	2	1	no	—
105	C₂²×C₁₉	#390	1	1	yes	characteristic
106	C₂²×C₁₉	#467	1	2	yes	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	8	2	no	—
110	C₄×C₁₉	—	8	2	no	—
111	C₄×C₁₉	#421	1	2	yes	—
112	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
113	C₄×C₁₉	#444	1	2	yes	—
114	C₄×C₁₉	#494	1	1	yes	characteristic
115	C₄×C₁₉	#495	1	1	yes	characteristic
116	Dic₁₉	—	4	4	no	—
117	#533	C₂×D₁₉	1	2	yes	—
118	#500	Dic₁₉	1	1	yes	characteristic, complemented
119	#494	Dic₁₉	1	1	yes	characteristic, complemented
120	#487	Dic₁₉	1	2	yes	complemented
121	#467	—	2	2	no	—
122	C₄×Q₁₆	—	2	2	no	—
123	#423	—	19	2	no	—
124	C₂×C₄×C₈	—	19	1	no	—
125	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
126	C₄³	—	19	1	no	—
127	#339	—	38	4	no	—
128	#336	—	38	2	no	—
129	#335	—	38	2	no	—
130	Q₈⋊C₈	—	38	4	no	—
131	C₂×C₁₉	—	2	2	no	—
132	C₂×C₁₉	#1963	1	1	yes	characteristic
133	C₂×C₁₉	#1969	1	1	yes	characteristic
134	C₂×C₁₉	#1975	1	1	yes	characteristic
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×M₁₆	—	38	2	no	—
137	C₂²×C₈	—	38	1	no	—
138	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
139	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
140	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
141	#125	—	2	2	no	—
142	C₂²⋊Q₈	—	2	2	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	#117	—	2	2	no	—
147	C₂×C₄²	—	19	2	no	—
148	C₂×C₄²	—	38	1	no	—
149	C₂×C₄²	—	38	1	no	—
150	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
151	#107	—	2	2	no	—
152	C₄⋊C₈	—	38	2	no	—
153	C₄⋊C₈	—	38	2	no	—
154	#103	—	2	4	no	—
155	C₄×C₈	—	19	2	no	—
156	C₄×C₈	—	38	1	no	—
157	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
158	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
160	C₁₉	#9848	1	1	yes	characteristic, complemented, Sylow
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂²×C₄	—	38	2	no	—
164	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
165	C₂²×C₄	#64543	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
167	Q₁₆	—	4	4	no	—
168	M₁₆	—	76	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	38	2	no	—
171	C₂×C₈	—	76	2	no	—
172	C₂×C₈	—	76	2	no	—
173	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
174	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	—	4	2	no	—
183	C₄²	—	19	4	no	—
184	C₄²	—	38	2	no	—
185	C₄²	—	76	2	no	—
186	C₄²	—	76	2	no	—
187	C₄²	D₄×D₁₉	1	1	yes	characteristic
188	C₄²	#64543	1	1	yes	characteristic
189	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
191	C₂³	#10597384	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	4	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	38	4	no	—
199	C₂×C₄	—	76	2	no	—
200	C₂×C₄	—	76	2	no	—
201	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
202	C₂×C₄	#10597365	1	2	yes	—
203	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
204	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
205	C₂×C₄	#10597382	1	1	yes	characteristic
206	C₂×C₄	#10597384	1	1	yes	characteristic
207	C₂×C₄	#10597386	1	1	yes	characteristic
208	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	76	2	no	—
212	C₈	—	152	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#11926447	1	1	yes	characteristic
216	C₂²	#11926782	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	76	4	no	—
222	C₄	#11926561	1	2	yes	—
223	C₄	Q₁₆×Dic₁₉	1	2	yes	—
224	C₄	#11926666	1	2	yes	—
225	C₄	#11926922	1	1	yes	characteristic
226	C₄	#11926929	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#14564468	1	1	yes	characteristic
229	C₂	#14564497	1	1	yes	characteristic
230	C₂	#14564529	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564613

C₂

yes

maximal

#14563380

C₂

yes

maximal, characteristic

#14562394

C₂

yes

maximal, characteristic

#14562090

C₂

yes

maximal

C₁₉×#3170

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

—

—

—

Q₈⋊(C₁₉⋊C₈)

