Group #18069686 — subgroups

Subgroups — #18069686

Order 4864.

342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 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×C₂²⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#14563664	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₉⋊C₁₆	—	2	1	no	—
5	C₂×#10597275	C₄	1	2	yes	—
6	#11926404	—	2	1	no	—
7	C₂²⋊(C₁₉⋊C₁₆)	—	2	1	no	—
8	C₂²⋊(C₁₉⋊C₁₆)	C₄	1	2	yes	complemented
9	#11926307	—	2	1	no	—
10	C₂²×M₁₆×C₁₉	—	2	1	no	—
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#341	—	2	1	no	—
13	C₁₉×#341	C₄	1	2	yes	complemented
14	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂×M₁₆×C₁₉	—	2	4	no	—
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₂×M₁₆×C₁₉	—	4	2	no	—
18	C₂×M₁₆×C₁₉	—	4	1	no	—
19	C₂²×C₈×C₁₉	—	4	2	no	—
20	C₂²×C₈×C₁₉	—	4	1	no	—
21	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₉	—	4	1	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₁₉⋊#95	—	4	1	no	—
30	#10597275	—	4	2	no	—
31	C₂×C₁₉⋊C₁₆	—	2	2	no	—
32	C₂×C₁₉⋊C₁₆	—	4	2	no	—
33	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	4	2	no	—
43	M₁₆×C₁₉	—	2	4	no	—
44	M₁₆×C₁₉	—	4	4	no	—
45	M₁₆×C₁₉	—	4	2	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	4	1	no	—
49	C₂×C₈×C₁₉	—	4	1	no	—
50	C₂×C₈×C₁₉	—	4	1	no	—
51	C₂×C₈×C₁₉	—	4	1	no	—
52	C₂×C₈×C₁₉	—	4	4	no	—
53	C₂×C₈×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂²⋊Dic₁₉	—	8	2	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₁₉⋊C₁₆	—	4	2	no	—
62	#7259	—	19	1	no	maximal, Sylow
63	C₂³×C₁₉	—	2	2	no	—
64	C₂³×C₁₉	—	2	2	no	—
65	C₂³×C₁₉	—	2	1	no	—
66	C₂³×C₁₉	—	2	1	no	—
67	C₂³×C₁₉	#102	1	1	yes	characteristic
68	C₂³×C₁₉	#103	1	1	yes	characteristic
69	C₂³×C₁₉	#106	1	1	yes	characteristic
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#99	1	2	yes	—
79	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#104	1	2	yes	—
82	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
83	C₂×Dic₁₉	—	8	2	no	—
84	C₂×Dic₁₉	—	8	2	no	—
85	C₂×Dic₁₉	—	8	2	no	—
86	C₈×C₁₉	—	2	1	no	—
87	C₈×C₁₉	—	2	1	no	—
88	C₈×C₁₉	—	2	1	no	—
89	C₈×C₁₉	—	2	1	no	—
90	C₈×C₁₉	—	4	4	no	—
91	C₂×C₂²⋊C₁₆	—	19	1	no	—
92	#1808	—	19	1	no	—
93	C₂×#341	D₁₉	1	1	yes	characteristic
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	—	4	2	no	—
101	C₂²×C₁₉	—	4	2	no	—
102	C₂²×C₁₉	#327	1	2	yes	—
103	C₂²×C₁₉	#340	1	1	yes	characteristic
104	C₂²×C₁₉	#359	1	2	yes	—
105	C₂²×C₁₉	#361	1	1	yes	characteristic
106	C₂²×C₁₉	#362	1	1	yes	characteristic
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	#328	1	2	yes	—
110	C₄×C₁₉	#339	1	1	yes	characteristic
111	C₄×C₁₉	#342	1	1	yes	characteristic
112	Dic₁₉	—	16	2	no	—
113	C₂²×M₁₆	—	2	1	no	—
114	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
115	C₂²×C₁₆	—	38	1	no	—
116	C₂×#107	—	19	2	no	—
117	#380	—	38	1	no	—
118	C₂²⋊C₁₆	—	19	2	no	—
119	C₂²⋊C₁₆	—	38	1	no	—
120	#341	—	2	1	no	—
121	#341	Dic₁₉	1	2	yes	complemented
122	#340	—	38	1	no	—
123	C₂×C₁₉	—	4	1	no	—
124	C₂×C₁₉	—	4	1	no	—
125	C₂×C₁₉	#1294	1	1	yes	characteristic
126	C₂×C₁₉	#1349	1	2	yes	—
127	C₂×C₁₉	#1350	1	2	yes	—
