Group #18085353 — subgroups

Subgroups — #18085353

Order 4864.

638 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11926892	C₂	1	2	yes	maximal
2	#14564441	C₂	1	1	yes	maximal, characteristic
3	#14564438	C₂	1	2	yes	maximal, complemented
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	#11926892	—	2	4	no	—
8	#11926892	—	2	4	no	—
9	C₂×#10597292	—	2	4	no	—
10	C₂×#10597278	—	2	2	no	—
11	C₂×#10597266	—	2	4	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
13	#11926414	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₁₉×#498	—	2	4	no	—
16	C₂×C₁₉×#106	—	2	2	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	—	2	2	no	—
19	C₂²×D₇₆	—	2	2	no	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
32	#10597320	—	2	2	no	—
33	#10597320	—	2	1	no	—
34	#10597320	D₄	1	2	yes	—
35	C₁₉×#106	—	2	8	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	#10597292	—	4	8	no	—
38	#10597278	—	4	4	no	—
39	#10597266	—	2	16	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₂³×D₁₉	—	4	1	no	—
43	C₂×Q₈×C₁₉	—	2	4	no	—
44	C₂×Q₈×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	4	4	no	—
46	C₂×Q₈×C₁₉	—	4	4	no	—
47	C₂²×C₄×C₁₉	—	4	2	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	4	1	no	—
51	C₂×D₇₆	—	2	4	no	—
52	C₂×D₇₆	—	2	2	no	—
53	C₂×D₇₆	—	4	2	no	—
54	C₂×D₇₆	—	4	4	no	—
55	C₂×D₇₆	—	4	4	no	—
56	C₂×D₇₆	—	4	2	no	—
57	C₂×D₇₆	—	4	1	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×C₈×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	—	2	2	no	—
61	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
62	C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×D₄	1	2	yes	—
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₄⋊Dic₁₉	—	4	2	no	—
70	C₄⋊Dic₁₉	—	4	4	no	—
71	C₂×C₁₉⋊C₈	—	2	4	no	—
72	C₂×C₁₉⋊C₈	—	2	4	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	#10312	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	#127	1	1	yes	characteristic
76	C₂²×D₁₉	—	4	2	no	—
77	C₂²×D₁₉	—	8	1	no	—
78	C₂²×D₁₉	—	8	2	no	—
79	C₂²×D₁₉	—	8	2	no	—
80	C₂²×D₁₉	—	8	1	no	—
81	Q₈×C₁₉	—	4	8	no	—
82	Q₈×C₁₉	—	8	4	no	—
83	C₂×C₄×C₁₉	—	4	4	no	—
84	C₂×C₄×C₁₉	—	8	2	no	—
85	C₂×C₄×C₁₉	—	8	2	no	—
86	C₂×C₄×C₁₉	#120	1	2	yes	—
87	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#121	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₁₉	#135	1	4	yes	—
92	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
93	C₂×C₄×C₁₉	#137	1	2	yes	—
94	C₂×Dic₁₉	—	8	1	no	—
95	C₂×Dic₁₉	—	8	2	no	—
96	D₇₆	—	4	8	no	—
97	D₇₆	—	4	4	no	—
98	D₇₆	—	8	2	no	—
99	D₇₆	—	8	4	no	—
100	C₈×C₁₉	—	2	4	no	—
101	C₁₉⋊C₈	—	4	4	no	—
102	C₂×#498	D₁₉	1	1	yes	characteristic, complemented
103	C₂×#486	—	19	2	no	—
104	#1957	—	19	1	no	—
105	#1956	—	19	2	no	—
106	#1273	—	19	1	no	—
107	C₂²×C₁₉	#392	1	1	yes	characteristic
108	C₂²×C₁₉	#492	1	1	yes	characteristic
109	C₂²×C₁₉	#495	1	2	yes	—
110	C₂²×C₁₉	#496	1	2	yes	—
111	C₂²×C₁₉	#497	1	1	yes	characteristic
112	C₂×D₁₉	—	8	4	no	—
113	C₂×D₁₉	—	8	2	no	—
114	C₂×D₁₉	—	16	1	no	—
115	C₂×D₁₉	—	16	1	no	—
116	C₂×D₁₉	—	16	2	no	—
117	C₄×C₁₉	—	8	4	no	—
118	C₄×C₁₉	#448	1	2	yes	—
119	C₄×C₁₉	#449	1	4	yes	—
120	C₄×C₁₉	#461	1	2	yes	—
121	C₄×C₁₉	#463	1	4	yes	—
122	Dic₁₉	—	16	1	no	—
123	C₂×C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
