Group #14564719 — subgroups

Subgroups — #14564719

Order 2432.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₂²×#64516	C₂	1	1	yes	maximal, characteristic
2	C₂²×#64527	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597267	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926445	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₇₆	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	#10597390	—	2	2	no	—
14	#10597390	—	2	2	no	—
15	C₂×#64527	—	2	2	no	—
16	C₂×#64527	—	2	2	no	—
17	C₂×#64527	—	2	2	no	—
18	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
19	C₂×Dic₁₉⋊C₄	—	2	2	no	—
20	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×#64516	—	2	2	no	—
23	C₂×#64516	—	2	2	no	—
24	C₂×#64516	—	2	2	no	—
25	C₁₉×#103	—	2	2	no	—
26	#10597267	—	2	2	no	—
27	C₂³×D₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	—	2	1	no	—
29	C₂×Q₈×C₁₉	—	2	1	no	—
30	C₂×Q₈×C₁₉	—	2	1	no	—
31	C₂×Q₈×C₁₉	—	2	1	no	—
32	C₂×Q₈×C₁₉	—	2	1	no	—
33	C₂×Q₈×C₁₉	D₄	1	2	yes	—
34	C₂²×C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄×C₁₉	—	2	1	no	—
36	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₉	—	2	1	no	—
38	C₂²×Dic₁₉	D₄	1	2	yes	—
39	C₂×D₇₆	—	2	1	no	—
40	C₂×D₇₆	—	2	1	no	—
41	C₂×D₇₆	—	2	1	no	—
42	C₂×D₇₆	—	2	1	no	—
43	C₂×D₇₆	—	2	1	no	—
44	C₂×D₇₆	D₄	1	2	yes	—
45	C₂×Dic₃₈	—	2	1	no	—
46	C₂×Dic₃₈	—	2	1	no	—
47	C₂×Dic₃₈	—	2	1	no	—
48	C₂×Dic₃₈	—	2	1	no	—
49	C₂×Dic₃₈	—	2	1	no	—
50	C₂×Dic₃₈	D₄	1	2	yes	—
51	C₂×C₈×C₁₉	—	2	1	no	—
52	C₂×C₈×C₁₉	—	2	1	no	—
53	C₂×C₈×C₁₉	D₄	1	2	yes	—
54	C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₄⋊C₄×C₁₉	—	2	1	no	—
56	#64527	—	2	8	no	—
57	(C₂×D₁₉)⋊C₄	—	4	4	no	—
58	Dic₁₉⋊C₄	—	2	8	no	—
59	C₄×Dic₁₉	—	2	1	no	—
60	C₄×Dic₁₉	—	2	1	no	—
61	C₂×C₁₉⋊C₈	—	2	1	no	—
62	C₂×C₁₉⋊C₈	—	2	1	no	—
63	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
64	#64516	—	2	8	no	—
65	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×D₁₉	—	2	2	no	—
67	C₂²×D₁₉	—	4	1	no	—
68	C₂²×D₁₉	—	4	1	no	—
69	C₂²×D₁₉	—	4	2	no	—
70	C₂²×D₁₉	—	4	2	no	—
71	Q₈×C₁₉	—	2	2	no	—
72	Q₈×C₁₉	—	2	2	no	—
73	Q₈×C₁₉	—	4	1	no	—
74	Q₈×C₁₉	—	4	1	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	4	1	no	—
77	C₂×C₄×C₁₉	—	4	1	no	—
78	C₂×C₄×C₁₉	—	4	1	no	—
79	C₂×C₄×C₁₉	—	4	2	no	—
80	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
86	C₂×Dic₁₉	—	2	2	no	—
87	C₂×Dic₁₉	—	2	2	no	—
88	C₂×Dic₁₉	—	2	2	no	—
89	C₂×Dic₁₉	—	4	1	no	—
90	C₂×Dic₁₉	—	4	1	no	—
91	C₂×Dic₁₉	SD₁₆	1	4	yes	complemented
92	D₇₆	—	2	2	no	—
93	D₇₆	—	2	2	no	—
94	D₇₆	—	4	1	no	—
95	D₇₆	—	4	1	no	—
96	Dic₃₈	—	2	2	no	—
97	Dic₃₈	—	2	2	no	—
98	Dic₃₈	—	4	1	no	—
99	Dic₃₈	—	4	1	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₁₉⋊C₈	—	2	2	no	—
102	#2013	—	19	1	no	maximal, Sylow
103	C₂²×C₁₉	#120	1	1	yes	characteristic
104	C₂²×C₁₉	#121	1	1	yes	characteristic
105	C₂²×C₁₉	#127	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
107	C₂²×C₁₉	#137	1	2	yes	—
108	C₂×D₁₉	—	4	2	no	—
109	C₂×D₁₉	—	4	4	no	—
110	C₂×D₁₉	—	8	2	no	—
111	C₂×D₁₉	—	8	1	no	—
112	C₂×D₁₉	—	8	1	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	8	1	no	—
115	C₄×C₁₉	#120	1	1	yes	characteristic
116	C₄×C₁₉	#120	1	1	yes	characteristic
117	C₄×C₁₉	#121	1	1	yes	characteristic
118	C₄×C₁₉	#121	1	1	yes	characteristic
119	Dic₁₉	—	2	4	no	—
120	Dic₁₉	—	4	2	no	—
121	C₂²×SD₁₆	—	19	1	no	—
122	C₂²×SD₁₆	—	19	1	no	—
123	C₂×C₄⋊Q₈	—	19	1	no	—
124	C₂×#103	—	19	1	no	—
125	C₂×#103	D₁₉	1	1	yes	characteristic, complemented
