Group #18085162 — subgroups

Subgroups — #18085162

Order 4864.

510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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×#11926836	C₂	1	2	yes	maximal
2	#14564571	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926293	C₂	1	2	yes	maximal
4	#14561470	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#500	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	#11926836	—	2	4	no	—
8	#11926836	—	2	4	no	—
9	C₂×#10597264	—	2	2	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#10597267	—	2	2	no	—
13	#11926298	—	2	2	no	—
14	#11926293	—	2	4	no	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₁₉×#500	—	2	4	no	—
17	C₂×C₁₉×#107	—	2	2	no	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₁₉	—	2	2	no	—
20	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
30	C₂×Dic₁₉⋊C₄	—	2	1	no	—
31	C₂×C₄×Dic₁₉	—	2	1	no	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	C₂²×C₁₉⋊C₈	—	2	1	no	—
34	C₄×Dic₃₈	—	2	2	no	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₁₉×#107	—	2	8	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	#10597267	—	2	8	no	—
39	#10597264	—	2	8	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
43	C₂×Q₈×C₁₉	—	2	4	no	—
44	C₂×Q₈×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	8	4	no	—
46	C₂²×C₄×C₁₉	—	4	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	1	no	—
51	C₂²×Dic₁₉	—	2	1	no	—
52	C₂×Dic₃₈	—	2	2	no	—
53	C₂×Dic₃₈	—	2	2	no	—
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×Dic₃₈	Q₁₆	1	2	yes	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
59	C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄⋊C₄×C₁₉	—	4	2	no	—
63	C₄²×C₁₉	C₂×D₄	1	2	yes	—
64	C₄²×C₁₉	C₂×D₄	1	2	yes	—
65	C₄⋊Dic₁₉	—	2	2	no	—
66	Dic₁₉⋊C₄	—	4	2	no	—
67	C₄×Dic₁₉	—	4	1	no	—
68	C₄×Dic₁₉	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	2	4	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	2	no	—
74	#10279	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	#121	1	1	yes	characteristic
76	Q₈×C₁₉	—	8	4	no	—
77	Q₈×C₁₉	—	8	4	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	8	4	no	—
81	C₂×C₄×C₁₉	#120	1	2	yes	—
82	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#121	1	2	yes	—
84	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#137	1	2	yes	—
89	C₂×C₄×C₁₉	#137	1	2	yes	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	4	1	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₂×Dic₁₉	—	4	1	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	Dic₃₈	—	2	4	no	—
96	Dic₃₈	—	4	2	no	—
97	C₈×C₁₉	—	2	4	no	—
98	C₁₉⋊C₈	—	4	4	no	—
99	C₁₉⋊C₈	—	8	1	no	—
100	C₂×#500	D₁₉	1	1	yes	characteristic
101	C₂×#477	—	19	2	no	—
102	#1984	—	19	1	no	—
103	C₂×#333	—	19	2	no	—
104	#1277	—	19	1	no	—
105	C₂²×C₁₉	#392	1	1	yes	characteristic
106	C₂²×C₁₉	#462	1	2	yes	—
107	C₂²×C₁₉	#467	1	1	yes	characteristic
108	C₂²×C₁₉	#470	1	1	yes	characteristic
109	C₂²×C₁₉	#472	1	2	yes	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	8	4	no	—
112	C₄×C₁₉	#451	1	2	yes	—
113	C₄×C₁₉	#451	1	2	yes	—
114	C₄×C₁₉	#452	1	2	yes	—
115	C₄×C₁₉	#494	1	1	yes	characteristic
116	C₄×C₁₉	#497	1	1	yes	characteristic
117	Dic₁₉	—	4	2	no	—
118	Dic₁₉	—	8	1	no	—