124	C₂×#127	—	19	1	no	—
125	#498	—	2	4	no	—
126	#486	—	38	4	no	—
127	#486	—	38	4	no	—
128	C₂×#106	—	2	2	no	—
129	C₂×#103	—	38	4	no	—
130	C₂×#102	—	38	4	no	—
131	C₂×#102	—	38	2	no	—
132	C₂×C₄×C₈	—	19	2	no	—
133	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
134	#384	—	19	1	no	—
135	C₂×C₁₉	#1708	1	1	yes	characteristic
136	C₂×C₁₉	#1715	1	1	yes	characteristic
137	C₂×C₁₉	#1720	1	2	yes	—
138	C₂×C₁₉	#2012	1	2	yes	—
139	C₂×C₁₉	#2013	1	1	yes	characteristic
140	D₁₉	—	16	2	no	—
141	C₂²×Q₈	—	2	2	no	—
142	C₂²×D₄	—	38	2	no	—
143	C₂²×D₄	—	38	1	no	—
144	C₂²×C₈	—	19	4	no	—
145	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
150	#127	—	19	2	no	—
151	#127	—	38	1	no	—
152	#127	—	38	2	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	38	2	no	—
156	C₂×C₄⋊C₄	—	38	1	no	—
157	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
158	#106	—	2	8	no	—
159	#103	—	76	8	no	—
160	#102	—	38	16	no	—
161	#102	—	76	4	no	—
162	C₄×C₈	—	2	2	no	—
163	C₄×C₈	—	38	2	no	—
164	C₄×C₈	—	38	2	no	—
165	C₁₉	#10312	1	1	yes	characteristic, complemented, Sylow
166	C₂⁴	—	76	1	no	—
167	C₂×Q₈	—	2	4	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	4	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×D₄	—	38	4	no	—
172	C₂×D₄	—	38	2	no	—
173	C₂×D₄	—	76	2	no	—
174	C₂×D₄	—	76	2	no	—
175	C₂×D₄	—	76	2	no	—
176	C₂×D₄	—	76	1	no	—
177	C₂×D₄	—	76	4	no	—
178	C₂×D₄	—	76	4	no	—
179	C₂²×C₄	—	4	2	no	—
180	C₂²×C₄	—	76	1	no	—
181	C₂²×C₄	D₄×D₁₉	1	2	yes	—
182	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	38	4	no	—
186	C₂×C₈	—	38	4	no	—
187	C₂×C₈	—	38	4	no	—
188	C₂×C₈	#64527	1	4	yes	—
189	C₄⋊C₄	—	2	4	no	—
190	C₄⋊C₄	—	2	4	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	76	2	no	—
194	C₄⋊C₄	—	76	4	no	—
195	C₄²	D₄×D₁₉	1	1	yes	characteristic
196	C₄²	#64543	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
198	C₂³	—	76	2	no	—
199	C₂³	—	152	1	no	—
200	C₂³	—	152	2	no	—
201	C₂³	—	152	2	no	—
202	C₂³	—	152	1	no	—
203	C₂³	#10597386	1	1	yes	characteristic
204	Q₈	—	4	8	no	—
205	Q₈	—	8	4	no	—
206	D₄	—	76	8	no	—
207	D₄	—	76	4	no	—
208	D₄	—	152	2	no	—
209	D₄	—	152	4	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	8	2	no	—
212	C₂×C₄	—	8	2	no	—
213	C₂×C₄	—	152	1	no	—
214	C₂×C₄	—	152	2	no	—
215	C₂×C₄	#10597360	1	4	yes	—
216	C₂×C₄	#10597362	1	4	yes	—
217	C₂×C₄	#10597383	1	2	yes	—
218	C₂×C₄	#10597384	1	1	yes	characteristic
219	C₂×C₄	#10597385	1	2	yes	—
220	C₂×C₄	C₂×#64527	1	2	yes	—
221	C₂×C₄	#10597388	1	2	yes	—
222	C₂×C₄	#10597399	1	1	yes	characteristic
223	C₈	—	2	4	no	—
224	C₈	—	76	4	no	—
225	C₂²	—	304	1	no	—
226	C₂²	—	304	1	no	—
227	C₂²	—	304	2	no	—
228	C₂²	—	152	4	no	—
229	C₂²	—	152	2	no	—
230	C₂²	#11926452	1	1	yes	characteristic
231	C₂²	#11926918	1	1	yes	characteristic
232	C₂²	#11926925	1	2	yes	—
233	C₂²	#11926930	1	2	yes	—
234	C₂²	#11926936	1	1	yes	characteristic
235	C₄	—	8	4	no	—
236	C₄	—	304	1	no	—
237	C₄	#11926683	1	2	yes	—
238	C₄	#11926688	1	4	yes	—
239	C₄	#11926746	1	2	yes	—
240	C₄	#11926761	1	4	yes	—
241	C₂	—	304	2	no	—
242	C₂	#14563237	1	1	yes	characteristic
243	C₂	#14563264	1	1	yes	characteristic
244	C₂	#14563293	1	2	yes	—
245	C₂	#14564709	1	2	yes	—
246	C₂	#14564718	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926892