126	#390	—	19	1	no	—
127	#336	—	19	1	no	—
128	C₂×C₁₉	#392	1	1	yes	characteristic
129	C₂×C₁₉	#448	1	2	yes	—
130	C₂×C₁₉	#461	1	2	yes	—
131	C₂×C₁₉	#492	1	1	yes	characteristic
132	C₂×C₁₉	#497	1	1	yes	characteristic
133	D₁₉	—	8	2	no	—
134	C₂²×Q₈	—	19	1	no	—
135	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
136	C₂²×D₄	—	19	1	no	—
137	C₂×SD₁₆	—	38	2	no	—
138	C₂×SD₁₆	—	38	2	no	—
139	C₂×SD₁₆	—	38	2	no	—
140	C₂×SD₁₆	—	38	2	no	—
141	C₂×SD₁₆	—	38	2	no	—
142	C₂×SD₁₆	—	38	2	no	—
143	C₂²×C₈	—	19	1	no	—
144	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
145	C₄⋊Q₈	—	38	2	no	—
146	C₄⋊Q₈	—	38	2	no	—
147	C₂×C₄⋊C₄	—	38	2	no	—
148	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
149	C₂×C₂²⋊C₄	—	38	2	no	—
150	C₂×C₄²	—	19	1	no	—
151	#103	—	2	2	no	—
152	#103	—	38	2	no	—
153	C₁₉	#2013	1	1	yes	characteristic, complemented, Sylow
154	C₂⁴	—	38	1	no	—
155	C₂×Q₈	—	2	1	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	2	1	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	19	2	no	—
161	C₂×Q₈	—	38	1	no	—
162	C₂×Q₈	—	38	1	no	—
163	C₂×Q₈	—	38	1	no	—
164	C₂×Q₈	—	38	1	no	—
165	C₂×Q₈	—	38	1	no	—
166	C₂×Q₈	D₇₆	1	2	yes	—
167	C₂×D₄	—	19	2	no	—
168	C₂×D₄	—	38	1	no	—
169	C₂×D₄	—	38	1	no	—
170	C₂×D₄	—	38	1	no	—
171	C₂×D₄	—	38	1	no	—
172	C₂×D₄	—	38	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	2	1	no	—
175	C₂²×C₄	—	19	2	no	—
176	C₂²×C₄	—	38	1	no	—
177	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
178	SD₁₆	—	38	8	no	—
179	SD₁₆	—	38	8	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	1	no	—
182	C₂×C₈	—	19	2	no	—
183	C₂×C₈	—	38	1	no	—
184	C₂×C₈	—	38	1	no	—
185	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	38	8	no	—
189	C₂²⋊C₄	—	76	4	no	—
190	C₄²	—	38	1	no	—
191	C₄²	—	38	1	no	—
192	C₂³	—	38	2	no	—
193	C₂³	—	76	1	no	—
194	C₂³	—	76	1	no	—
195	C₂³	—	76	2	no	—
196	C₂³	—	76	2	no	—
197	C₂³	D₄×D₁₉	1	1	yes	characteristic
198	Q₈	—	2	2	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	4	1	no	—
201	Q₈	—	4	1	no	—
202	Q₈	—	38	2	no	—
203	Q₈	—	38	2	no	—
204	Q₈	—	76	1	no	—
205	Q₈	—	76	1	no	—
206	D₄	—	38	2	no	—
207	D₄	—	38	2	no	—
208	D₄	—	76	1	no	—
209	D₄	—	76	1	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	19	4	no	—
216	C₂×C₄	—	38	2	no	—
217	C₂×C₄	—	38	2	no	—
218	C₂×C₄	—	38	2	no	—
219	C₂×C₄	—	76	1	no	—
220	C₂×C₄	—	76	1	no	—
221	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
222	C₂×C₄	#64541	1	1	yes	characteristic
223	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
224	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
226	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
227	C₈	—	2	2	no	—
228	C₈	—	38	2	no	—
229	C₂²	—	76	2	no	—
230	C₂²	—	76	4	no	—
231	C₂²	—	152	1	no	—
232	C₂²	—	152	1	no	—
233	C₂²	—	152	2	no	—
234	C₂²	#10597328	1	1	yes	characteristic
235	C₂²	#10597330	1	1	yes	characteristic
236	C₂²	SD₁₆×D₁₉	1	2	yes	—
237	C₂²	#10597364	1	2	yes	—
238	C₂²	#10597386	1	1	yes	characteristic
239	C₄	—	4	2	no	—
240	C₄	—	8	1	no	—
241	C₄	—	38	4	no	—
242	C₄	—	76	2	no	—
243	C₄	#10597328	1	1	yes	characteristic
244	C₄	#10597330	1	1	yes	characteristic
245	C₄	#10597376	1	1	yes	characteristic
246	C₄	#10597383	1	1	yes	characteristic
247	C₂	—	152	2	no	—
248	C₂	#11926453	1	1	yes	characteristic
249	C₂	#11926684	1	2	yes	—
250	C₂	#11926748	1	2	yes	—
251	C₂	#11926915	1	1	yes	characteristic
252	C₂	#11926937	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64516