—

C₁₉×#533

C₂²

yes

—

C₁₉×#500

C₄

yes

characteristic, complemented

C₁₉×#494

C₄

yes

characteristic, complemented

C₁₉×#487

C₄

yes

complemented

C₁₉×#467

—

C₄×Q₁₆×C₁₉

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#107

—

C₁₉×#103

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₁₆

yes

complemented

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3170

D₁₉

yes

characteristic

#1994

—

100

#1744

—

101

#1567

—

102

#1493

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#390

yes

characteristic

106

C₂²×C₁₉

#467

yes

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

#421

yes

—

112

C₄×C₁₉

C₄×Q₁₆

yes

—

113

C₄×C₁₉

#444

yes

—

114

C₄×C₁₉

#494

yes

characteristic

115

C₄×C₁₉

#495

yes

characteristic

116

Dic₁₉

—

117

#533

C₂×D₁₉

yes

—

118

#500

Dic₁₉

yes

characteristic, complemented

119

#494

Dic₁₉

yes

characteristic, complemented

120

#487

Dic₁₉

yes

complemented

121

#467

—

122

C₄×Q₁₆

—

123

#423

—

124

C₂×C₄×C₈

—

125

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

126

C₄³

—

127

#339

—

128

#336

—

129

#335

—

130

Q₈⋊C₈

—

131

C₂×C₁₉

—

132

C₂×C₁₉

#1963

yes

characteristic

133

C₂×C₁₉

#1969

yes

characteristic

134

C₂×C₁₉

#1975

yes

characteristic

135

C₂×Q₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂²⋊D₁₉

yes

—

139

C₄⋊Q₈

C₂×Dic₁₉

yes

—

140

C₄⋊Q₈

C₂×Dic₁₉

yes

—

141

#125

—

142

C₂²⋊Q₈

—

143

C₂²⋊Q₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

#117

—

147

C₂×C₄²

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₂²×D₁₉

yes

characteristic

151

#107

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₄×C₈

C₂×Dic₁₉

yes

characteristic

158

C₄×C₈

C₂×Dic₁₉

yes

characteristic

159

C₄×C₈

C₂²⋊D₁₉

yes

—

160

C₁₉

#9848

yes

characteristic, complemented, Sylow

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

164

C₂²×C₄

D₄×D₁₉

yes

characteristic

165

C₂²×C₄

#64543

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

167

Q₁₆

—

168

M₁₆

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

C₂²⋊Dic₁₉

yes

—

174

C₂×C₈

C₂²⋊Dic₁₉

yes

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

D₄×D₁₉

yes

characteristic

188

C₄²

#64543

yes

characteristic

189

C₄²

C₂²×Dic₁₉

yes

characteristic

190

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

191

C₂³

#10597384

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

Q₁₆×D₁₉

yes

—

202

C₂×C₄

#10597365

yes

—

203

C₂×C₄

D₄×Dic₁₉

yes

characteristic

204

C₂×C₄

D₄×Dic₁₉

yes

characteristic

205

C₂×C₄

#10597382

yes

characteristic

206

C₂×C₄

#10597384

yes

characteristic

207

C₂×C₄

#10597386

yes

characteristic

208

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

152

—

213

C₂²

—

214

C₂²

—

215

C₂²

#11926447

yes

characteristic

216

C₂²

#11926782

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#11926561

yes

—

223

C₄

Q₁₆×Dic₁₉

yes

—

224

C₄

#11926666

yes

—

225

C₄

#11926922

yes

characteristic

226

C₄

#11926929

yes

characteristic

227

C₂

—

228

C₂

#14564468

yes

characteristic

229

C₂

#14564497

yes

characteristic

230

C₂

#14564529

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3170	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3170	D₁₉
hypocenter	C₁₉	#9848
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3170

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. C₁₉×#500	C₄	semidirect
15. C₁₉×#494	C₄	semidirect
16. C₁₉×#487	C₄	semidirect
70. C₄×Dic₁₉	Q₁₆	semidirect
118. #500	Dic₁₉	semidirect
119. #494	Dic₁₉	semidirect
120. #487	Dic₁₉	semidirect
160. C₁₉	#9848	semidirect

H ≅ G/N

type

14. C₁₉×#500

C₄

semidirect

15. C₁₉×#494

C₄

semidirect

16. C₁₉×#487

C₄

semidirect

70. C₄×Dic₁₉

Q₁₆

semidirect

118. #500

Dic₁₉

semidirect

119. #494

Dic₁₉

semidirect

120. #487

Dic₁₉

semidirect

160. C₁₉

#9848

semidirect

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

subgroup	index
#14564613	2
#14563380	2
#14562394	2
#14562090	2
C₁₉×#3170	2
#9848	19

subgroup

index

C₁₉×#3170

Subgroups — #18082440

Conjugacy classes of subgroups

Complements

Maximal subgroups