128	C₂×C₁₉	#1382	1	1	yes	characteristic
129	C₂×C₁₉	#1387	1	1	yes	characteristic
130	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
131	C₂×M₁₆	—	2	4	no	—
132	C₂×M₁₆	—	2	2	no	—
133	C₂×M₁₆	—	4	2	no	—
134	C₂×M₁₆	—	4	1	no	—
135	C₂²×C₈	—	4	2	no	—
136	C₂²×C₈	—	4	1	no	—
137	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
138	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
139	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
140	C₂²×C₈	D₇₆	1	1	yes	characteristic
141	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
142	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
143	C₂×C₄⋊C₄	—	38	2	no	—
144	C₂×C₂²⋊C₄	—	76	1	no	—
145	C₂×C₁₆	—	38	2	no	—
146	C₂×C₁₆	—	76	2	no	—
147	#107	—	76	2	no	—
148	#95	—	76	1	no	—
149	C₁₉	#7259	1	1	yes	characteristic, complemented, Sylow
150	C₂⁴	#64527	1	1	yes	characteristic
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	76	2	no	—
154	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
155	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
156	C₂²×C₄	#64525	1	1	yes	characteristic
157	C₂²×C₄	#64526	1	1	yes	characteristic
158	C₂²×C₄	#64528	1	1	yes	characteristic
159	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
160	M₁₆	—	2	4	no	—
161	M₁₆	—	4	4	no	—
162	M₁₆	—	4	2	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	1	no	—
168	C₂×C₈	—	4	1	no	—
169	C₂×C₈	—	4	4	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
172	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
173	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
174	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
175	C₄⋊C₄	—	76	2	no	—
176	C₄⋊C₄	—	76	2	no	—
177	C₂²⋊C₄	—	152	2	no	—
178	C₁₆	—	76	2	no	—
179	C₂³	—	2	2	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	1	no	—
182	C₂³	—	2	1	no	—
183	C₂³	#10597265	1	1	yes	characteristic
184	C₂³	#10597266	1	1	yes	characteristic
185	C₂³	#10597292	1	1	yes	characteristic
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	152	2	no	—
194	C₂×C₄	—	152	2	no	—
195	C₂×C₄	—	152	2	no	—
196	C₂×C₄	#10597262	1	2	yes	—
197	C₂×C₄	#10597263	1	2	yes	—
198	C₂×C₄	#10597264	1	1	yes	characteristic
199	C₂×C₄	#10597267	1	1	yes	characteristic
200	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
201	C₂×C₄	#10597289	1	1	yes	characteristic
202	C₈	—	2	1	no	—
203	C₈	—	2	1	no	—
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	4	4	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	2	no	—
215	C₂²	#11926277	1	2	yes	—
216	C₂²	#11926306	1	1	yes	characteristic
217	C₂²	#11926350	1	2	yes	—
218	C₂²	#11926356	1	1	yes	characteristic
219	C₂²	#11926359	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	304	2	no	—
223	C₄	#11926280	1	2	yes	—
224	C₄	#11926304	1	1	yes	characteristic
225	C₄	#11926310	1	1	yes	characteristic
226	C₂	—	4	1	no	—
227	C₂	—	4	1	no	—
228	C₂	#14561514	1	1	yes	characteristic
229	C₂	#14561649	1	2	yes	—
230	C₂	#14561652	1	2	yes	—
231	C₂	#14561732	1	1	yes	characteristic
232	C₂	#14561745	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂²⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic

