Group #18087672 — subgroups

Subgroups — #18087672

Order 4864.

264 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14564359	C₂	1	1	yes	maximal, characteristic
2	#14563809	C₂	1	1	yes	maximal, characteristic
3	#14561538	C₂	1	1	yes	maximal, characteristic
4	#14561531	C₂	1	1	yes	maximal, characteristic
5	#14561530	C₂	1	1	yes	maximal, characteristic
6	#14561465	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	C₂×#10597279	—	2	1	no	—
10	C₂×#10597279	—	2	1	no	—
11	#11926568	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597260	C₂²	1	1	yes	characteristic
15	#11926299	—	2	1	no	—
16	C₁₉×#431	C₂²	1	1	yes	characteristic
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₁₉	—	2	1	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
21	C₂×C₄²×C₁₉	—	2	1	no	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂×#64520	—	2	1	no	—
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
27	C₁₉×C₄⋊C₈	—	2	1	no	—
28	C₁₉×C₄⋊C₈	—	2	1	no	—
29	C₁₉×C₄⋊C₈	—	2	1	no	—
30	C₁₉×C₂²⋊C₈	—	2	1	no	—
31	C₄×C₈×C₁₉	—	2	1	no	—
32	C₁₉×#95	Q₈	1	1	yes	characteristic
33	C₁₉×#95	Q₈	1	1	yes	characteristic
34	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
35	#10597279	—	4	2	no	—
36	#10597279	—	4	2	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
43	#10597260	—	2	1	no	—
44	#10597260	—	2	1	no	—
45	C₄×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	2	1	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
51	M₁₆×C₁₉	—	4	1	no	—
52	M₁₆×C₁₉	—	4	1	no	—
53	C₂×C₈×C₁₉	—	4	1	no	—
54	C₂×C₈×C₁₉	—	4	1	no	—
55	C₄⋊C₄×C₁₉	—	4	2	no	—
56	C₄²×C₁₉	—	4	1	no	—
57	C₄²×C₁₉	—	4	1	no	—
58	C₄²×C₁₉	#41	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₄²×C₁₉	#41	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	1	yes	characteristic
62	#64520	—	4	1	no	—
63	#64520	—	4	1	no	—
64	C₂×C₁₉⋊C₈	—	2	1	no	—
65	C₂×C₁₉⋊C₈	—	2	1	no	—
66	C₂×C₁₉⋊C₈	—	2	1	no	—
67	C₂×C₁₉⋊C₈	—	2	1	no	—
68	C₂×C₁₉⋊C₈	—	4	1	no	—
69	C₂×C₁₉⋊C₈	—	4	1	no	—
70	C₂×C₁₉⋊C₈	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	4	1	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
74	C₂×C₁₉⋊C₈	Q₁₆	1	2	yes	—
75	#10688	—	19	1	no	maximal, Sylow
76	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	4	1	no	—
79	C₂×C₄×C₁₉	—	4	1	no	—
80	C₂×C₄×C₁₉	—	4	1	no	—
81	C₂×C₄×C₁₉	—	4	1	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	4	1	no	—
85	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
90	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₈×C₁₉	—	8	1	no	—
96	C₈×C₁₉	—	8	1	no	—
97	C₁₉⋊C₈	—	2	2	no	—
98	C₁₉⋊C₈	—	2	2	no	—
99	C₁₉⋊C₈	—	8	1	no	—
100	C₁₉⋊C₈	—	8	1	no	—
101	C₁₉⋊C₈	—	8	1	no	—
102	#1940	—	19	1	no	—
103	#1849	—	19	1	no	—
104	#1303	—	19	1	no	—
105	#1303	D₁₉	1	1	yes	characteristic
106	#1301	—	19	1	no	—
107	#1301	—	19	1	no	—
108	#1275	—	19	1	no	—
109	C₂²×C₁₉	—	2	1	no	—
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	#400	1	1	yes	characteristic
112	C₂²×C₁₉	#476	1	1	yes	characteristic
113	C₂²×C₁₉	#477	1	1	yes	characteristic
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	1	no	—
118	C₄×C₁₉	—	4	2	no	—
119	C₄×C₁₉	—	8	1	no	—
120	C₄×C₁₉	#481	1	1	yes	characteristic
121	C₄×C₁₉	#484	1	1	yes	characteristic
122	C₄×C₁₉	#487	1	1	yes	characteristic
123	C₄×C₁₉	#490	1	1	yes	characteristic
124	#431	—	19	1	no	—
125	#431	C₂×D₁₉	1	1	yes	characteristic