119	C₂×C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
120	C₂×C₄×Q₈	—	19	1	no	—
121	#500	—	2	4	no	—
122	#477	—	38	4	no	—
123	#477	—	38	4	no	—
124	C₂×#107	—	2	2	no	—
125	C₂×#107	—	38	2	no	—
126	C₂×C₄⋊C₈	—	19	2	no	—
127	C₂×C₄⋊C₈	—	19	1	no	—
128	C₂×#103	—	38	2	no	—
129	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
130	#336	—	38	2	no	—
131	#333	—	38	4	no	—
132	C₂×C₁₉	#1676	1	2	yes	—
133	C₂×C₁₉	#1696	1	2	yes	—
134	C₂×C₁₉	#2001	1	1	yes	characteristic
135	C₂×C₁₉	#2016	1	1	yes	characteristic
136	C₂×C₁₉	#2018	1	1	yes	characteristic
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	19	1	no	—
139	C₂²×C₈	—	38	2	no	—
140	C₂²×C₈	—	38	1	no	—
141	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
146	C₄×Q₈	—	38	2	no	—
147	C₄×Q₈	—	38	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	19	1	no	—
151	C₂×C₄⋊C₄	—	38	1	no	—
152	C₂×C₄²	—	38	1	no	—
153	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
154	#107	—	2	8	no	—
155	#107	—	38	8	no	—
156	C₄⋊C₈	—	19	4	no	—
157	C₄⋊C₈	—	38	2	no	—
158	C₄⋊C₈	—	38	2	no	—
159	#103	—	38	8	no	—
160	C₄×C₈	—	2	2	no	—
161	C₁₉	#10279	1	1	yes	characteristic, complemented, Sylow
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	8	4	no	—
165	C₂×Q₈	—	19	2	no	—
166	C₂×Q₈	—	38	1	no	—
167	C₂×Q₈	—	38	2	no	—
168	C₂×Q₈	—	38	2	no	—
169	C₂²×C₄	—	4	2	no	—
170	C₂²×C₄	—	38	1	no	—
171	C₂²×C₄	—	38	1	no	—
172	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
173	C₂²×C₄	#64543	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	2	2	no	—
177	C₂×C₈	—	38	4	no	—
178	C₂×C₈	—	76	2	no	—
179	C₂×C₈	—	76	2	no	—
180	C₂×C₈	—	76	1	no	—
181	C₂×C₈	—	76	2	no	—
182	C₂×C₈	#64528	1	4	yes	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	38	2	no	—
188	C₄⋊C₄	—	76	2	no	—
189	C₄²	—	76	1	no	—
190	C₄²	—	76	1	no	—
191	C₄²	D₄×D₁₉	1	2	yes	—
192	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
193	C₂³	#10597384	1	1	yes	characteristic
194	Q₈	—	8	4	no	—
195	Q₈	—	8	4	no	—
196	Q₈	—	38	4	no	—
197	Q₈	—	76	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	8	4	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	76	1	no	—
203	C₂×C₄	—	76	1	no	—
204	C₂×C₄	—	76	2	no	—
205	C₂×C₄	—	76	1	no	—
206	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
207	C₂×C₄	#10597364	1	2	yes	—
208	C₂×C₄	#10597365	1	1	yes	characteristic
209	C₂×C₄	#10597383	1	2	yes	—
210	C₂×C₄	#10597385	1	2	yes	—
211	C₂×C₄	#10597386	1	1	yes	characteristic
212	C₂×C₄	#10597388	1	2	yes	—
213	C₂×C₄	C₂×#64528	1	2	yes	—
214	C₂×C₄	#10597399	1	1	yes	characteristic
215	C₈	—	2	4	no	—
216	C₈	—	76	4	no	—
217	C₈	—	152	1	no	—
218	C₂²	#11926452	1	1	yes	characteristic
219	C₂²	#11926751	1	2	yes	—
220	C₂²	#11926782	1	1	yes	characteristic
221	C₂²	#11926799	1	1	yes	characteristic
222	C₂²	#11926811	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	4	no	—
225	C₄	—	76	2	no	—
226	C₄	—	152	1	no	—
227	C₄	#11926698	1	2	yes	—
228	C₄	#11926700	1	2	yes	—
229	C₄	#11926705	1	2	yes	—
230	C₄	#11926923	1	1	yes	characteristic
231	C₄	#11926936	1	1	yes	characteristic
232	C₂	#14563036	1	2	yes	—
233	C₂	#14563160	1	2	yes	—
234	C₂	#14564642	1	1	yes	characteristic
235	C₂	#14564735	1	1	yes	characteristic
236	C₂	#14564742	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926836