#14563664

C₂

yes

maximal, characteristic

C₂×C₁₉×#341

C₂

yes

maximal, characteristic

C₂²×C₁₉⋊C₁₆

—

C₂×#10597275

C₄

yes

—

#11926404

—

C₂²⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

C₄

yes

complemented

#11926307

—

C₂²×M₁₆×C₁₉

—

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#341

—

C₁₉×#341

C₄

yes

complemented

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

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

Q₈

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₁₉⋊#95

—

#10597275

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂⁴×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

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

—

C₁₉⋊C₁₆

—

#7259

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#107

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₂×C₂²⋊C₁₆

—

#1808

—

C₂×#341

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

#327

yes

—

103

C₂²×C₁₉

#340

yes

characteristic

104

C₂²×C₁₉

#359

yes

—

105

C₂²×C₁₉

#361

yes

characteristic

106

C₂²×C₁₉

#362

yes

characteristic

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#328

yes

—

110

C₄×C₁₉

#339

yes

characteristic

111

C₄×C₁₉

#342

yes

characteristic

112

Dic₁₉

—

113

C₂²×M₁₆

—

114

C₂³×C₈

C₂×D₁₉

yes

characteristic

115

C₂²×C₁₆

—

116

C₂×#107

—

117

#380

—

118

C₂²⋊C₁₆

—

119

C₂²⋊C₁₆

—

120

#341

—

121

#341

Dic₁₉

yes

complemented

122

#340

—

123

C₂×C₁₉

—

124

C₂×C₁₉

—

125

C₂×C₁₉

#1294

yes

characteristic

126

C₂×C₁₉

#1349

yes

—

127

C₂×C₁₉

#1350

yes

—

128

C₂×C₁₉

#1382

yes

characteristic

129

C₂×C₁₉

#1387

yes

characteristic

130

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

131

C₂×M₁₆

—

132

C₂×M₁₆

—

133

C₂×M₁₆

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

Dic₃₈

yes

characteristic

138

C₂²×C₈

C₄×D₁₉

yes

characteristic

139

C₂²×C₈

C₄×D₁₉

yes

characteristic

140

C₂²×C₈

D₇₆

yes

characteristic

141

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

142

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

143

C₂×C₄⋊C₄

—

144

C₂×C₂²⋊C₄

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

#107

—

148

#95

—

149

C₁₉

#7259

yes

characteristic, complemented, Sylow

150

C₂⁴

#64527

yes

characteristic

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

155

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

156

C₂²×C₄

#64525

yes

characteristic

157

C₂²×C₄

#64526

yes

characteristic

158

C₂²×C₄

#64528

yes

characteristic

159

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

160

M₁₆

—

161

M₁₆

—

162

M₁₆

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

C₄×Dic₁₉

yes

characteristic

172

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

173

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

174

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₂²⋊C₄

—

152

—

178

C₁₆

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

#10597265

yes

characteristic

184

C₂³

#10597266

yes

characteristic

185

C₂³

#10597292

yes

characteristic

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

152

—

194

C₂×C₄

—

152

—

195

C₂×C₄

—

152

—

196

C₂×C₄

#10597262

yes

—

197

C₂×C₄

#10597263

yes

—

198

C₂×C₄

#10597264

yes

characteristic

199

C₂×C₄

#10597267

yes

characteristic

200

C₂×C₄

C₁₉⋊#95

yes

characteristic

201

C₂×C₄

#10597289

yes

characteristic

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

#11926277

yes

—

216

C₂²

#11926306

yes

characteristic

217

C₂²

#11926350

yes

—

218

C₂²

#11926356

yes

characteristic

219

C₂²

#11926359

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

304

—

223

C₄

#11926280

yes

—

224

C₄

#11926304

yes

characteristic

225

C₄

#11926310

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

#14561514

yes

characteristic

229

C₂

#14561649

yes

—

230

C₂

#14561652

yes

—

231

C₂

#14561732

yes

characteristic

232

C₂

#14561745

yes

characteristic

	subgroup	G/H
center	C₂³	#10597266
commutator	C₂×C₈×C₁₉	C₄²
Frattini	C₂³×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#341	C₂
socle	C₂³×C₁₉	#102
prime radical	C₂⁴×C₁₉	SD₁₆
cosocle	C₂³×C₈×C₁₉	C₂²
hypercenter	C₂×#341	D₁₉
hypocenter	C₁₉	#7259
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#341

subgroup

G/H

center

C₂³

#10597266

commutator

C₂×C₈×C₁₉

C₄²

Frattini

C₂³×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#341

C₂

socle

C₂³×C₁₉

#102

prime radical

C₂⁴×C₁₉

SD₁₆

cosocle

C₂³×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#341

N	H ≅ G/N	type
8. C₂²⋊(C₁₉⋊C₁₆)	C₄	semidirect
13. C₁₉×#341	C₄	semidirect
121. #341	Dic₁₉	semidirect
149. C₁₉	#7259	semidirect

H ≅ G/N

type

8. C₂²⋊(C₁₉⋊C₁₆)

C₄

semidirect

13. C₁₉×#341

C₄

semidirect

121. #341

Dic₁₉

semidirect

149. C₁₉

#7259

semidirect

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

subgroup	index
C₂×C₂²⋊(C₁₉⋊C₁₆)	2
#14563664	2
C₂×C₁₉×#341	2
#7259	19

subgroup

index

C₂×C₂²⋊(C₁₉⋊C₁₆)

#14563664

C₂×C₁₉×#341

#7259

Subgroups — #18069686

Conjugacy classes of subgroups

Complements

Maximal subgroups