Group #18076406 — subgroups

Subgroups — #18076406

Order 4864.

410 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14564572	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597293	C₂	1	1	yes	maximal, characteristic
3	#14562388	C₂	1	2	yes	maximal
4	#14561471	C₂	1	2	yes	maximal
5	C₁₉×#2982	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂×#10597293	C₄	1	1	yes	characteristic
8	C₂×#10597293	C₄	1	1	yes	characteristic
9	C₄×#64520	C₂²	1	2	yes	—
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#11926313	C₄	1	2	yes	—
12	#11926299	—	2	2	no	—
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₁₉	—	2	2	no	—
17	C₈×Q₈×C₁₉	—	2	2	no	—
18	C₁₉×#431	—	2	2	no	—
19	C₁₉×#431	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Q₈×C₁₉	—	2	2	no	—
22	C₄×Q₈×C₁₉	—	2	2	no	—
23	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×#64520	C₂×C₄	1	2	yes	—
28	C₂×#64520	C₂×C₄	1	2	yes	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
34	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
35	C₁₉×C₂²⋊C₈	—	2	2	no	—
36	C₄×C₈×C₁₉	—	2	4	no	—
37	C₄×C₈×C₁₉	—	2	2	no	—
38	#10597293	—	2	2	no	—
39	#10597293	C₈	1	4	yes	complemented
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	#10597260	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	C₄×C₁₉⋊C₈	—	2	2	no	—
44	C₂×Q₈×C₁₉	—	2	2	no	—
45	C₂×Q₈×C₁₉	—	2	2	no	—
46	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
47	C₂×Q₈×C₁₉	M₁₆	1	2	yes	—
48	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	C₂×D₄	1	2	yes	—
60	C₄²×C₁₉	#41	1	2	yes	—
61	#64520	—	2	2	no	—
62	#64520	—	2	2	no	—
63	#64520	—	2	2	no	—
64	#64520	C₂×C₈	1	4	yes	—
65	C₂×C₁₉⋊C₈	—	2	2	no	—
66	C₂×C₁₉⋊C₈	—	2	2	no	—
67	C₂×C₁₉⋊C₈	—	2	2	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	2	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	#8836	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	Q₈×C₁₉	—	2	4	no	—
75	Q₈×C₁₉	—	2	4	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
87	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#131	1	2	yes	—
91	C₈×C₁₉	—	4	2	no	—
92	C₈×C₁₉	—	4	2	no	—
93	C₁₉⋊C₈	—	2	4	no	—
94	C₁₉⋊C₈	—	4	2	no	—
95	C₁₉⋊C₈	—	4	2	no	—
96	C₁₉⋊C₈	—	8	1	no	—
97	#2982	D₁₉	1	1	yes	characteristic
98	#1984	—	19	1	no	—
99	C₄×#101	—	19	1	no	—
100	#1565	—	19	2	no	—
101	#1278	—	19	2	no	—
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	—	2	1	no	—
104	C₂²×C₁₉	#385	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
106	C₂²×C₁₉	#424	1	1	yes	characteristic
107	C₄×C₁₉	—	2	4	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	4	2	no	—
111	C₄×C₁₉	C₈×D₄	1	2	yes	—
112	C₄×C₁₉	#435	1	2	yes	—
113	C₄×C₁₉	#454	1	1	yes	characteristic
114	C₄×C₁₉	#456	1	1	yes	characteristic
115	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
116	C₈×Q₈	—	2	2	no	—
117	C₈×Q₈	—	2	2	no	—
118	#431	—	2	2	no	—
119	#431	C₂×D₁₉	1	2	yes	—
120	C₂×C₄⋊C₈	—	19	1	no	—
121	C₂×#101	—	19	1	no	—
