Group #18076121 — subgroups

Subgroups — #18076121

Order 4864.

422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14566556	C₂	1	1	yes	maximal, characteristic
2	#14563631	C₂	1	1	yes	maximal, characteristic
3	#14561537	C₂	1	2	yes	maximal
4	#14561494	C₂	1	2	yes	maximal
5	C₁₉×#1461	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×Dic₁₉	—	2	1	no	—
7	#11926568	C₂²	1	2	yes	—
8	C₂×#10597293	—	2	1	no	—
9	#11926443	—	2	1	no	—
10	#11926443	—	2	2	no	—
11	#11926410	C₄	1	2	yes	—
12	#11926410	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₁₉	C₄	1	2	yes	—
14	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926313	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#431	C₂²	1	2	yes	—
18	C₁₉×#324	—	2	2	no	—
19	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
20	C₄×Q₈×C₁₉	—	2	2	no	—
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	Q₈×Dic₁₉	—	4	4	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄×Dic₁₉	—	2	2	no	—
32	C₂×C₄×Dic₁₉	—	2	1	no	—
33	C₂×#64520	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₂²⋊C₈	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	#10597293	—	4	2	no	—
38	C₁₉⋊#95	—	2	2	no	—
39	C₁₉⋊#95	—	2	1	no	—
40	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
41	C₁₉⋊#95	C₂×C₄	1	2	yes	—
42	C₁₉⋊#95	C₂×C₄	1	1	yes	characteristic
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	—	2	2	no	—
47	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
48	C₂×Q₈×C₁₉	Q₁₆	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₁₉	—	2	1	no	—
55	C₂²×Dic₁₉	—	2	1	no	—
56	C₂²×Dic₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₄²×C₁₉	—	2	2	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	#41	1	2	yes	—
63	C₄²×C₁₉	#41	1	2	yes	—
64	C₄⋊Dic₁₉	—	4	2	no	—
65	C₄⋊Dic₁₉	—	4	4	no	—
66	C₄⋊Dic₁₉	—	4	4	no	—
67	C₄⋊Dic₁₉	—	4	2	no	—
68	C₄×Dic₁₉	—	4	4	no	—
69	C₄×Dic₁₉	—	4	2	no	—
70	#64520	—	4	2	no	—
71	#64520	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	2	no	—
73	#8767	—	19	1	no	maximal, Sylow
74	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₁₉	—	2	4	no	—
76	Q₈×C₁₉	—	2	4	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	#103	1	4	yes	—
84	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#123	1	2	yes	—
87	C₂×C₄×C₁₉	#123	1	2	yes	—
88	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	4	1	no	—
93	C₂×Dic₁₉	—	4	1	no	—
94	C₂×Dic₁₉	—	4	1	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	1	no	—
97	C₂×Dic₁₉	—	4	2	no	—
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	1	no	—
100	C₈×C₁₉	—	8	2	no	—
101	C₁₉⋊C₈	—	8	2	no	—
102	#2351	—	19	1	no	—
103	#1801	—	19	1	no	—
104	#1461	D₁₉	1	1	yes	characteristic
105	#1303	—	19	2	no	—
106	#1286	—	19	2	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	#381	1	1	yes	characteristic
110	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
111	C₂²×C₁₉	#418	1	1	yes	characteristic
112	C₄×C₁₉	—	2	4	no	—
113	C₄×C₁₉	—	2	2	no	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	4	2	no	—
117	C₄×C₁₉	#481	1	2	yes	—
118	C₄×C₁₉	#484	1	2	yes	—
119	Dic₁₉	—	4	2	no	—
120	Dic₁₉	—	8	2	no	—
121	Dic₁₉	—	8	1	no	—
122	C₂×C₄×Q₈	—	38	1	no	—
123	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
