Group #18075566 — subgroups

Subgroups — #18075566

Order 4864.

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

normal subgroups only

This group has 336 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	#14572569	C₂	1	1	yes	maximal, characteristic
2	#14562394	C₂	1	1	yes	maximal, characteristic
3	#14562372	C₂	1	2	yes	maximal
4	C₁₉⋊#1309	C₂	1	2	yes	maximal
5	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926674	—	2	1	no	—
8	#11926674	—	2	1	no	—
9	C₈×Dic₃₈	—	2	1	no	—
10	C₈×Dic₃₈	—	2	1	no	—
11	#11926570	C₄	1	2	yes	—
12	#11926568	C₂²	1	2	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926499	C₄	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926297	—	2	1	no	—
17	#11926291	—	2	2	no	—
18	#11926289	—	2	2	no	—
19	C₁₉×#423	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#335	—	2	1	no	—
22	C₁₉×#335	—	2	1	no	—
23	C₂×M₁₆×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#10597372	C₂×C₄	1	2	yes	—
28	#10597370	—	2	1	no	—
29	#10597370	—	2	1	no	—
30	C₂×#64520	—	2	2	no	—
31	C₂×#64520	C₂×C₄	1	2	yes	—
32	#10597316	Q₈	1	2	yes	—
33	#10597315	D₄	1	1	yes	characteristic
34	#10597315	D₄	1	1	yes	characteristic
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	—	2	1	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
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	#10597272	—	2	2	no	—
44	Dic₁₉⋊C₈	—	2	2	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	C₈×Dic₁₉	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₃₈	—	2	1	no	—
55	C₂×Dic₃₈	—	2	1	no	—
56	M₁₆×C₁₉	—	8	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
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	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
68	C₂²⋊Dic₁₉	—	2	2	no	—
69	C₄⋊Dic₁₉	—	2	1	no	—
70	C₄⋊Dic₁₉	—	2	1	no	—
71	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
72	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
73	Dic₁₉⋊C₄	—	2	2	no	—
74	Dic₁₉⋊C₄	—	2	2	no	—
75	C₄×Dic₁₉	—	2	2	no	—
76	#64520	—	4	2	no	—
77	#64520	—	8	2	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#8639	—	19	1	no	maximal, Sylow
81	C₂³×C₁₉	#117	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×Dic₁₉	—	2	2	no	—
95	C₂×Dic₁₉	—	2	2	no	—
96	Dic₃₈	—	4	1	no	—
97	Dic₃₈	—	4	1	no	—
98	Dic₃₈	—	4	1	no	—
99	Dic₃₈	—	4	1	no	—
100	C₈×C₁₉	—	2	1	no	—
101	C₈×C₁₉	—	2	1	no	—
102	C₈×C₁₉	—	2	1	no	—
103	C₈×C₁₉	—	8	2	no	—
104	C₈×C₁₉	#101	1	2	yes	—
105	C₁₉⋊C₈	—	4	2	no	—
106	C₁₉⋊C₈	—	8	2	no	—
107	#2960	—	19	1	no	—
108	#1567	—	19	1	no	—
109	#1567	D₁₉	1	1	yes	characteristic
110	#1561	—	19	2	no	—
111	#1309	—	19	2	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	—	2	1	no	—
114	C₂²×C₁₉	—	2	1	no	—
115	C₂²×C₁₉	#380	1	1	yes	characteristic
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	C₂×#101	1	1	yes	characteristic
120	C₄×C₁₉	#413	1	1	yes	characteristic
121	C₄×C₁₉	#472	1	1	yes	characteristic
122	C₄×C₁₉	#472	1	1	yes	characteristic
123	C₄×C₁₉	#473	1	1	yes	characteristic
124	C₄×C₁₉	#473	1	1	yes	characteristic
125	Dic₁₉	—	4	2	no	—
126	Dic₁₉	—	4	2	no	—
127	#533	—	19	1	no	—
128	#446	—	38	1	no	—
129	#446	—	38	1	no	—
130	C₈×Q₈	—	38	1	no	—
131	C₈×Q₈	—	38	1	no	—
132	#424	—	19	2	no	—
133	#423	—	19	1	no	—
134	#423	—	19	2	no	—
135	#423	C₂×D₁₉	1	2	yes	—
136	#405	—	19	2	no	—
137	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
