Group #18082432 — subgroups

Subgroups — #18082432

Order 4864.

498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14574214	C₂	1	1	yes	maximal, characteristic
2	#14564462	C₂	1	2	yes	maximal, complemented
3	#14563380	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562085	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926921	C₄	1	1	yes	characteristic, complemented
9	#11926891	C₄	1	2	yes	complemented
10	#11926780	—	2	2	no	—
11	C₄×D₁₅₂	—	2	2	no	—
12	C₂×#10597282	—	2	4	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
15	#11926298	—	2	2	no	—
16	#11926271	—	2	4	no	—
17	C₁₉×#423	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#335	—	2	2	no	—
20	C₂×#64541	—	2	2	no	—
21	C₂×M₁₆×C₁₉	—	2	2	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	#10597376	—	2	2	no	—
25	#10597376	—	2	2	no	—
26	C₂×C₄×Dic₁₉	—	2	1	no	—
27	C₂×C₄×Dic₁₉	—	2	1	no	—
28	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂×D₁₅₂	—	2	2	no	—
31	#10597321	—	2	2	no	—
32	#10597320	C₂×C₄	1	2	yes	—
33	C₄×D₇₆	—	2	2	no	—
34	C₄×D₇₆	—	2	2	no	—
35	#10597315	C₂×C₄	1	2	yes	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	#10597282	—	4	8	no	—
42	#10597278	—	2	4	no	—
43	#10597275	—	2	2	no	—
44	C₄×C₁₉⋊C₈	—	2	1	no	—
45	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂×C₂²⋊D₁₉	—	4	2	no	—
50	C₂²×Dic₁₉	—	2	2	no	—
51	#64541	—	4	4	no	—
52	#64541	—	4	4	no	—
53	C₂×D₇₆	—	2	2	no	—
54	C₂×D₇₆	—	2	2	no	—
55	C₂×D₇₆	—	2	2	no	—
56	C₂×C₄×D₁₉	—	4	2	no	—
57	C₂×Dic₃₈	—	2	2	no	—
58	M₁₆×C₁₉	—	4	4	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₄²×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	#41	1	1	yes	characteristic
67	(C₂×D₁₉)⋊C₄	—	4	2	no	—
68	(C₂×D₁₉)⋊C₄	—	4	2	no	—
69	C₄⋊Dic₁₉	—	2	2	no	—
70	C₄⋊Dic₁₉	—	2	2	no	—
71	C₄×Dic₁₉	—	2	2	no	—
72	C₄×Dic₁₉	—	4	2	no	—
73	C₄×Dic₁₉	—	4	2	no	—
74	C₄×Dic₁₉	D₈	1	4	yes	complemented
75	C₂×C₁₉⋊C₈	—	2	2	no	—
76	C₂×C₁₉⋊C₈	—	4	2	no	—
77	D₁₅₂	—	4	4	no	—
78	#9847	—	19	1	no	maximal, Sylow
79	C₂³×C₁₉	#121	1	1	yes	characteristic
80	C₂²×D₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
90	C₂×C₄×C₁₉	#135	1	2	yes	—
91	C₂²⋊D₁₉	—	8	4	no	—
92	C₂×Dic₁₉	—	2	4	no	—
93	C₂×Dic₁₉	—	4	2	no	—
94	C₂×Dic₁₉	—	4	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	D₇₆	—	4	4	no	—