124	#431	C₂×D₁₉	1	2	yes	—
125	#423	—	19	2	no	—
126	C₂×#101	—	38	1	no	—
127	#389	—	38	1	no	—
128	#389	—	38	2	no	—
129	#382	—	19	2	no	—
130	#382	—	19	1	no	—
131	C₄×C₄⋊C₄	—	19	2	no	—
132	C₄×C₄⋊C₄	—	19	1	no	—
133	#343	—	38	1	no	—
134	#324	—	2	2	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	—	2	1	no	—
137	C₂×C₁₉	#1824	1	1	yes	characteristic
138	C₂×C₁₉	#1827	1	1	yes	characteristic
139	C₂×C₁₉	#1830	1	1	yes	characteristic
140	C₂²×Q₈	D₇₆	1	1	yes	characteristic
141	C₂×M₁₆	—	38	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	76	4	no	—
145	C₂×C₄⋊C₄	—	38	2	no	—
146	C₂×C₄⋊C₄	—	38	2	no	—
147	C₂×C₄⋊C₄	—	38	1	no	—
148	C₂×C₄⋊C₄	—	38	1	no	—
149	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
150	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
151	C₂×C₄²	—	38	2	no	—
152	C₂×C₄²	—	38	1	no	—
153	C₂×C₄²	C₄×D₁₉	1	2	yes	—
154	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	38	2	no	—
157	C₄⋊C₈	—	38	2	no	—
158	#101	—	76	2	no	—
159	C₂²⋊C₈	—	2	2	no	—
160	C₄×C₈	—	2	2	no	—
161	#95	—	19	1	no	—
162	#95	—	19	2	no	—
163	#95	—	19	1	no	—
164	#95	—	38	2	no	—
165	#95	—	38	1	no	—
166	C₁₉	#8767	1	1	yes	characteristic, complemented, Sylow
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	#64516	1	2	yes	—
170	C₂×Q₈	Dic₇₆	1	2	yes	—
171	C₂²×C₄	—	38	1	no	—
172	C₂²×C₄	—	38	1	no	—
173	C₂²×C₄	—	38	2	no	—
174	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
175	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
176	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
179	M₁₆	—	76	2	no	—
180	M₁₆	—	76	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	76	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	76	4	no	—
186	C₄⋊C₄	—	76	2	no	—
187	C₄⋊C₄	—	76	4	no	—
188	C₄⋊C₄	—	76	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	76	4	no	—
192	C₄²	—	76	2	no	—
193	C₄²	#64543	1	2	yes	—
194	C₄²	#64543	1	2	yes	—
195	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
196	Q₈	—	2	4	no	—
197	Q₈	—	2	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	38	2	no	—
205	C₂×C₄	—	76	1	no	—
206	C₂×C₄	—	76	1	no	—
207	C₂×C₄	—	76	1	no	—
208	C₂×C₄	—	76	2	no	—
209	C₂×C₄	—	76	1	no	—
210	C₂×C₄	—	76	2	no	—
211	C₂×C₄	—	76	2	no	—
212	C₂×C₄	—	76	1	no	—
213	C₂×C₄	#10597273	1	4	yes	—
214	C₂×C₄	#10597323	1	1	yes	characteristic
215	C₂×C₄	#10597323	1	1	yes	characteristic
216	C₂×C₄	#10597332	1	2	yes	—
217	C₂×C₄	C₂×#64516	1	1	yes	characteristic
218	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
219	C₂×C₄	#10597354	1	2	yes	—
220	C₂×C₄	#10597381	1	2	yes	—
221	C₈	—	8	2	no	—
222	C₈	—	152	2	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#11926405	1	1	yes	characteristic
226	C₂²	C₂×#10597273	1	1	yes	characteristic
227	C₂²	#11926550	1	1	yes	characteristic
228	C₄	—	2	4	no	—
229	C₄	—	2	2	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	4	2	no	—
233	C₄	—	76	2	no	—
234	C₄	—	152	2	no	—
235	C₄	—	152	1	no	—
236	C₄	#11926863	1	2	yes	—
237	C₄	#11926880	1	2	yes	—
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	#14563726	1	1	yes	characteristic
241	C₂	#14563736	1	1	yes	characteristic
242	C₂	#14563747	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14566556

