Group #18076580 — subgroups

Subgroups — #18076580

Order 4864.

348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14572720	C₂	1	1	yes	maximal, characteristic
2	#14562418	C₂	1	2	yes	maximal
3	#14561959	C₂	1	1	yes	maximal, characteristic
4	#14561534	C₂	1	2	yes	maximal
5	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
6	#11926675	—	2	2	no	—
7	#11926675	—	2	2	no	—
8	#11926601	—	2	1	no	—
9	#11926601	C₂²	1	2	yes	—
10	#11926597	—	2	1	no	—
11	#11926597	C₂²	1	2	yes	—
12	#11926296	—	2	2	no	—
13	#11926294	—	2	2	no	—
14	#11926270	C₄	1	2	yes	—
15	#11926270	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₁₉×#336	—	2	1	no	—
21	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	—	2	1	no	—
23	C₂²×C₈×C₁₉	—	2	1	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×#97	—	2	2	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
36	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
42	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
43	#10597260	—	2	2	no	—
44	#10597260	—	2	2	no	—
45	C₄×C₁₉⋊C₈	—	2	2	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	C₂×Q₈×C₁₉	—	2	2	no	—
48	C₂×Q₈×C₁₉	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	—	4	1	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄²×C₁₉	—	2	1	no	—
66	C₄²×C₁₉	—	2	1	no	—
67	C₄²×C₁₉	—	2	1	no	—
68	C₄²×C₁₉	—	2	1	no	—
69	C₄²×C₁₉	C₂×D₄	1	2	yes	—
70	C₄²×C₁₉	#41	1	2	yes	—
71	C₂×C₁₉⋊C₈	—	2	4	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	—	2	2	no	—
74	#8865	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
76	Q₈×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	—	4	1	no	—
90	C₂×C₄×C₁₉	—	4	1	no	—
91	C₂×C₄×C₁₉	#108	1	2	yes	—
92	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
95	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
96	C₈×C₁₉	—	4	2	no	—
97	C₈×C₁₉	—	8	1	no	—
98	C₁₉⋊C₈	—	4	4	no	—
99	C₁₉⋊C₈	—	4	2	no	—
100	C₁₉⋊C₈	—	4	2	no	—
101	#2983	—	19	1	no	—
102	#1985	D₁₉	1	1	yes	characteristic
103	#1573	—	19	2	no	—
104	#1461	—	19	1	no	—
105	#1302	—	19	2	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	#385	1	1	yes	characteristic
109	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
110	C₂²×C₁₉	#430	1	1	yes	characteristic
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	2	2	no	—
115	C₄×C₁₉	—	4	1	no	—
116	C₄×C₁₉	—	4	1	no	—
117	C₄×C₁₉	—	4	1	no	—
118	C₄×C₁₉	#454	1	1	yes	characteristic
119	C₄×C₁₉	#456	1	1	yes	characteristic
120	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
121	#446	—	38	2	no	—
122	#446	—	38	2	no	—
123	#432	—	19	2	no	—
124	#432	—	38	1	no	—
125	#431	—	19	2	no	—
126	#431	—	38	1	no	—
127	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
128	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
129	#336	—	2	1	no	—
130	#336	—	2	1	no	—
131	#335	—	38	2	no	—
132	#334	—	38	2	no	—
133	#324	—	19	2	no	—
134	#324	—	19	2	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	—	2	1	no	—
137	C₂×C₁₉	#1855	1	1	yes	characteristic
138	C₂×C₁₉	#1857	1	1	yes	characteristic
139	C₂×C₁₉	#1868	1	1	yes	characteristic
140	C₂²×Q₈	Dic₃₈	1	1	yes	characteristic
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	2	1	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₂×C₄⋊C₄	Dic₃₈	1	1	yes	characteristic
146	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
148	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
149	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
150	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	19	2	no	—
153	C₄⋊C₈	—	19	2	no	—
154	C₄⋊C₈	—	38	1	no	—
155	C₄⋊C₈	—	38	1	no	—
156	C₄⋊C₈	—	38	1	no	—
157	C₄⋊C₈	—	38	1	no	—
158	C₄⋊C₈	—	38	2	no	—
159	C₂²⋊C₈	—	19	4	no	—
160	C₂²⋊C₈	—	38	2	no	—
161	#97	—	2	2	no	—
162	#97	—	38	2	no	—
163	#97	—	38	2	no	—
164	C₄×C₈	—	38	2	no	—
165	C₄×C₈	—	38	2	no	—
166	C₁₉	#8865	1	1	yes	characteristic, complemented, Sylow
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	4	1	no	—
170	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
171	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
172	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
173	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
174	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	4	1	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	4	1	no	—
182	C₂×C₈	—	38	2	no	—
183	C₂×C₈	—	38	2	no	—
184	C₂×C₈	—	38	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	2	1	no	—
191	C₄²	—	2	1	no	—
192	C₄²	D₄×D₁₉	1	2	yes	—
193	C₄²	#64543	1	2	yes	—
194	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	#10597279	1	2	yes	—
211	C₂×C₄	#10597324	1	2	yes	—
212	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
213	C₂×C₄	#10597381	1	1	yes	characteristic
214	C₂×C₄	#10597383	1	1	yes	characteristic
215	C₈	—	4	2	no	—
216	C₈	—	8	1	no	—
217	C₈	—	76	4	no	—
218	C₈	—	76	2	no	—
219	C₈	—	76	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#11926416	1	1	yes	characteristic
223	C₂²	C₂×#10597279	1	1	yes	characteristic
224	C₂²	#11926592	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	1	no	—
230	C₄	—	4	1	no	—
231	C₄	—	4	1	no	—
232	C₄	#11926716	1	1	yes	characteristic
233	C₄	#11926726	1	1	yes	characteristic
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#14563839	1	1	yes	characteristic
237	C₂	#14563849	1	1	yes	characteristic
238	C₂	#14563920	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572720