97	D₇₆	—	4	4	no	—
98	D₇₆	—	4	4	no	—
99	C₄×D₁₉	—	8	2	no	—
100	C₄×D₁₉	—	8	2	no	—
101	Dic₃₈	—	4	4	no	—
102	C₈×C₁₉	—	2	2	no	—
103	C₈×C₁₉	—	2	2	no	—
104	C₈×C₁₉	—	8	2	no	—
105	C₁₉⋊C₈	—	4	2	no	—
106	#3169	—	19	1	no	—
107	#1962	—	19	2	no	—
108	#1744	—	19	1	no	—
109	#1567	D₁₉	1	1	yes	characteristic, complemented
110	#1492	—	19	2	no	—
111	C₂²×C₁₉	—	2	1	no	—
112	C₂²×C₁₉	—	2	1	no	—
113	C₂²×C₁₉	#390	1	1	yes	characteristic
114	C₂²×C₁₉	#466	1	2	yes	—
115	C₂×D₁₉	—	8	2	no	—
116	C₂×D₁₉	—	8	2	no	—
117	C₂×D₁₉	—	8	2	no	—
118	C₄×C₁₉	—	2	1	no	—
119	C₄×C₁₉	—	2	1	no	—
120	C₄×C₁₉	#421	1	2	yes	—
121	C₄×C₁₉	C₄×D₈	1	2	yes	—
122	C₄×C₁₉	#444	1	2	yes	—
123	C₄×C₁₉	#493	1	1	yes	characteristic
124	C₄×C₁₉	#495	1	1	yes	characteristic
125	Dic₁₉	—	4	4	no	—
126	Dic₁₉	—	8	2	no	—
127	#532	—	19	2	no	—
128	#500	—	19	1	no	—
129	#493	—	19	1	no	—
130	#486	—	19	2	no	—
131	#466	—	38	2	no	—
132	C₄×D₈	—	38	2	no	—
133	#423	C₂×D₁₉	1	2	yes	—
134	C₂×#104	—	38	4	no	—
135	C₂×C₄×C₈	—	19	1	no	—
136	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
137	C₄³	—	19	1	no	—
138	#336	—	38	2	no	—
139	#335	—	2	2	no	—
140	D₄⋊C₈	—	38	4	no	—
141	C₂×C₁₉	—	2	2	no	—
142	C₂×C₁₉	#1963	1	1	yes	characteristic
143	C₂×C₁₉	#1970	1	1	yes	characteristic
144	C₂×C₁₉	#1975	1	1	yes	characteristic
145	D₁₉	—	16	2	no	—
146	C₂×#41	—	38	2	no	—
147	C₂×D₈	—	38	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂²×C₈	—	38	1	no	—
150	C₂²×C₈	D₇₆	1	2	yes	—
151	C₄⋊Q₈	—	19	2	no	—
152	#127	—	19	2	no	—
153	#124	—	38	2	no	—
154	#121	—	38	2	no	—
155	#121	—	38	2	no	—
156	C₄×D₄	—	38	2	no	—
157	C₄×D₄	—	38	2	no	—
158	C₂×C₄²	—	19	2	no	—
159	C₂×C₄²	—	38	1	no	—
160	C₂×C₄²	—	38	1	no	—
161	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
162	#107	—	38	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	#104	—	76	8	no	—
166	#102	—	38	4	no	—
167	C₄×C₈	—	19	2	no	—
168	C₄×C₈	—	38	1	no	—
169	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
170	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
171	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
172	C₁₉	#9847	1	1	yes	characteristic, complemented, Sylow
173	#41	—	76	4	no	—
174	#41	—	76	4	no	—
175	C₂×Q₈	—	38	2	no	—
176	C₂×D₄	—	38	2	no	—
177	C₂×D₄	—	38	2	no	—