C₂

yes

maximal, characteristic

#14563631

C₂

yes

maximal, characteristic

#14561537

C₂

yes

maximal

#14561494

C₂

yes

maximal

C₁₉×#1461

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₁₉

—

#11926568

C₂²

yes

—

—

—

—

C₄

yes

—

#11926410

C₂²

yes

characteristic

C₄×C₄⋊Dic₁₉

C₄

yes

—

C₄×C₄⋊Dic₁₉

C₂²

yes

characteristic

#11926313

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

—

C₁₉×#324

—

C₂²×Q₈×C₁₉

D₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

Q₈×Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597293

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₁₉⋊#95

C₂×C₄

yes

—

C₁₉⋊#95

C₂×C₄

yes

characteristic

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

—

C₂×Q₈×C₁₉

Q₁₆

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

#8767

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

#2351

—

103

#1801

—

104

#1461

D₁₉

yes

characteristic

105

#1303

—

106

#1286

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#381

yes

characteristic

110

C₂²×C₁₉

C₂×#103

yes

characteristic

111

C₂²×C₁₉

#418

yes

characteristic

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

#481

yes

—

118

C₄×C₁₉

#484

yes

—

119

Dic₁₉

—

120

Dic₁₉

—

121

Dic₁₉

—

122

C₂×C₄×Q₈

—

123

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

124

#431

C₂×D₁₉

yes

—

125

#423

—

126

C₂×#101

—

127

#389

—

128

#389

—

129

#382

—

130

#382

—

131

C₄×C₄⋊C₄

—

132

C₄×C₄⋊C₄

—

133

#343

—

134

#324

—

135

C₂×C₁₉

—

136

C₂×C₁₉

—

137

C₂×C₁₉

#1824

yes

characteristic

138

C₂×C₁₉

#1827

yes

characteristic

139

C₂×C₁₉

#1830

yes

characteristic

140

C₂²×Q₈

D₇₆

yes

characteristic

141

C₂×M₁₆

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

D₇₆

yes

characteristic

150

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

C₄×D₁₉

yes

—

154

C₂×C₄²

C₂²×D₁₉

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

#101

—

159

C₂²⋊C₈

—

160

C₄×C₈

—

161

#95

—

162

#95

—

163

#95

—

164

#95

—

165

#95

—

166

C₁₉

#8767

yes

characteristic, complemented, Sylow

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

#64516

yes

—

170

C₂×Q₈

Dic₇₆

yes

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

175

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

176

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

177

C₂²×C₄

C₂×D₇₆

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

#64543

yes

—

194

C₄²

#64543

yes

—

195

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

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

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

#10597273

yes

—

214

C₂×C₄

#10597323

yes

characteristic

215

C₂×C₄

#10597323

yes

characteristic

216

C₂×C₄

#10597332

yes

—

217

C₂×C₄

C₂×#64516

yes

characteristic

218

C₂×C₄

C₂×Dic₇₆

yes

characteristic

219

C₂×C₄

#10597354

yes

—

220

C₂×C₄

#10597381

yes

—

221

C₈

—

222

C₈

—

152

—

223

C₂²

—

224

C₂²

—

225

C₂²

#11926405

yes

characteristic

226

C₂²

C₂×#10597273

yes

characteristic

227

C₂²

#11926550

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

152

—

235

C₄

—

152

—

236

C₄

#11926863

yes

—

237

C₄

#11926880

yes

—

238

C₂

—

239

C₂

—

240

C₂

#14563726

yes

characteristic

241

C₂

#14563736

yes

characteristic

242

C₂

#14563747

yes

characteristic

	subgroup	G/H
center	C₂²	#11926405
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1461	C₂
socle	C₂²×C₁₉	#381
prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1461	D₁₉
hypocenter	C₁₉	#8767
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1461

subgroup

G/H

center

C₂²

#11926405

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1461

C₂

socle

C₂²×C₁₉

#381

prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1461

N	H ≅ G/N	type
166. C₁₉	#8767	semidirect

H ≅ G/N

type

166. C₁₉

#8767

semidirect

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

subgroup	index
#14566556	2
#14563631	2
#14561537	2
#14561494	2
C₁₉×#1461	2
#8767	19

subgroup

index

C₁₉×#1461

Subgroups — #18076121

Conjugacy classes of subgroups

Complements

Maximal subgroups