C₂

yes

maximal

#14564571

C₂

yes

maximal, characteristic

C₂×#11926293

C₂

yes

maximal

#14561470

C₂

yes

maximal, characteristic

C₂×C₁₉×#500

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597267

—

#11926298

—

#11926293

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#500

—

C₂×C₁₉×#107

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

D₄

yes

characteristic

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

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#107

—

C₄×C₈×C₁₉

—

#10597267

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₁₆

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

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

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

C₂×#500

D₁₉

yes

characteristic

101

C₂×#477

—

102

#1984

—

103

C₂×#333

—

104

#1277

—

105

C₂²×C₁₉

#392

yes

characteristic

106

C₂²×C₁₉

#462

yes

—

107

C₂²×C₁₉

#467

yes

characteristic

108

C₂²×C₁₉

#470

yes

characteristic

109

C₂²×C₁₉

#472

yes

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

#451

yes

—

113

C₄×C₁₉

#451

yes

—

114

C₄×C₁₉

#452

yes

—

115

C₄×C₁₉

#494

yes

characteristic

116

C₄×C₁₉

#497

yes

characteristic

117

Dic₁₉

—

118

Dic₁₉

—

119

C₂×C₄⋊Q₈

C₂×D₁₉

yes

—

120

C₂×C₄×Q₈

—

121

#500

—

122

#477

—

123

#477

—

124

C₂×#107

—

125

C₂×#107

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

—

128

C₂×#103

—

129

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

130

#336

—

131

#333

—

132

C₂×C₁₉

#1676

yes

—

133

C₂×C₁₉

#1696

yes

—

134

C₂×C₁₉

#2001

yes

characteristic

135

C₂×C₁₉

#2016

yes

characteristic

136

C₂×C₁₉

#2018

yes

characteristic

137

C₂²×Q₈

—

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

C₂²⋊D₁₉

yes

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

C₂²×D₁₉

yes

characteristic

154

#107

—

155

#107

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#103

—

160

C₄×C₈

—

161

C₁₉

#10279

yes

characteristic, complemented, Sylow

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

D₄×D₁₉

yes

characteristic

173

C₂²×C₄

#64543

yes

characteristic

174

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

#64528

yes

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

D₄×D₁₉

yes

—

192

C₄²

C₂×C₂²⋊D₁₉

yes

—

193

C₂³

#10597384

yes

characteristic

194

Q₈

—

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

207

C₂×C₄

#10597364

yes

—

208

C₂×C₄

#10597365

yes

characteristic

209

C₂×C₄

#10597383

yes

—

210

C₂×C₄

#10597385

yes

—

211

C₂×C₄

#10597386

yes

characteristic

212

C₂×C₄

#10597388

yes

—

213

C₂×C₄

C₂×#64528

yes

—

214

C₂×C₄

#10597399

yes

characteristic

215

C₈

—

216

C₈

—

217

C₈

—

152

—

218

C₂²

#11926452

yes

characteristic

219

C₂²

#11926751

yes

—

220

C₂²

#11926782

yes

characteristic

221

C₂²

#11926799

yes

characteristic

222

C₂²

#11926811

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

152

—

227

C₄

#11926698

yes

—

228

C₄

#11926700

yes

—

229

C₄

#11926705

yes

—

230

C₄

#11926923

yes

characteristic

231

C₄

#11926936

yes

characteristic

232

C₂

#14563036

yes

—

233

C₂

#14563160

yes

—

234

C₂

#14564642

yes

characteristic

235

C₂

#14564735

yes

characteristic

236

C₂

#14564742

yes

characteristic

	subgroup	G/H
center	C₂³	#10597384
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#500	C₂
socle, prime radical	C₂³×C₁₉	#121
hypercenter	C₂×#500	D₁₉
hypocenter	C₁₉	#10279
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

subgroup

G/H

center

C₂³

#10597384

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#500

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

N	H ≅ G/N	type
161. C₁₉	#10279	semidirect

H ≅ G/N

type

161. C₁₉

#10279

semidirect

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

subgroup	index
C₂×#11926836	2
#14564571	2
C₂×#11926293	2
#14561470	2
C₂×C₁₉×#500	2
#10279	19

subgroup

index

C₂×C₁₉×#500

Subgroups — #18085162

Conjugacy classes of subgroups

Complements

Maximal subgroups