Group #18075528 — subgroups

Subgroups — #18075528

Order 4864.

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

normal subgroups only

This group has 388 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	#14572348	C₂	1	1	yes	maximal, characteristic
2	#14562398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562269	C₂	1	2	yes	maximal
4	#14561545	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597347	C₄	1	2	yes	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926623	—	2	1	no	—
9	#11926623	—	2	1	no	—
10	C₈×D₇₆	—	2	1	no	—
11	C₈×D₇₆	—	2	1	no	—
12	#11926601	C₂²	1	2	yes	—
13	#11926568	C₂²	1	1	yes	characteristic
14	#11926510	C₄	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926283	—	2	4	no	—
18	C₁₉×#432	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	1	no	—
21	C₁₉×#334	—	2	1	no	—
22	C₂×#64541	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	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#10597376	—	2	1	no	—
27	#10597376	—	2	1	no	—
28	C₂×#64520	C₂×C₄	1	2	yes	—
29	#10597347	—	4	4	no	—
30	C₂×#64515	—	2	2	no	—
31	C₂×C₈×D₁₉	—	2	2	no	—
32	#10597321	D₄	1	2	yes	—
33	#10597320	Q₈	1	1	yes	characteristic
34	C₄×D₇₆	—	2	1	no	—
35	C₄×D₇₆	—	2	1	no	—
36	#10597315	Q₈	1	1	yes	characteristic
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₂²⋊C₈	—	2	2	no	—
39	C₁₉×#97	—	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	(C₂×D₁₉)⋊C₈	—	2	2	no	—
46	(C₂×D₁₉)⋊C₈	—	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	#10597260	—	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×C₂²⋊D₁₉	—	2	2	no	—
55	#64541	—	4	2	no	—
56	#64541	—	4	2	no	—
57	C₂×D₇₆	—	2	1	no	—
58	C₂×D₇₆	—	2	1	no	—
59	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
60	C₂×C₄×D₁₉	—	2	2	no	—
61	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	2	no	—
65	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
73	(C₂×D₁₉)⋊C₄	—	2	2	no	—
74	(C₂×D₁₉)⋊C₄	—	2	2	no	—
75	C₄⋊Dic₁₉	—	2	1	no	—
76	C₄⋊Dic₁₉	—	2	1	no	—
77	#64520	—	4	2	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	#64515	—	4	4	no	—
81	C₈×D₁₉	—	4	4	no	—
82	#8630	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	#117	1	1	yes	characteristic
84	C₂²×D₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂²⋊D₁₉	—	4	4	no	—
96	C₂×Dic₁₉	—	2	2	no	—
97	D₇₆	—	4	2	no	—
98	D₇₆	—	4	2	no	—
99	D₇₆	—	4	2	no	—
100	C₄×D₁₉	—	4	2	no	—
101	C₄×D₁₉	—	4	2	no	—
102	Dic₃₈	—	4	2	no	—
103	C₈×C₁₉	—	2	1	no	—
104	C₈×C₁₉	—	2	1	no	—
105	C₈×C₁₉	—	2	1	no	—
106	C₈×C₁₉	—	8	2	no	—
107	C₈×C₁₉	#100	1	2	yes	—
108	C₁₉⋊C₈	—	4	2	no	—
109	C₁₉⋊C₈	—	8	2	no	—
110	#2931	—	19	1	no	—
111	#1568	—	19	1	no	—
112	#1568	D₁₉	1	1	yes	characteristic, complemented
113	#1536	—	19	2	no	—
114	#1307	—	19	2	no	—
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	#380	1	1	yes	characteristic
119	C₂×D₁₉	—	4	2	no	—
120	C₂×D₁₉	—	4	2	no	—
121	C₂×D₁₉	—	4	2	no	—
122	C₄×C₁₉	—	2	1	no	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	1	no	—
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
128	C₄×C₁₉	#413	1	1	yes	characteristic
129	Dic₁₉	—	4	2	no	—
130	C₂×#131	—	19	2	no	—
131	#532	—	19	1	no	—
132	#436	—	38	1	no	—
133	#436	—	38	1	no	—
134	C₈×D₄	—	38	1	no	—
135	C₈×D₄	—	38	1	no	—
136	#432	—	19	2	no	—
137	#432	C₂×D₁₉	1	2	yes	—