C₂

yes

maximal, characteristic

#14562418

C₂

yes

maximal

#14561959

C₂

yes

maximal, characteristic

#14561534

C₂

yes

maximal

C₁₉×#1985

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#11926597

—

#11926597

C₂²

yes

—

#11926296

—

#11926294

—

#11926270

C₄

yes

—

#11926270

C₄

yes

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₂²×Q₈×C₁₉

Q₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8865

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#108

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

—

101

#2983

—

102

#1985

D₁₉

yes

characteristic

103

#1573

—

104

#1461

—

105

#1302

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

#385

yes

characteristic

109

C₂²×C₁₉

C₂×#108

yes

characteristic

110

C₂²×C₁₉

#430

yes

characteristic

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

#454

yes

characteristic

119

C₄×C₁₉

#456

yes

characteristic

120

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

121

#446

—

122

#446

—

123

#432

—

124

#432

—

125

#431

—

126

#431

—

127

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

128

C₂×#97

C₂×D₁₉

yes

characteristic

129

#336

—

130

#336

—

131

#335

—

132

#334

—

133

#324

—

134

#324

—

135

C₂×C₁₉

—

136

C₂×C₁₉

—

137

C₂×C₁₉

#1855

yes

characteristic

138

C₂×C₁₉

#1857

yes

characteristic

139

C₂×C₁₉

#1868

yes

characteristic

140

C₂²×Q₈

Dic₃₈

yes

characteristic

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₂×C₄⋊C₄

Dic₃₈

yes

characteristic

146

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

147

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

148

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

149

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

150

C₂×C₄²

C₂²×D₁₉

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₂²⋊C₈

—

160

C₂²⋊C₈

—

161

#97

—

162

#97

—

163

#97

—

164

C₄×C₈

—

165

C₄×C₈

—

166

C₁₉

#8865

yes

characteristic, complemented, Sylow

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

171

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

172

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

173

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

174

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

175

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

176

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

D₄×D₁₉

yes

—

193

C₄²

#64543

yes

—

194

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

195

Q₈

—

196

C₂×C₄

—

197

C₂×C₄

—

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

#10597279

yes

—

211

C₂×C₄

#10597324

yes

—

212

C₂×C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

213

C₂×C₄

#10597381

yes

characteristic

214

C₂×C₄

#10597383

yes

characteristic

215

C₈

—

216

C₈

—

217

C₈

—

218

C₈

—

219

C₈

—

220

C₂²

—

221

C₂²

—

222

C₂²

#11926416

yes

characteristic

223

C₂²

C₂×#10597279

yes

characteristic

224

C₂²

#11926592

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

#11926716

yes

characteristic

233

C₄

#11926726

yes

characteristic

234

C₂

—

235

C₂

—

236

C₂

#14563839

yes

characteristic

237

C₂

#14563849

yes

characteristic

238

C₂

#14563920

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1985	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1985	D₁₉
hypocenter	C₁₉	#8865
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

subgroup

G/H

center

C₂×C₄

#10597383

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1985

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1985

N	H ≅ G/N	type
166. C₁₉	#8865	semidirect

H ≅ G/N

type

166. C₁₉

#8865

semidirect

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

subgroup	index
#14572720	2
#14562418	2
#14561959	2
#14561534	2
C₁₉×#1985	2
#8865	19

subgroup

index

C₁₉×#1985

Subgroups — #18076580

Conjugacy classes of subgroups

Complements

Maximal subgroups