Group #18075552 — subgroups

Subgroups — #18075552

Order 4864.

320 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14562398	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic
3	#14562273	C₂	1	2	yes	maximal
4	#14561546	C₂	1	2	yes	maximal
5	C₁₉×#2960	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	#11926601	C₂²	1	2	yes	—
8	#11926297	—	2	1	no	—
9	#11926297	—	2	1	no	—
10	#11926295	—	2	1	no	—
11	#11926295	—	2	1	no	—
12	#11926286	—	2	4	no	—
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#446	—	2	1	no	—
15	C₁₉×#446	—	2	1	no	—
16	C₈×Q₈×C₁₉	—	2	1	no	—
17	C₈×Q₈×C₁₉	—	2	1	no	—
18	C₁₉×#424	C₄	1	2	yes	—
19	C₁₉×#423	C₂²	1	1	yes	characteristic
20	C₁₉×#405	C₄	1	2	yes	—
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
26	C₁₉×C₄⋊Q₈	Q₈	1	1	yes	characteristic
27	C₁₉×#125	D₄	1	2	yes	—
28	C₁₉×C₂²⋊Q₈	—	2	1	no	—
29	C₁₉×C₂²⋊Q₈	—	2	1	no	—
30	C₄×Q₈×C₁₉	—	2	1	no	—
31	C₄×Q₈×C₁₉	—	2	1	no	—
32	C₁₉×#117	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₄⋊C₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	1	no	—
38	C₁₉×#97	—	2	2	no	—
39	C₄×C₈×C₁₉	—	2	2	no	—
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	#10597260	—	2	2	no	—
49	#10597260	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	1	no	—
51	C₂×Q₈×C₁₉	—	2	1	no	—
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
55	M₁₆×C₁₉	—	4	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
68	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
69	C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	#8635	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	#117	1	1	yes	characteristic
79	Q₈×C₁₉	—	4	2	no	—
80	Q₈×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	4	1	no	—
86	C₂×C₄×C₁₉	—	4	1	no	—
87	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₈×C₁₉	—	2	1	no	—
94	C₈×C₁₉	—	2	1	no	—
95	C₈×C₁₉	—	2	1	no	—
96	C₈×C₁₉	—	4	2	no	—
97	C₈×C₁₉	#101	1	2	yes	—
98	C₁₉⋊C₈	—	8	2	no	—
99	C₁₉⋊C₈	—	8	2	no	—
100	#2960	D₁₉	1	1	yes	characteristic
101	#1568	—	19	1	no	—
102	#1568	—	19	1	no	—
103	#1537	—	19	2	no	—
104	#1307	—	19	2	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	#380	1	1	yes	characteristic
109	C₄×C₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	2	1	no	—
113	C₄×C₁₉	—	2	1	no	—
114	C₄×C₁₉	—	4	2	no	—
115	C₄×C₁₉	—	4	2	no	—
116	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
117	C₄×C₁₉	#413	1	1	yes	characteristic
118	#533	C₂×D₁₉	1	1	yes	characteristic
119	#446	—	2	1	no	—
120	#446	—	2	1	no	—
121	C₈×Q₈	—	2	1	no	—
122	C₈×Q₈	—	2	1	no	—
123	#432	—	19	2	no	—
124	#432	—	19	2	no	—
125	#424	Dic₁₉	1	2	yes	—
126	#423	C₂×D₁₉	1	1	yes	characteristic
127	#405	Dic₁₉	1	2	yes	—
128	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
129	#335	—	38	1	no	—
130	#335	—	38	1	no	—
131	#334	—	38	1	no	—
132	#334	—	38	1	no	—
133	#330	—	38	4	no	—
134	C₂×C₁₉	—	4	1	no	—
135	C₂×C₁₉	#1801	1	1	yes	characteristic
136	C₂×C₁₉	#1814	1	1	yes	characteristic
137	C₂×C₁₉	#1814	1	1	yes	characteristic
138	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
139	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
140	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
141	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
142	C₄⋊Q₈	Dic₃₈	1	1	yes	characteristic
143	#125	D₇₆	1	2	yes	—
144	C₂²⋊Q₈	—	2	1	no	—
145	C₂²⋊Q₈	—	2	1	no	—
146	C₄×Q₈	—	2	1	no	—
147	C₄×Q₈	—	2	1	no	—
148	#117	C₂×Dic₁₉	1	2	yes	—
149	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	38	2	no	—
155	C₄⋊C₈	—	38	2	no	—
156	C₂²⋊C₈	—	38	2	no	—
157	C₂²⋊C₈	—	38	2	no	—
158	#97	—	2	2	no	—
159	#97	—	38	2	no	—
160	#97	—	38	2	no	—
161	C₄×C₈	—	2	2	no	—
162	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
163	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
164	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
166	C₁₉	#8635	1	1	yes	characteristic, complemented, Sylow
167	C₂×Q₈	—	2	1	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂²×C₄	#64541	1	1	yes	characteristic
170	C₂²×C₄	#64541	1	1	yes	characteristic
171	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	76	2	no	—
177	C₂×C₈	—	76	2	no	—
178	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
179	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
180	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
181	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
187	C₄⋊C₄	C₄⋊Dic₁₉	1	2	yes	—
188	C₂²⋊C₄	—	2	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
191	C₄²	C₂×D₇₆	1	1	yes	characteristic
192	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
193	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
194	C₂³	#10597372	1	1	yes	characteristic
195	Q₈	—	4	2	no	—
196	Q₈	—	4	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	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	#10597370	1	1	yes	characteristic
204	C₂×C₄	#10597370	1	1	yes	characteristic
205	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
206	C₂×C₄	#10597376	1	1	yes	characteristic
207	C₂×C₄	#10597376	1	1	yes	characteristic
208	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	4	2	no	—
213	C₈	—	152	2	no	—
214	C₈	—	152	2	no	—
215	C₈	#10597293	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#11926404	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	4	2	no	—
226	C₄	—	4	2	no	—
227	C₄	C₂×#10597293	1	1	yes	characteristic
228	C₄	#11926528	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	#14563631	1	1	yes	characteristic
231	C₂	#14563689	1	1	yes	characteristic
232	C₂	#14563689	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562398