138	#423	—	19	1	no	—
139	#408	—	19	2	no	—
140	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
141	#335	—	2	1	no	—
142	#335	—	38	1	no	—
143	#334	—	2	1	no	—
144	#334	—	38	1	no	—
145	#329	—	38	4	no	—
146	C₂×C₁₉	—	4	1	no	—
147	C₂×C₁₉	#1800	1	1	yes	characteristic
148	C₂×C₁₉	#1814	1	1	yes	characteristic
149	C₂×C₁₉	#1814	1	1	yes	characteristic
150	D₁₉	—	8	2	no	—
151	C₂×#41	—	19	2	no	—
152	#131	—	76	4	no	—
153	C₂×M₁₆	—	19	2	no	—
154	C₂×M₁₆	—	38	2	no	—
155	C₂²×C₈	—	38	2	no	—
156	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
157	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
158	C₄⋊Q₈	—	19	1	no	—
159	#127	—	19	1	no	—
160	#124	—	19	2	no	—
161	#121	—	38	1	no	—
162	#121	—	38	1	no	—
163	C₄×D₄	—	38	1	no	—
164	C₄×D₄	—	38	1	no	—
165	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
166	C₄⋊C₈	—	2	2	no	—
167	C₄⋊C₈	—	38	1	no	—
168	C₄⋊C₈	—	38	2	no	—
169	C₄⋊C₈	—	38	1	no	—
170	C₂²⋊C₈	—	2	2	no	—
171	C₂²⋊C₈	—	38	2	no	—
172	C₂²⋊C₈	—	38	2	no	—
173	C₂²⋊C₈	—	38	2	no	—
174	#97	—	2	2	no	—
175	#97	—	38	2	no	—
176	C₄×C₈	D₇₆	1	1	yes	characteristic
177	C₄×C₈	D₇₆	1	1	yes	characteristic
178	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
180	C₁₉	#8630	1	1	yes	characteristic, complemented, Sylow
181	#41	—	76	2	no	—
182	#41	—	76	2	no	—
183	C₂×Q₈	—	19	2	no	—
184	C₂×D₄	—	19	2	no	—
185	C₂×D₄	—	38	2	no	—
186	C₂×D₄	—	38	1	no	—
187	C₂×D₄	—	38	1	no	—
188	C₂²×C₄	—	38	2	no	—
189	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
190	C₂²×C₄	#64543	1	1	yes	characteristic
191	C₂²×C₄	#64545	1	1	yes	characteristic
192	M₁₆	—	76	4	no	—
193	M₁₆	—	76	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	38	2	no	—
198	C₂×C₈	—	76	4	no	—
199	C₂×C₈	—	76	2	no	—
200	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
201	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
204	C₄⋊C₄	—	38	1	no	—
205	C₄⋊C₄	—	38	1	no	—
206	C₂²⋊C₄	—	38	2	no	—
207	C₂²⋊C₄	—	38	2	no	—
208	C₄²	C₂×D₇₆	1	1	yes	characteristic
209	C₄²	D₄×D₁₉	1	1	yes	characteristic
210	C₄²	Q₈×D₁₉	1	1	yes	characteristic
211	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
212	C₂³	—	38	2	no	—
213	C₂³	#10597338	1	1	yes	characteristic
214	Q₈	—	76	2	no	—
215	D₄	—	76	2	no	—
216	D₄	—	76	2	no	—
217	D₄	—	76	2	no	—
218	D₄	—	76	4	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	—	76	2	no	—
225	C₂×C₄	—	76	2	no	—
226	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
227	C₂×C₄	#10597341	1	1	yes	characteristic
228	C₂×C₄	#10597343	1	1	yes	characteristic
229	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
230	C₂×C₄	#10597384	1	1	yes	characteristic
231	C₂×C₄	#10597392	1	1	yes	characteristic
232	C₈	—	2	1	no	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	8	2	no	—
236	C₈	—	76	2	no	—
237	C₈	—	152	2	no	—
238	C₈	#10597280	1	2	yes	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	76	2	no	—
243	C₂²	—	76	2	no	—
244	C₂²	—	76	2	no	—
245	C₂²	#11926401	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	76	2	no	—
252	C₄	C₂×#10597280	1	1	yes	characteristic
253	C₄	#11926526	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	152	2	no	—
256	C₂	#14563624	1	1	yes	characteristic
257	C₂	#14563686	1	1	yes	characteristic
258	C₂	#14563690	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14572348