138	#335	—	2	1	no	—
139	#335	—	2	1	no	—
140	#335	—	38	1	no	—
141	#335	—	38	1	no	—
142	#332	—	38	2	no	—
143	#332	—	38	2	no	—
144	C₂×C₁₉	—	4	1	no	—
145	C₂×C₁₉	#1801	1	1	yes	characteristic
146	C₂×C₁₉	#1816	1	1	yes	characteristic
147	C₂×C₁₉	#1816	1	1	yes	characteristic
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	19	2	no	—
150	C₂×M₁₆	—	38	2	no	—
151	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
152	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
153	C₄⋊Q₈	—	19	1	no	—
154	C₄⋊Q₈	—	19	1	no	—
155	#125	—	19	2	no	—
156	C₂²⋊Q₈	—	38	1	no	—
157	C₂²⋊Q₈	—	38	1	no	—
158	C₄×Q₈	—	38	1	no	—
159	C₄×Q₈	—	38	1	no	—
160	#117	—	19	2	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	38	2	no	—
165	C₄⋊C₈	—	38	2	no	—
166	C₄⋊C₈	—	38	1	no	—
167	C₄⋊C₈	—	38	2	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	1	no	—
170	#97	—	38	2	no	—
171	C₄×C₈	—	38	2	no	—
172	C₄×C₈	D₇₆	1	1	yes	characteristic
173	C₄×C₈	D₇₆	1	1	yes	characteristic
174	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
175	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
176	C₁₉	#8639	1	1	yes	characteristic, complemented, Sylow
177	C₂×Q₈	—	38	1	no	—
178	C₂×Q₈	—	38	1	no	—
179	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
180	C₂²×C₄	#64543	1	1	yes	characteristic
181	C₂²×C₄	#64545	1	1	yes	characteristic
182	M₁₆	—	8	2	no	—
183	M₁₆	—	76	2	no	—
184	M₁₆	—	152	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	1	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	38	2	no	—
189	C₂×C₈	—	76	2	no	—
190	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
191	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
193	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
194	C₄⋊C₄	—	19	2	no	—
195	C₄⋊C₄	—	19	2	no	—
196	C₄⋊C₄	—	38	1	no	—
197	C₄⋊C₄	—	38	2	no	—
198	C₄⋊C₄	—	38	1	no	—
199	C₄⋊C₄	—	38	2	no	—
200	C₂²⋊C₄	—	38	2	no	—
201	C₄²	—	38	2	no	—
202	C₄²	C₂×D₇₆	1	1	yes	characteristic
203	C₄²	D₄×D₁₉	1	1	yes	characteristic
204	C₄²	Q₈×D₁₉	1	1	yes	characteristic
205	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
206	C₂³	#10597338	1	1	yes	characteristic
207	Q₈	—	76	1	no	—
208	Q₈	—	76	1	no	—
209	Q₈	—	76	1	no	—
210	Q₈	—	76	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	38	2	no	—
218	C₂×C₄	—	38	2	no	—
219	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
220	C₂×C₄	#10597341	1	1	yes	characteristic
221	C₂×C₄	#10597343	1	1	yes	characteristic
222	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
223	C₂×C₄	#10597384	1	1	yes	characteristic
224	C₂×C₄	#10597392	1	1	yes	characteristic
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	2	1	no	—
228	C₈	—	8	2	no	—
229	C₈	—	76	2	no	—
230	C₈	—	152	2	no	—
231	C₈	#10597281	1	2	yes	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	2	1	no	—
235	C₂²	#11926401	1	1	yes	characteristic
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	76	2	no	—
240	C₄	—	76	2	no	—
241	C₄	C₂×#10597281	1	1	yes	characteristic
242	C₄	#11926526	1	1	yes	characteristic
243	C₄	#11926811	1	1	yes	characteristic
244	C₄	#11926815	1	1	yes	characteristic
245	C₄	#11926816	1	1	yes	characteristic
246	C₄	#11926820	1	1	yes	characteristic
247	C₂	—	4	1	no	—
248	C₂	#14563628	1	1	yes	characteristic
249	C₂	#14563696	1	1	yes	characteristic
250	C₂	#14563700	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572569