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic

#14562273

C₂

yes

maximal

#14561546

C₂

yes

maximal

C₁₉×#2960

C₂

yes

maximal, characteristic

#11926601

C₂²

yes

—

#11926601

C₂²

yes

—

—

—

—

—

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#446

—

C₁₉×#446

—

C₈×Q₈×C₁₉

—

C₈×Q₈×C₁₉

—

C₁₉×#424

C₄

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#405

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₁₉×C₄⋊Q₈

Q₈

yes

characteristic

C₁₉×#125

D₄

yes

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₄⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#101

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

#2960

D₁₉

yes

characteristic

101

#1568

—

102

#1568

—

103

#1537

—

104

#1307

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

#380

yes

characteristic

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

C₂×#101

yes

characteristic

117

C₄×C₁₉

#413

yes

characteristic

118

#533

C₂×D₁₉

yes

characteristic

119

#446

—

120

#446

—

121

C₈×Q₈

—

122

C₈×Q₈

—

123

#432

—

124

#432

—

125

#424

Dic₁₉

yes

—

126

#423

C₂×D₁₉

yes

characteristic

127

#405

Dic₁₉

yes

—

128

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

129

#335

—

130

#335

—

131

#334

—

132

#334

—

133

#330

—

134

C₂×C₁₉

—

135

C₂×C₁₉

#1801

yes

characteristic

136

C₂×C₁₉

#1814

yes

characteristic

137

C₂×C₁₉

#1814

yes

characteristic

138

C₂×M₁₆

C₂×Dic₁₉

yes

—

139

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

140

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

141

C₄⋊Q₈

Dic₃₈

yes

characteristic

142

C₄⋊Q₈

Dic₃₈

yes

characteristic

143

#125

D₇₆

yes

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

#117

C₂×Dic₁₉

yes

—

149

C₂×C₄²

C₂²×D₁₉

yes

characteristic

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₂²⋊C₈

—

157

C₂²⋊C₈

—

158

#97

—

159

#97

—

160

#97

—

161

C₄×C₈

—

162

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

163

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

164

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

165

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

166

C₁₉

#8635

yes

characteristic, complemented, Sylow

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂²×C₄

#64541

yes

characteristic

170

C₂²×C₄

#64541

yes

characteristic

171

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

179

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

180

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

181

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

C₄⋊Dic₁₉

yes

—

187

C₄⋊C₄

C₄⋊Dic₁₉

yes

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

C₂×Dic₃₈

yes

characteristic

191

C₄²

C₂×D₇₆

yes

characteristic

192

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

193

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

194

C₂³

#10597372

yes

characteristic

195

Q₈

—

196

Q₈

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

#10597370

yes

characteristic

204

C₂×C₄

#10597370

yes

characteristic

205

C₂×C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

206

C₂×C₄

#10597376

yes

characteristic

207

C₂×C₄

#10597376

yes

characteristic

208

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₈

—

152

—

214

C₈

—

152

—

215

C₈

#10597293

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

#11926404

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

C₂×#10597293

yes

characteristic

228

C₄

#11926528

yes

characteristic

229

C₂

—

230

C₂

#14563631

yes

characteristic

231

C₂

#14563689

yes

characteristic

232

C₂

#14563689

yes

characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2960	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2960	D₁₉
hypocenter	C₁₉	#8635
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

subgroup

G/H

center

C₂²

#11926404

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2960

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

N	H ≅ G/N	type
166. C₁₉	#8635	semidirect

H ≅ G/N

type

166. C₁₉

#8635

semidirect

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

subgroup	index
#14562398	2
#14562273	2
#14561546	2
C₁₉×#2960	2
#8635	19

subgroup

index

C₁₉×#2960

Subgroups — #18075552

Conjugacy classes of subgroups

Complements

Maximal subgroups