C₂

yes

maximal, characteristic

#14562398

C₂

yes

maximal, characteristic, complemented

#14562269

C₂

yes

maximal

#14561545

C₂

yes

maximal, complemented

C₁₉×#1568

C₂

yes

maximal, characteristic, complemented

C₂×#10597347

C₄

yes

—

#11927094

C₂²

yes

characteristic

#11926623

—

#11926623

—

C₈×D₇₆

—

C₈×D₇₆

—

#11926601

C₂²

yes

—

#11926568

C₂²

yes

characteristic

#11926510

C₄

yes

—

#11926297

—

#11926295

—

#11926283

—

C₁₉×#432

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₁₉×#334

—

C₂×#64541

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

—

—

C₂×C₄

yes

—

#10597347

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

D₄

yes

—

#10597320

Q₈

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

Q₈

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

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)

—

(C₂×D₁₉)⋊C₈

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

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

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

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

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

100

C₄×D₁₉

—

101

C₄×D₁₉

—

102

Dic₃₈

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₈×C₁₉

—

106

C₈×C₁₉

—

107

C₈×C₁₉

#100

yes

—

108

C₁₉⋊C₈

—

109

C₁₉⋊C₈

—

110

#2931

—

111

#1568

—

112

#1568

D₁₉

yes

characteristic, complemented

113

#1536

—

114

#1307

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

#380

yes

characteristic

119

C₂×D₁₉

—

120

C₂×D₁₉

—

121

C₂×D₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

C₂×#100

yes

characteristic

128

C₄×C₁₉

#413

yes

characteristic

129

Dic₁₉

—

130

C₂×#131

—

131

#532

—

132

#436

—

133

#436

—

134

C₈×D₄

—

135

C₈×D₄

—

136

#432

—

137

#432

C₂×D₁₉

yes

—

138

#423

—

139

#408

—

140

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

141

#335

—

142

#335

—

143

#334

—

144

#334

—

145

#329

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1800

yes

characteristic

148

C₂×C₁₉

#1814

yes

characteristic

149

C₂×C₁₉

#1814

yes

characteristic

150

D₁₉

—

151

C₂×#41

—

152

#131

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

156

C₂²×C₈

C₄×D₁₉

yes

characteristic

157

C₂²×C₈

C₄×D₁₉

yes

characteristic

158

C₄⋊Q₈

—

159

#127

—

160

#124

—

161

#121

—

162

#121

—

163

C₄×D₄

—

164

C₄×D₄

—

165

C₂×C₄²

C₂²×D₁₉

yes

characteristic

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₂²⋊C₈

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

C₂²⋊C₈

—

174

#97

—

175

#97

—

176

C₄×C₈

D₇₆

yes

characteristic

177

C₄×C₈

D₇₆

yes

characteristic

178

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

179

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

180

C₁₉

#8630

yes

characteristic, complemented, Sylow

181

#41

—

182

#41

—

183

C₂×Q₈

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

190

C₂²×C₄

#64543

yes

characteristic

191

C₂²×C₄

#64545

yes

characteristic

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

201

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

202

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

203

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

C₂×D₇₆

yes

characteristic

209

C₄²

D₄×D₁₉

yes

characteristic

210

C₄²

Q₈×D₁₉

yes

characteristic

211

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

212

C₂³

—

213

C₂³

#10597338

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

227

C₂×C₄

#10597341

yes

characteristic

228

C₂×C₄

#10597343

yes

characteristic

229

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

230

C₂×C₄

#10597384

yes

characteristic

231

C₂×C₄

#10597392

yes

characteristic

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

237

C₈

—

152

—

238

C₈

#10597280

yes

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#11926401

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

C₂×#10597280

yes

characteristic

253

C₄

#11926526

yes

characteristic

254

C₂

—

255

C₂

—

152

—

256

C₂

#14563624

yes

characteristic

257

C₂

#14563686

yes

characteristic

258

C₂

#14563690

yes

characteristic

	subgroup	G/H
center	C₂²	#11926401
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1568	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1568	D₁₉
hypocenter	C₁₉	#8630
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#11926401

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1568

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
2. #14562398	C₂	semidirect
4. #14561545	C₂	semidirect
5. C₁₉×#1568	C₂	semidirect
112. #1568	D₁₉	semidirect
180. C₁₉	#8630	semidirect

H ≅ G/N

type

2. #14562398

C₂

semidirect

4. #14561545

C₂

semidirect

5. C₁₉×#1568

C₂

semidirect

112. #1568

D₁₉

semidirect

180. C₁₉

#8630

semidirect

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

subgroup	index
#14572348	2
#14562398	2
#14562269	2
#14561545	2
C₁₉×#1568	2
#8630	19

subgroup

index

C₁₉×#1568

Subgroups — #18075528

Conjugacy classes of subgroups

Complements

Maximal subgroups