C₂

yes

maximal

#14564441

C₂

yes

maximal, characteristic

#14564438

C₂

yes

maximal, complemented

C₁₉⋊#1273

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#498

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

—

—

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#498

—

C₂×C₁₉×#106

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

#10597320

—

#10597320

—

#10597320

D₄

yes

—

C₁₉×#106

—

C₄×C₈×C₁₉

—

#10597292

—

#10597278

—

#10597266

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

C₂×#498

D₁₉

yes

characteristic, complemented

103

C₂×#486

—

104

#1957

—

105

#1956

—

106

#1273

—

107

C₂²×C₁₉

#392

yes

characteristic

108

C₂²×C₁₉

#492

yes

characteristic

109

C₂²×C₁₉

#495

yes

—

110

C₂²×C₁₉

#496

yes

—

111

C₂²×C₁₉

#497

yes

characteristic

112

C₂×D₁₉

—

113

C₂×D₁₉

—

114

C₂×D₁₉

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

#448

yes

—

119

C₄×C₁₉

#449

yes

—

120

C₄×C₁₉

#461

yes

—

121

C₄×C₁₉

#463

yes

—

122

Dic₁₉

—

123

C₂×C₄⋊Q₈

C₂×D₁₉

yes

—

124

C₂×#127

—

125

#498

—

126

#486

—

127

#486

—

128

C₂×#106

—

129

C₂×#103

—

130

C₂×#102

—

131

C₂×#102

—

132

C₂×C₄×C₈

—

133

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

134

#384

—

135

C₂×C₁₉

#1708

yes

characteristic

136

C₂×C₁₉

#1715

yes

characteristic

137

C₂×C₁₉

#1720

yes

—

138

C₂×C₁₉

#2012

yes

—

139

C₂×C₁₉

#2013

yes

characteristic

140

D₁₉

—

141

C₂²×Q₈

—

142

C₂²×D₄

—

143

C₂²×D₄

—

144

C₂²×C₈

—

145

C₂²×C₈

C₂²⋊D₁₉

yes

—

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

150

#127

—

151

#127

—

152

#127

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄²

C₂²×D₁₉

yes

characteristic

158

#106

—

159

#103

—

160

#102

—

161

#102

—

162

C₄×C₈

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₁₉

#10312

yes

characteristic, complemented, Sylow

166

C₂⁴

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

D₄×D₁₉

yes

—

182

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

#64527

yes

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄²

D₄×D₁₉

yes

characteristic

196

C₄²

#64543

yes

characteristic

197

C₄²

C₂×C₂²⋊D₁₉

yes

—

198

C₂³

—

199

C₂³

—

152

—

200

C₂³

—

152

—

201

C₂³

—

152

—

202

C₂³

—

152

—

203

C₂³

#10597386

yes

characteristic

204

Q₈

—

205

Q₈

—

206

D₄

—

207

D₄

—

208

D₄

—

152

—

209

D₄

—

152

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

152

—

214

C₂×C₄

—

152

—

215

C₂×C₄

#10597360

yes

—

216

C₂×C₄

#10597362

yes

—

217

C₂×C₄

#10597383

yes

—

218

C₂×C₄

#10597384

yes

characteristic

219

C₂×C₄

#10597385

yes

—

220

C₂×C₄

C₂×#64527

yes

—

221

C₂×C₄

#10597388

yes

—

222

C₂×C₄

#10597399

yes

characteristic

223

C₈

—

224

C₈

—

225

C₂²

—

304

—

226

C₂²

—

304

—

227

C₂²

—

304

—

228

C₂²

—

152

—

229

C₂²

—

152

—

230

C₂²

#11926452

yes

characteristic

231

C₂²

#11926918

yes

characteristic

232

C₂²

#11926925

yes

—

233

C₂²

#11926930

yes

—

234

C₂²

#11926936

yes

characteristic

235

C₄

—

236

C₄

—

304

—

237

C₄

#11926683

yes

—

238

C₄

#11926688

yes

—

239

C₄

#11926746

yes

—

240

C₄

#11926761

yes

—

241

C₂

—

304

—

242

C₂

#14563237

yes

characteristic

243

C₂

#14563264

yes

characteristic

244

C₂

#14563293

yes

—

245

C₂

#14564709

yes

—

246

C₂

#14564718

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#498	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
hypercenter	C₂×#498	D₁₉
hypocenter	C₁₉	#10312
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#498

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

N	H ≅ G/N	type
3. #14564438	C₂	semidirect
4. C₁₉⋊#1273	C₂	semidirect
5. C₂×C₁₉×#498	C₂	semidirect
102. C₂×#498	D₁₉	semidirect
165. C₁₉	#10312	semidirect

H ≅ G/N

type

3. #14564438

C₂

semidirect

4. C₁₉⋊#1273

C₂

semidirect

5. C₂×C₁₉×#498

C₂

semidirect

102. C₂×#498

D₁₉

semidirect

165. C₁₉

#10312

semidirect

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

subgroup	index
C₂×#11926892	2
#14564441	2
#14564438	2
C₁₉⋊#1273	2
C₂×C₁₉×#498	2
#10312	19

subgroup

index

C₂×#11926892

#14564441

#14564438

C₁₉⋊#1273

C₂×C₁₉×#498

#10312

Subgroups — #18085353

Conjugacy classes of subgroups

Complements

Maximal subgroups