Group #18087326 — subgroups

Subgroups — #18087326

Order 4864.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14564615	C₂	1	1	yes	maximal, characteristic
2	#14563754	C₂	1	1	yes	maximal, characteristic
3	#14562293	C₂	1	1	yes	maximal, characteristic
4	#14562290	C₂	1	1	yes	maximal, characteristic
5	#14561530	C₂	1	1	yes	maximal, characteristic
6	#14561463	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1301	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926597	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	#11926390	C₂²	1	1	yes	characteristic
12	#11926305	—	2	1	no	—
13	#11926305	—	2	1	no	—
14	#11926298	—	2	1	no	—
15	#11926298	—	2	1	no	—
16	#11926292	—	2	1	no	—
17	#11926292	—	2	1	no	—
18	#11926291	—	2	1	no	—
19	#11926289	—	2	1	no	—
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₁₉×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×M₁₆×C₁₉	—	2	1	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#10597372	—	2	1	no	—
27	#10597370	—	2	1	no	—
28	#10597370	—	2	1	no	—
29	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	—	2	1	no	—
32	#10597316	—	2	1	no	—
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	1	no	—
38	C₁₉×C₄⋊C₈	—	2	1	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₄⋊C₈	—	2	1	no	—
42	C₁₉×C₂²⋊C₈	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₁₉⋊#95	—	2	1	no	—
45	C₁₉⋊#95	—	2	1	no	—
46	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂²×Dic₁₉	—	2	1	no	—
55	C₂²×Dic₁₉	—	2	1	no	—
56	C₂×Dic₃₈	—	2	1	no	—
57	C₂×Dic₃₈	—	2	1	no	—
58	M₁₆×C₁₉	—	4	1	no	—
59	M₁₆×C₁₉	—	4	1	no	—
60	C₂×C₈×C₁₉	—	4	1	no	—
61	C₂×C₈×C₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	4	1	no	—
63	C₂×C₈×C₁₉	—	4	1	no	—
64	C₂×C₈×C₁₉	—	4	1	no	—
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	#41	1	1	yes	characteristic
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	C₄²×C₁₉	#41	1	1	yes	characteristic
69	C₂²⋊Dic₁₉	—	4	1	no	—
70	C₄⋊Dic₁₉	—	2	1	no	—
71	C₄⋊Dic₁₉	—	2	1	no	—
72	C₄⋊Dic₁₉	—	2	1	no	—
73	C₄⋊Dic₁₉	—	2	1	no	—
74	Dic₁₉⋊C₄	—	4	1	no	—
75	Dic₁₉⋊C₄	—	4	1	no	—
76	C₄×Dic₁₉	—	2	1	no	—
77	C₄×Dic₁₉	—	2	1	no	—
78	C₄×Dic₁₉	—	2	1	no	—
79	C₄×Dic₁₉	—	2	1	no	—
80	C₄×Dic₁₉	—	4	1	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	C₂×C₁₉⋊C₈	—	4	1	no	—
83	C₂×C₁₉⋊C₈	—	4	1	no	—
84	C₂×C₁₉⋊C₈	—	4	1	no	—
85	#10630	—	19	1	no	maximal, Sylow
86	C₂³×C₁₉	#123	1	1	yes	characteristic