122	C₂×#101	—	19	1	no	—
123	C₄×M₁₆	—	19	2	no	—
124	C₂×C₄×C₈	—	19	1	no	—
125	#343	—	19	2	no	—
126	#336	—	38	2	no	—
127	#335	—	38	2	no	—
128	#334	—	38	2	no	—
129	C₂×C₁₉	—	2	1	no	—
130	C₂×C₁₉	—	2	1	no	—
131	C₂×C₁₉	#1850	1	1	yes	characteristic
132	C₂×C₁₉	#1857	1	1	yes	characteristic
133	C₂×C₁₉	#1858	1	1	yes	characteristic
134	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
135	C₂×M₁₆	—	19	2	no	—
136	C₂×M₁₆	—	19	2	no	—
137	C₂²×C₈	—	38	1	no	—
138	C₂²×C₈	—	38	1	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
142	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
143	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
144	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	38	2	no	—
148	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
149	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
150	#101	—	19	4	no	—
151	#101	—	38	2	no	—
152	C₂²⋊C₈	—	2	2	no	—
153	#97	—	38	2	no	—
154	C₄×C₈	—	2	4	no	—
155	C₄×C₈	—	2	2	no	—
156	C₄×C₈	—	38	2	no	—
157	C₄×C₈	—	38	2	no	—
158	C₁₉	#8836	1	1	yes	characteristic, complemented, Sylow
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	C₈×D₁₉	1	2	yes	—
162	C₂×Q₈	#64515	1	2	yes	—
163	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
164	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
165	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	M₁₆	—	19	4	no	—
169	M₁₆	—	38	2	no	—
170	M₁₆	—	38	2	no	—
171	M₁₆	—	38	2	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	38	2	no	—
175	C₂×C₈	—	38	2	no	—
176	C₂×C₈	—	38	2	no	—
177	C₂×C₈	—	76	1	no	—
178	C₂×C₈	—	76	1	no	—
179	C₂×C₈	—	76	2	no	—
180	C₂×C₈	—	76	1	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	#64541	1	2	yes	—
186	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
187	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
188	Q₈	—	2	4	no	—
189	Q₈	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
198	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
199	C₂×C₄	C₂×#64515	1	1	yes	characteristic
200	C₂×C₄	#10597347	1	2	yes	—
201	C₂×C₄	#10597370	1	2	yes	—
202	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
203	C₂×C₄	#10597375	1	1	yes	characteristic
204	C₂×C₄	#10597399	1	1	yes	characteristic
205	C₈	—	4	2	no	—
206	C₈	—	4	2	no	—
207	C₈	—	38	4	no	—
208	C₈	—	76	2	no	—
209	C₈	—	76	2	no	—
210	C₈	—	152	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	#11926417	1	1	yes	characteristic
214	C₂²	C₂×Dic₁₉⋊C₈	1	1	yes	characteristic
215	C₂²	#11926570	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	4	no	—
219	C₄	—	4	2	no	—
220	C₄	C₈×C₂²⋊D₁₉	1	2	yes	—
221	C₄	#11926615	1	2	yes	—
222	C₄	#11926717	1	1	yes	characteristic
223	C₄	#11926727	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	#14563813	1	1	yes	characteristic
227	C₂	#14563850	1	1	yes	characteristic
228	C₂	#14563855	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564572