126	C₂×#108	—	38	1	no	—
127	C₂×#108	—	38	1	no	—
128	#423	—	19	1	no	—
129	#423	C₂×D₁₉	1	1	yes	characteristic
130	C₂×C₄⋊C₈	—	19	1	no	—
131	C₂×C₄⋊C₈	—	38	1	no	—
132	C₂×#97	—	19	1	no	—
133	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
134	#336	—	38	1	no	—
135	C₂×C₁₉	—	2	1	no	—
136	C₂×C₁₉	—	2	1	no	—
137	C₂×C₁₉	#2100	1	1	yes	characteristic
138	C₂×C₁₉	#2102	1	1	yes	characteristic
139	C₂×C₁₉	#2103	1	1	yes	characteristic
140	C₂×M₁₆	—	2	1	no	—
141	C₂×M₁₆	—	38	1	no	—
142	C₂²×C₈	—	19	1	no	—
143	C₂²×C₈	—	19	1	no	—
144	C₂²×C₈	—	38	1	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄²	—	2	1	no	—
147	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
148	#108	—	76	2	no	—
149	#108	—	76	2	no	—
150	C₄⋊C₈	—	2	1	no	—
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	2	1	no	—
153	C₄⋊C₈	—	38	1	no	—
154	C₄⋊C₈	—	38	1	no	—
155	C₄⋊C₈	—	38	1	no	—
156	C₄⋊C₈	—	38	1	no	—
157	C₄⋊C₈	—	38	1	no	—
158	C₄⋊C₈	—	76	2	no	—
159	C₂²⋊C₈	—	2	1	no	—
160	C₂²⋊C₈	—	38	1	no	—
161	#97	—	38	1	no	—
162	#97	—	38	1	no	—
163	C₄×C₈	—	2	1	no	—
164	C₄×C₈	—	38	1	no	—
165	#95	Dic₃₈	1	1	yes	characteristic
166	#95	Dic₃₈	1	1	yes	characteristic
167	C₁₉	#10688	1	1	yes	characteristic, complemented, Sylow
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
171	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
172	C₂²×C₄	#64543	1	1	yes	characteristic
173	M₁₆	—	4	1	no	—
174	M₁₆	—	4	1	no	—
175	M₁₆	—	76	1	no	—
176	M₁₆	—	76	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	19	2	no	—
180	C₂×C₈	—	19	2	no	—
181	C₂×C₈	—	38	1	no	—
182	C₂×C₈	—	38	1	no	—
183	C₂×C₈	—	38	1	no	—
184	C₂×C₈	—	38	1	no	—
185	C₂×C₈	—	76	1	no	—
186	C₂×C₈	—	76	1	no	—
187	C₂×C₈	—	76	1	no	—
188	C₂×C₈	—	76	1	no	—
189	C₂×C₈	—	76	1	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄²	—	4	1	no	—
192	C₄²	—	4	1	no	—
193	C₄²	#64541	1	1	yes	characteristic
194	C₄²	#64541	1	1	yes	characteristic
195	C₄²	#64543	1	1	yes	characteristic
196	C₄²	#64545	1	1	yes	characteristic
197	C₂³	#10597324	1	1	yes	characteristic
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	#10597316	1	1	yes	characteristic
207	C₂×C₄	#10597325	1	1	yes	characteristic
208	C₂×C₄	#10597331	1	1	yes	characteristic
209	C₂×C₄	#10597336	1	1	yes	characteristic
210	C₂×C₄	#10597340	1	1	yes	characteristic
211	C₂×C₄	#10597344	1	1	yes	characteristic
212	C₂×C₄	#10597357	1	1	yes	characteristic
213	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
214	C₂×C₄	#10597360	1	1	yes	characteristic
215	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
216	C₈	—	8	1	no	—
217	C₈	—	8	1	no	—
218	C₈	—	38	2	no	—
219	C₈	—	38	2	no	—
220	C₈	—	152	1	no	—
221	C₈	—	152	1	no	—
222	C₈	—	152	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	#11926486	1	1	yes	characteristic
226	C₂²	#11926832	1	1	yes	characteristic
227	C₂²	#11926837	1	1	yes	characteristic
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	4	2	no	—
233	C₄	—	8	1	no	—
234	C₄	#11926864	1	1	yes	characteristic
235	C₄	#11926881	1	1	yes	characteristic
236	C₄	#11926893	1	1	yes	characteristic
237	C₄	#11926907	1	1	yes	characteristic
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	#14565201	1	1	yes	characteristic
241	C₂	#14565213	1	1	yes	characteristic
242	C₂	#14565218	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564359