87	C₂×C₄×C₁₉	—	4	1	no	—
88	C₂×C₄×C₁₉	—	4	1	no	—
89	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
95	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
99	C₂×Dic₁₉	—	4	1	no	—
100	C₂×Dic₁₉	—	4	1	no	—
101	C₂×Dic₁₉	—	4	1	no	—
102	C₂×Dic₁₉	—	4	1	no	—
103	C₂×Dic₁₉	—	4	1	no	—
104	C₂×Dic₁₉	—	4	1	no	—
105	C₂×Dic₁₉	—	4	1	no	—
106	C₂×Dic₁₉	—	4	1	no	—
107	Dic₃₈	—	8	1	no	—
108	Dic₃₈	—	8	1	no	—
109	C₈×C₁₉	—	8	1	no	—
110	C₈×C₁₉	—	8	1	no	—
111	C₈×C₁₉	—	8	1	no	—
112	C₁₉⋊C₈	—	8	1	no	—
113	C₁₉⋊C₈	—	8	1	no	—
114	#1995	—	19	1	no	—
115	#1832	—	19	1	no	—
116	#1542	—	19	1	no	—
117	#1542	—	19	1	no	—
118	#1301	—	19	1	no	—
119	#1301	D₁₉	1	1	yes	characteristic
120	#1274	—	19	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	—	2	1	no	—
123	C₂²×C₁₉	#397	1	1	yes	characteristic
124	C₂²×C₁₉	#485	1	1	yes	characteristic
125	C₂²×C₁₉	#485	1	1	yes	characteristic
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	—	2	1	no	—
129	C₄×C₁₉	—	2	1	no	—
130	C₄×C₁₉	#464	1	1	yes	characteristic
131	C₄×C₁₉	#464	1	1	yes	characteristic
132	C₄×C₁₉	#488	1	1	yes	characteristic
133	C₄×C₁₉	#491	1	1	yes	characteristic
134	Dic₁₉	—	8	1	no	—
135	Dic₁₉	—	8	1	no	—
136	Dic₁₉	—	8	1	no	—
137	Dic₁₉	—	8	1	no	—
138	#533	—	19	1	no	—
139	#431	—	19	1	no	—
140	#431	C₂×D₁₉	1	1	yes	characteristic
141	#423	C₂×D₁₉	1	1	yes	characteristic
142	C₂×C₄⋊C₈	—	19	1	no	—
143	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
144	#376	—	19	1	no	—
145	#339	—	38	1	no	—
146	#339	—	38	1	no	—
147	#336	—	38	1	no	—
148	#336	—	38	1	no	—
149	#333	—	38	1	no	—
150	#333	—	38	1	no	—
151	#332	—	38	1	no	—
152	#332	—	38	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	2	1	no	—
155	C₂×C₁₉	#2074	1	1	yes	characteristic
156	C₂×C₁₉	#2080	1	1	yes	characteristic
157	C₂×C₁₉	#2080	1	1	yes	characteristic
158	C₂×M₁₆	—	2	1	no	—
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	—	38	1	no	—
161	C₄⋊Q₈	—	19	1	no	—
162	C₄⋊Q₈	—	19	1	no	—
163	#125	—	38	1	no	—
164	C₂²⋊Q₈	—	38	1	no	—
165	C₂²⋊Q₈	—	38	1	no	—
166	C₄×Q₈	—	38	1	no	—
167	C₄×Q₈	—	38	1	no	—
168	#117	—	38	1	no	—
169	C₂×C₄²	—	19	1	no	—
170	C₂×C₄²	—	19	1	no	—
171	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	38	1	no	—
178	C₄⋊C₈	—	38	1	no	—
179	C₄⋊C₈	—	38	1	no	—
180	C₂²⋊C₈	—	2	1	no	—
181	C₂²⋊C₈	—	38	1	no	—
182	C₄×C₈	—	2	1	no	—
183	C₄×C₈	—	38	1	no	—
184	#95	—	38	1	no	—
185	#95	—	38	1	no	—