C₂

yes

maximal, characteristic

C₄×#10597293

C₂

yes

maximal, characteristic

#14562388

C₂

yes

maximal

#14561471

C₂

yes

maximal

C₁₉×#2982

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597293

C₄

yes

characteristic

C₂×#10597293

C₄

yes

characteristic

C₄×#64520

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926313

C₄

yes

—

#11926299

—

#11926296

—

#11926294

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₈×Q₈×C₁₉

—

C₈×Q₈×C₁₉

—

C₁₉×#431

—

C₁₉×#431

C₂²

yes

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

C₂×C₄

yes

—

C₂×#64520

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

#10597293

—

#10597293

C₈

yes

complemented

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

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

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

—

—

—

C₂×C₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8836

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊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

—

C₂×C₄×C₁₉

C₄⋊C₈

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

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

#131

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2982

D₁₉

yes

characteristic

#1984

—

C₄×#101

—

100

#1565

—

101

#1278

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

#385

yes

characteristic

105

C₂²×C₁₉

C₂×C₄⋊C₈

yes

characteristic

106

C₂²×C₁₉

#424

yes

characteristic

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

C₈×D₄

yes

—

112

C₄×C₁₉

#435

yes

—

113

C₄×C₁₉

#454

yes

characteristic

114

C₄×C₁₉

#456

yes

characteristic

115

C₂×C₄×Q₈

C₂×D₁₉

yes

characteristic

116

C₈×Q₈

—

117

C₈×Q₈

—

118

#431

—

119

#431

C₂×D₁₉

yes

—

120

C₂×C₄⋊C₈

—

121

C₂×#101

—

122

C₂×#101

—

123

C₄×M₁₆

—

124

C₂×C₄×C₈

—

125

#343

—

126

#336

—

127

#335

—

128

#334

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1850

yes

characteristic

132

C₂×C₁₉

#1857

yes

characteristic

133

C₂×C₁₉

#1858

yes

characteristic

134

C₂²×Q₈

C₄×D₁₉

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

Dic₃₈

yes

—

142

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

143

C₂×C₄²

C₂²⋊D₁₉

yes

—

144

C₂×C₄²

C₂²×D₁₉

yes

characteristic

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

C₂²⋊D₁₉

yes

—

149

C₄⋊C₈

C₂²⋊D₁₉

yes

—

150

#101

—

151

#101

—

152

C₂²⋊C₈

—

153

#97

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₁₉

#8836

yes

characteristic, complemented, Sylow

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₈×D₁₉

yes

—

162

C₂×Q₈

#64515

yes

—

163

C₂²×C₄

Dic₁₉⋊C₄

yes

—

164

C₂²×C₄

Dic₁₉⋊C₄

yes

—

165

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

166

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

167

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

M₁₆

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

#64541

yes

—

186

C₄²

C₂×C₂²⋊D₁₉

yes

—

187

C₂³

C₂×Dic₁₉⋊C₄

yes

characteristic

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

Dic₁₉⋊C₈

yes

—

198

C₂×C₄

C₂×C₈×D₁₉

yes

characteristic

199

C₂×C₄

C₂×#64515

yes

characteristic

200

C₂×C₄

#10597347

yes

—

201

C₂×C₄

#10597370

yes

—

202

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

203

C₂×C₄

#10597375

yes

characteristic

204

C₂×C₄

#10597399

yes

characteristic

205

C₈

—

206

C₈

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

152

—

211

C₂²

—

212

C₂²

—

213

C₂²

#11926417

yes

characteristic

214

C₂²

C₂×Dic₁₉⋊C₈

yes

characteristic

215

C₂²

#11926570

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₈×C₂²⋊D₁₉

yes

—

221

C₄

#11926615

yes

—

222

C₄

#11926717

yes

characteristic

223

C₄

#11926727

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#14563813

yes

characteristic

227

C₂

#14563850

yes

characteristic

228

C₂

#14563855

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2982	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2982	D₁₉
hypocenter	C₁₉	#8836
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2982

subgroup

G/H

center

C₂×C₄

#10597399

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2982

C₂

socle

C₂²×C₁₉

#385

prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2982

N	H ≅ G/N	type
39. #10597293	C₈	semidirect
158. C₁₉	#8836	semidirect

H ≅ G/N

type

39. #10597293

C₈

semidirect

158. C₁₉

#8836

semidirect

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

subgroup	index
#14564572	2
C₄×#10597293	2
#14562388	2
#14561471	2
C₁₉×#2982	2
#8836	19

subgroup

index

C₁₉×#2982

Subgroups — #18076406

Conjugacy classes of subgroups

Complements

Maximal subgroups