178	C₂×D₄	—	38	2	no	—
179	C₂×D₄	—	76	2	no	—
180	C₂²×C₄	—	38	2	no	—
181	C₂²×C₄	—	76	2	no	—
182	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
183	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
184	C₂²×C₄	#64545	1	1	yes	characteristic
185	D₈	—	76	4	no	—
186	M₁₆	—	4	4	no	—
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	38	2	no	—
190	C₂×C₈	—	76	2	no	—
191	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
192	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
193	C₄⋊C₄	—	38	2	no	—
194	C₄⋊C₄	—	38	2	no	—
195	C₂²⋊C₄	—	76	2	no	—
196	C₂²⋊C₄	—	76	2	no	—
197	C₄²	—	19	4	no	—
198	C₄²	—	38	2	no	—
199	C₄²	—	76	2	no	—
200	C₄²	—	76	2	no	—
201	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
202	C₄²	D₄×D₁₉	1	1	yes	characteristic
203	C₄²	#64545	1	1	yes	characteristic
204	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂³	—	76	2	no	—
206	C₂³	#10597341	1	1	yes	characteristic
207	Q₈	—	76	4	no	—
208	D₄	—	76	4	no	—
209	D₄	—	76	4	no	—
210	D₄	—	76	4	no	—
211	D₄	—	152	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	38	4	no	—
215	C₂×C₄	—	76	2	no	—
216	C₂×C₄	—	76	2	no	—
217	C₂×C₄	—	76	2	no	—
218	C₂×C₄	—	152	2	no	—
219	C₂×C₄	—	152	2	no	—
220	C₂×C₄	#10597339	1	1	yes	characteristic
221	C₂×C₄	#10597339	1	1	yes	characteristic
222	C₂×C₄	#10597341	1	1	yes	characteristic
223	C₂×C₄	D₈×D₁₉	1	2	yes	—
224	C₂×C₄	#10597365	1	2	yes	—
225	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
226	C₂×C₄	#10597386	1	1	yes	characteristic
227	C₂×C₄	#10597393	1	1	yes	characteristic
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	8	2	no	—
231	C₈	—	76	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	152	2	no	—
235	C₂²	—	152	2	no	—
236	C₂²	—	152	2	no	—
237	C₂²	#11926445	1	1	yes	characteristic
238	C₂²	#11926781	1	2	yes	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	76	4	no	—
242	C₄	—	152	2	no	—
243	C₄	#11926560	1	2	yes	—
244	C₄	#11926626	1	2	yes	—
245	C₄	#11926665	1	2	yes	—
246	C₄	#11926919	1	1	yes	characteristic
247	C₄	#11926929	1	1	yes	characteristic
248	C₂	—	2	2	no	—
249	C₂	—	304	2	no	—
250	C₂	#14564466	1	1	yes	characteristic
251	C₂	#14564499	1	1	yes	characteristic
252	C₂	#14564526	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574214