186	C₁₉	#10630	1	1	yes	characteristic, complemented, Sylow
187	C₂×Q₈	—	38	1	no	—
188	C₂×Q₈	—	38	1	no	—
189	C₂²×C₄	—	38	1	no	—
190	C₂²×C₄	—	38	1	no	—
191	C₂²×C₄	#64541	1	1	yes	characteristic
192	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
193	C₂²×C₄	#64545	1	1	yes	characteristic
194	M₁₆	—	4	1	no	—
195	M₁₆	—	4	1	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	76	1	no	—
202	C₂×C₈	—	76	1	no	—
203	C₂×C₈	—	76	1	no	—
204	C₂×C₈	—	76	1	no	—
205	C₄⋊C₄	—	38	1	no	—
206	C₄⋊C₄	—	38	1	no	—
207	C₄⋊C₄	—	38	1	no	—
208	C₄⋊C₄	—	38	1	no	—
209	C₄⋊C₄	—	76	1	no	—
210	C₄⋊C₄	—	76	1	no	—
211	C₂²⋊C₄	—	76	1	no	—
212	C₄²	—	38	1	no	—
213	C₄²	—	38	1	no	—
214	C₄²	—	38	1	no	—
215	C₄²	—	38	1	no	—
216	C₄²	—	76	1	no	—
217	C₄²	#64541	1	1	yes	characteristic
218	C₄²	#64541	1	1	yes	characteristic
219	C₄²	D₄×D₁₉	1	1	yes	characteristic
220	C₄²	#64543	1	1	yes	characteristic
221	C₂³	#10597340	1	1	yes	characteristic
222	Q₈	—	152	1	no	—
223	Q₈	—	152	1	no	—
224	C₂×C₄	—	4	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	76	1	no	—
227	C₂×C₄	—	76	1	no	—
228	C₂×C₄	—	76	1	no	—
229	C₂×C₄	—	76	1	no	—
230	C₂×C₄	—	76	1	no	—
231	C₂×C₄	—	76	1	no	—
232	C₂×C₄	—	76	1	no	—
233	C₂×C₄	—	76	1	no	—
234	C₂×C₄	#10597322	1	1	yes	characteristic
235	C₂×C₄	#10597329	1	1	yes	characteristic
236	C₂×C₄	#10597330	1	1	yes	characteristic
237	C₂×C₄	#10597331	1	1	yes	characteristic
238	C₂×C₄	#10597340	1	1	yes	characteristic
239	C₂×C₄	#10597344	1	1	yes	characteristic
240	C₂×C₄	#10597358	1	1	yes	characteristic
241	C₂×C₄	#10597361	1	1	yes	characteristic
242	C₂×C₄	#10597362	1	1	yes	characteristic
243	C₂×C₄	#10597364	1	1	yes	characteristic
244	C₈	—	8	1	no	—
245	C₈	—	8	1	no	—
246	C₈	—	8	1	no	—
247	C₈	—	152	1	no	—
248	C₈	—	152	1	no	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	#11926473	1	1	yes	characteristic
252	C₂²	#11926887	1	1	yes	characteristic
253	C₂²	#11926888	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	152	1	no	—
259	C₄	—	152	1	no	—
260	C₄	—	152	1	no	—
261	C₄	—	152	1	no	—
262	C₄	#11926765	1	1	yes	characteristic
263	C₄	#11926769	1	1	yes	characteristic
264	C₄	#11926897	1	1	yes	characteristic
265	C₄	#11926911	1	1	yes	characteristic
266	C₂	—	2	1	no	—
267	C₂	—	2	1	no	—
268	C₂	#14565057	1	1	yes	characteristic
269	C₂	#14565090	1	1	yes	characteristic
270	C₂	#14565091	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564615