C₂

yes

maximal, characteristic

#14562394

C₂

yes

maximal, characteristic

#14562372

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal

C₁₉×#1567

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926674

—

#11926674

—

C₈×Dic₃₈

—

C₈×Dic₃₈

—

#11926570

C₄

yes

—

#11926568

C₂²

yes

—

#11926568

C₂²

yes

characteristic

#11926499

C₄

yes

—

—

—

—

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#335

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

#10597316

Q₈

yes

—

#10597315

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597272

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×Dic₃₈

—

C₂×Dic₃₈

—

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

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

C₄⋊Dic₁₉

C₄⋊C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

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×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

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

100

C₈×C₁₉

—

101

C₈×C₁₉

—

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

C₈×C₁₉

#101

yes

—

105

C₁₉⋊C₈

—

106

C₁₉⋊C₈

—

107

#2960

—

108

#1567

—

109

#1567

D₁₉

yes

characteristic

110

#1561

—

111

#1309

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

#380

yes

characteristic

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

C₂×#101

yes

characteristic

120

C₄×C₁₉

#413

yes

characteristic

121

C₄×C₁₉

#472

yes

characteristic

122

C₄×C₁₉

#472

yes

characteristic

123

C₄×C₁₉

#473

yes

characteristic

124

C₄×C₁₉

#473

yes

characteristic

125

Dic₁₉

—

126

Dic₁₉

—

127

#533

—

128

#446

—

129

#446

—

130

C₈×Q₈

—

131

C₈×Q₈

—

132

#424

—

133

#423

—

134

#423

—

135

#423

C₂×D₁₉

yes

—

136

#405

—

137

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

138

#335

—

139

#335

—

140

#335

—

141

#335

—

142

#332

—

143

#332

—

144

C₂×C₁₉

—

145

C₂×C₁₉

#1801

yes

characteristic

146

C₂×C₁₉

#1816

yes

characteristic

147

C₂×C₁₉

#1816

yes

characteristic

148

C₂×M₁₆

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂²×C₈

C₄×D₁₉

yes

characteristic

152

C₂²×C₈

C₄×D₁₉

yes

characteristic

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

#125

—

156

C₂²⋊Q₈

—

157

C₂²⋊Q₈

—

158

C₄×Q₈

—

159

C₄×Q₈

—

160

#117

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

#97

—

171

C₄×C₈

—

172

C₄×C₈

D₇₆

yes

characteristic

173

C₄×C₈

D₇₆

yes

characteristic

174

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

175

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

176

C₁₉

#8639

yes

characteristic, complemented, Sylow

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

180

C₂²×C₄

#64543

yes

characteristic

181

C₂²×C₄

#64545

yes

characteristic

182

M₁₆

—

183

M₁₆

—

184

M₁₆

—

152

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

191

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

192

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

193

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₄²

—

202

C₄²

C₂×D₇₆

yes

characteristic

203

C₄²

D₄×D₁₉

yes

characteristic

204

C₄²

Q₈×D₁₉

yes

characteristic

205

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

206

C₂³

#10597338

yes

characteristic

207

Q₈

—

208

Q₈

—

209

Q₈

—

210

Q₈

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

220

C₂×C₄

#10597341

yes

characteristic

221

C₂×C₄

#10597343

yes

characteristic

222

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

223

C₂×C₄

#10597384

yes

characteristic

224

C₂×C₄

#10597392

yes

characteristic

225

C₈

—

226

C₈

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

152

—

231

C₈

#10597281

yes

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

#11926401

yes

characteristic

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

C₂×#10597281

yes

characteristic

242

C₄

#11926526

yes

characteristic

243

C₄

#11926811

yes

characteristic

244

C₄

#11926815

yes

characteristic

245

C₄

#11926816

yes

characteristic

246

C₄

#11926820

yes

characteristic

247

C₂

—

248

C₂

#14563628

yes

characteristic

249

C₂

#14563696

yes

characteristic

250

C₂

#14563700

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#380
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#8639
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1567

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
176. C₁₉	#8639	semidirect

H ≅ G/N

type

176. C₁₉

#8639

semidirect

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

subgroup	index
#14572569	2
#14562394	2
#14562372	2
C₁₉⋊#1309	2
C₁₉×#1567	2
#8639	19

subgroup

index

#14572569

#14562394

#14562372

C₁₉⋊#1309

C₁₉×#1567

#8639

Subgroups — #18075566

Conjugacy classes of subgroups

Complements

Maximal subgroups