C₂

yes

maximal, characteristic

#14564462

C₂

yes

maximal, complemented

#14563380

C₂

yes

maximal, characteristic, complemented

#14562085

C₂

yes

maximal, complemented

C₁₉×#1567

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

#11926949

C₄

yes

characteristic, complemented

#11926921

C₄

yes

characteristic, complemented

#11926891

C₄

yes

complemented

#11926780

—

C₄×D₁₅₂

—

C₂×#10597282

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926298

—

#11926271

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₂×#64541

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597376

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂×D₁₅₂

—

#10597321

—

#10597320

C₂×C₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

—

#10597282

—

#10597278

—

#10597275

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₈

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

100

C₄×D₁₉

—

101

Dic₃₈

—

102

C₈×C₁₉

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

C₁₉⋊C₈

—

106

#3169

—

107

#1962

—

108

#1744

—

109

#1567

D₁₉

yes

characteristic, complemented

110

#1492

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

#390

yes

characteristic

114

C₂²×C₁₉

#466

yes

—

115

C₂×D₁₉

—

116

C₂×D₁₉

—

117

C₂×D₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

#421

yes

—

121

C₄×C₁₉

C₄×D₈

yes

—

122

C₄×C₁₉

#444

yes

—

123

C₄×C₁₉

#493

yes

characteristic

124

C₄×C₁₉

#495

yes

characteristic

125

Dic₁₉

—

126

Dic₁₉

—

127

#532

—

128

#500

—

129

#493

—

130

#486

—

131

#466

—

132

C₄×D₈

—

133

#423

C₂×D₁₉

yes

—

134

C₂×#104

—

135

C₂×C₄×C₈

—

136

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

137

C₄³

—

138

#336

—

139

#335

—

140

D₄⋊C₈

—

141

C₂×C₁₉

—

142

C₂×C₁₉

#1963

yes

characteristic

143

C₂×C₁₉

#1970

yes

characteristic

144

C₂×C₁₉

#1975

yes

characteristic

145

D₁₉

—

146

C₂×#41

—

147

C₂×D₈

—

148

C₂×M₁₆

—

149

C₂²×C₈

—

150

C₂²×C₈

D₇₆

yes

—

151

C₄⋊Q₈

—

152

#127

—

153

#124

—

154

#121

—

155

#121

—

156

C₄×D₄

—

157

C₄×D₄

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

C₂×C₄²

—

161

C₂×C₄²

C₂²×D₁₉

yes

characteristic

162

#107

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#104

—

166

#102

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

C₄×D₁₉

yes

characteristic

170

C₄×C₈

C₄×D₁₉

yes

characteristic

171

C₄×C₈

C₂²⋊D₁₉

yes

—

172

C₁₉

#9847

yes

characteristic, complemented, Sylow

173

#41

—

174

#41

—

175

C₂×Q₈

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂×D₇₆

yes

characteristic

183

C₂²×C₄

D₄×D₁₉

yes

characteristic

184

C₂²×C₄

#64545

yes

characteristic

185

D₈

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

192

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

C₂×C₄×D₁₉

yes

characteristic

202

C₄²

D₄×D₁₉

yes

characteristic

203

C₄²

#64545

yes

characteristic

204

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

205

C₂³

—

206

C₂³

#10597341

yes

characteristic

207

Q₈

—

208

D₄

—

209

D₄

—

210

D₄

—

211

D₄

—

152

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

152

—

219

C₂×C₄

—

152

—

220

C₂×C₄

#10597339

yes

characteristic

221

C₂×C₄

#10597339

yes

characteristic

222

C₂×C₄

#10597341

yes

characteristic

223

C₂×C₄

D₈×D₁₉

yes

—

224

C₂×C₄

#10597365

yes

—

225

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

226

C₂×C₄

#10597386

yes

characteristic

227

C₂×C₄

#10597393

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

152

—

235

C₂²

—

152

—

236

C₂²

—

152

—

237

C₂²

#11926445

yes

characteristic

238

C₂²

#11926781

yes

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

152

—

243

C₄

#11926560

yes

—

244

C₄

#11926626

yes

—

245

C₄

#11926665

yes

—

246

C₄

#11926919

yes

characteristic

247

C₄

#11926929

yes

characteristic

248

C₂

—

249

C₂

—

304

—

250

C₂

#14564466

yes

characteristic

251

C₂

#14564499

yes

characteristic

252

C₂

#14564526

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1567	C₂
socle	C₂²×C₁₉	#390
prime radical	#14574214	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1567	D₁₉
hypocenter	C₁₉	#9847
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1567

C₂

C₂²×C₁₉

C₂

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
2. #14564462	C₂	semidirect
3. #14563380	C₂	semidirect
4. #14562085	C₂	semidirect
5. C₁₉×#1567	C₂	semidirect
7. #11926949	C₄	semidirect
8. #11926921	C₄	semidirect
9. #11926891	C₄	semidirect
74. C₄×Dic₁₉	D₈	semidirect
109. #1567	D₁₉	semidirect
172. C₁₉	#9847	semidirect

H ≅ G/N

type

2. #14564462

C₂

semidirect

3. #14563380

C₂

semidirect

4. #14562085

C₂

semidirect

5. C₁₉×#1567

C₂

semidirect

7. #11926949

C₄

semidirect

8. #11926921

C₄

semidirect

9. #11926891

C₄

semidirect

74. C₄×Dic₁₉

D₈

semidirect

109. #1567

D₁₉

semidirect

172. C₁₉

#9847

semidirect

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

subgroup	index
#14574214	2
#14564462	2
#14563380	2
#14562085	2
C₁₉×#1567	2
#9847	19

subgroup

index

C₁₉×#1567

Subgroups — #18082432

Conjugacy classes of subgroups

Complements

Maximal subgroups