C₂

yes

maximal, characteristic

#14563809

C₂

yes

maximal, characteristic

#14561538

C₂

yes

maximal, characteristic

#14561531

C₂

yes

maximal, characteristic

#14561530

C₂

yes

maximal, characteristic

#14561465

C₂

yes

maximal, characteristic

C₁₉×#1303

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

characteristic

#11926299

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

Q₈

yes

characteristic

C₁₉×#95

Q₈

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

#10597279

—

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

C₂×C₁₉⋊C₈

Q₁₆

yes

—

#10688

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×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

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₁₆

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

C₁₉⋊C₈

—

101

C₁₉⋊C₈

—

102

#1940

—

103

#1849

—

104

#1303

—

105

#1303

D₁₉

yes

characteristic

106

#1301

—

107

#1301

—

108

#1275

—

109

C₂²×C₁₉

—

110

C₂²×C₁₉

—

111

C₂²×C₁₉

#400

yes

characteristic

112

C₂²×C₁₉

#476

yes

characteristic

113

C₂²×C₁₉

#477

yes

characteristic

114

C₄×C₁₉

—

115

C₄×C₁₉

—

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

#481

yes

characteristic

121

C₄×C₁₉

#484

yes

characteristic

122

C₄×C₁₉

#487

yes

characteristic

123

C₄×C₁₉

#490

yes

characteristic

124

#431

—

125

#431

C₂×D₁₉

yes

characteristic

126

C₂×#108

—

127

C₂×#108

—

128

#423

—

129

#423

C₂×D₁₉

yes

characteristic

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

132

C₂×#97

—

133

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

134

#336

—

135

C₂×C₁₉

—

136

C₂×C₁₉

—

137

C₂×C₁₉

#2100

yes

characteristic

138

C₂×C₁₉

#2102

yes

characteristic

139

C₂×C₁₉

#2103

yes

characteristic

140

C₂×M₁₆

—

141

C₂×M₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₂²×C₈

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄²

—

147

C₂×C₄²

C₂²×D₁₉

yes

characteristic

148

#108

—

149

#108

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₂²⋊C₈

—

160

C₂²⋊C₈

—

161

#97

—

162

#97

—

163

C₄×C₈

—

164

C₄×C₈

—

165

#95

Dic₃₈

yes

characteristic

166

#95

Dic₃₈

yes

characteristic

167

C₁₉

#10688

yes

characteristic, complemented, Sylow

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

171

C₂²×C₄

D₄×D₁₉

yes

characteristic

172

C₂²×C₄

#64543

yes

characteristic

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

176

M₁₆

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₄⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

#64541

yes

characteristic

194

C₄²

#64541

yes

characteristic

195

C₄²

#64543

yes

characteristic

196

C₄²

#64545

yes

characteristic

197

C₂³

#10597324

yes

characteristic

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

#10597316

yes

characteristic

207

C₂×C₄

#10597325

yes

characteristic

208

C₂×C₄

#10597331

yes

characteristic

209

C₂×C₄

#10597336

yes

characteristic

210

C₂×C₄

#10597340

yes

characteristic

211

C₂×C₄

#10597344

yes

characteristic

212

C₂×C₄

#10597357

yes

characteristic

213

C₂×C₄

SD₁₆×D₁₉

yes

characteristic

214

C₂×C₄

#10597360

yes

characteristic

215

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

216

C₈

—

217

C₈

—

218

C₈

—

219

C₈

—

220

C₈

—

152

—

221

C₈

—

152

—

222

C₈

—

152

—

223

C₂²

—

224

C₂²

—

225

C₂²

#11926486

yes

characteristic

226

C₂²

#11926832

yes

characteristic

227

C₂²

#11926837

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

#11926864

yes

characteristic

235

C₄

#11926881

yes

characteristic

236

C₄

#11926893

yes

characteristic

237

C₄

#11926907

yes

characteristic

238

C₂

—

239

C₂

—

240

C₂

#14565201

yes

characteristic

241

C₂

#14565213

yes

characteristic

242

C₂

#14565218

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597331
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1303	C₂
socle	C₂²×C₁₉	#400
prime radical	C₂³×C₁₉	C₂²⋊Q₈
hypercenter	#1303	D₁₉
hypocenter	C₁₉	#10688
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂×C₄

#10597331

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1303

C₂

socle

C₂²×C₁₉

#400

prime radical

C₂³×C₁₉

C₂²⋊Q₈

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
167. C₁₉	#10688	semidirect

H ≅ G/N

type

167. C₁₉

#10688

semidirect

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

subgroup	index
#14564359	2
#14563809	2
#14561538	2
#14561531	2
#14561530	2
#14561465	2
C₁₉×#1303	2
#10688	19

subgroup

index

C₁₉×#1303

Subgroups — #18087672

Conjugacy classes of subgroups

Complements

Maximal subgroups