C₂

yes

maximal, characteristic

#14563754

C₂

yes

maximal, characteristic

#14562293

C₂

yes

maximal, characteristic

#14562290

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal, characteristic

C₁₉×#1301

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#11926390

C₂²

yes

—

—

—

—

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

#10597316

—

#10597315

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×D₄

yes

C₂²×C₄×C₁₉

yes

C₂²×C₄×C₁₉

yes

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

100

C₂×Dic₁₉

—

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

C₂×Dic₁₉

—

107

Dic₃₈

—

108

Dic₃₈

—

109

C₈×C₁₉

—

110

C₈×C₁₉

—

111

C₈×C₁₉

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

#1995

—

115

#1832

—

116

#1542

—

117

#1542

—

118

#1301

—

119

#1301

D₁₉

yes

characteristic

120

#1274

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

#397

yes

characteristic

124

C₂²×C₁₉

#485

yes

characteristic

125

C₂²×C₁₉

#485

yes

characteristic

126

C₄×C₁₉

—

127

C₄×C₁₉

—

128

C₄×C₁₉

—

129

C₄×C₁₉

—

130

C₄×C₁₉

#464

yes

characteristic

131

C₄×C₁₉

#464

yes

characteristic

132

C₄×C₁₉

#488

yes

characteristic

133

C₄×C₁₉

#491

yes

characteristic

134

Dic₁₉

—

135

Dic₁₉

—

136

Dic₁₉

—

137

Dic₁₉

—

138

#533

—

139

#431

—

140

#431

C₂×D₁₉

yes

characteristic

141

#423

C₂×D₁₉

yes

characteristic

142

C₂×C₄⋊C₈

—

143

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

144

#376

—

145

#339

—

146

#339

—

147

#336

—

148

#336

—

149

#333

—

150

#333

—

151

#332

—

152

#332

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

#2074

yes

characteristic

156

C₂×C₁₉

#2080

yes

characteristic

157

C₂×C₁₉

#2080

yes

characteristic

158

C₂×M₁₆

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

#125

—

164

C₂²⋊Q₈

—

165

C₂²⋊Q₈

—

166

C₄×Q₈

—

167

C₄×Q₈

—

168

#117

—

169

C₂×C₄²

—

170

C₂×C₄²

—

171

C₂×C₄²

C₂²×D₁₉

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₄⋊C₈

—

175

C₄⋊C₈

—

176

C₄⋊C₈

—

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₂²⋊C₈

—

181

C₂²⋊C₈

—

182

C₄×C₈

—

183

C₄×C₈

—

184

#95

—

185

#95

—

186

C₁₉

#10630

yes

characteristic, complemented, Sylow

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

#64541

yes

characteristic

192

C₂²×C₄

D₄×D₁₉

yes

characteristic

193

C₂²×C₄

#64545

yes

characteristic

194

M₁₆

—

195

M₁₆

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₂²⋊C₄

—

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₄²

#64541

yes

characteristic

218

C₄²

#64541

yes

characteristic

219

C₄²

D₄×D₁₉

yes

characteristic

220

C₄²

#64543

yes

characteristic

221

C₂³

#10597340

yes

characteristic

222

Q₈

—

152

—

223

Q₈

—

152

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

#10597322

yes

characteristic

235

C₂×C₄

#10597329

yes

characteristic

236

C₂×C₄

#10597330

yes

characteristic

237

C₂×C₄

#10597331

yes

characteristic

238

C₂×C₄

#10597340

yes

characteristic

239

C₂×C₄

#10597344

yes

characteristic

240

C₂×C₄

#10597358

yes

characteristic

241

C₂×C₄

#10597361

yes

characteristic

242

C₂×C₄

#10597362

yes

characteristic

243

C₂×C₄

#10597364

yes

characteristic

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

152

—

248

C₈

—

152

—

249

C₂²

—

250

C₂²

—

251

C₂²

#11926473

yes

characteristic

252

C₂²

#11926887

yes

characteristic

253

C₂²

#11926888

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

152

—

259

C₄

—

152

—

260

C₄

—

152

—

261

C₄

—

152

—

262

C₄

#11926765

yes

characteristic

263

C₄

#11926769

yes

characteristic

264

C₄

#11926897

yes

characteristic

265

C₄

#11926911

yes

characteristic

266

C₂

—

267

C₂

—

268

C₂

#14565057

yes

characteristic

269

C₂

#14565090

yes

characteristic

270

C₂

#14565091

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597331
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1301	C₂
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#123
hypercenter	#1301	D₁₉
hypocenter	C₁₉	#10630
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

subgroup

G/H

center

C₂×C₄

#10597331

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1301

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

N	H ≅ G/N	type
186. C₁₉	#10630	semidirect

H ≅ G/N

type

186. C₁₉

#10630

semidirect

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

subgroup	index
#14564615	2
#14563754	2
#14562293	2
#14562290	2
#14561530	2
#14561463	2
C₁₉×#1301	2
#10630	19

subgroup

index

C₁₉×#1301

Subgroups — #18087326

Conjugacy classes of subgroups

Complements

Maximal subgroups