C₂

yes

maximal, characteristic

C₂²×#64527

C₂

yes

maximal, characteristic

C₂×#10597390

C₂

yes

maximal, characteristic, complemented

C₂×#10597267

C₂

yes

maximal, characteristic, complemented

#11926445

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#103

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

—

—

—

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#103

—

#10597267

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

#64527

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

#64516

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

complemented

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

#2013

—

maximal, Sylow

103

C₂²×C₁₉

#120

yes

characteristic

104

C₂²×C₁₉

#121

yes

characteristic

105

C₂²×C₁₉

#127

yes

characteristic

106

C₂²×C₁₉

C₂×SD₁₆

yes

—

107

C₂²×C₁₉

#137

yes

—

108

C₂×D₁₉

—

109

C₂×D₁₉

—

110

C₂×D₁₉

—

111

C₂×D₁₉

—

112

C₂×D₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#120

yes

characteristic

116

C₄×C₁₉

#120

yes

characteristic

117

C₄×C₁₉

#121

yes

characteristic

118

C₄×C₁₉

#121

yes

characteristic

119

Dic₁₉

—

120

Dic₁₉

—

121

C₂²×SD₁₆

—

122

C₂²×SD₁₆

—

123

C₂×C₄⋊Q₈

—

124

C₂×#103

—

125

C₂×#103

D₁₉

yes

characteristic, complemented

126

#390

—

127

#336

—

128

C₂×C₁₉

#392

yes

characteristic

129

C₂×C₁₉

#448

yes

—

130

C₂×C₁₉

#461

yes

—

131

C₂×C₁₉

#492

yes

characteristic

132

C₂×C₁₉

#497

yes

characteristic

133

D₁₉

—

134

C₂²×Q₈

—

135

C₂²×Q₈

C₂×D₁₉

yes

characteristic

136

C₂²×D₄

—

137

C₂×SD₁₆

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

—

141

C₂×SD₁₆

—

142

C₂×SD₁₆

—

143

C₂²×C₈

—

144

C₂²×C₈

C₂×D₁₉

yes

characteristic

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

149

C₂×C₂²⋊C₄

—

150

C₂×C₄²

—

151

#103

—

152

#103

—

153

C₁₉

#2013

yes

characteristic, complemented, Sylow

154

C₂⁴

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

D₇₆

yes

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂²×D₁₉

yes

characteristic

178

SD₁₆

—

179

SD₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

C₂²⋊D₁₉

yes

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

190

C₄²

—

191

C₄²

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

D₄×D₁₉

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

D₄

—

207

D₄

—

208

D₄

—

209

D₄

—

210

C₂×C₄

—

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

—

220

C₂×C₄

—

221

C₂×C₄

C₂×D₇₆

yes

characteristic

222

C₂×C₄

#64541

yes

characteristic

223

C₂×C₄

D₄×D₁₉

yes

characteristic

224

C₂×C₄

D₄×D₁₉

yes

characteristic

225

C₂×C₄

D₄×D₁₉

yes

characteristic

226

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

227

C₈

—

228

C₈

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

152

—

232

C₂²

—

152

—

233

C₂²

—

152

—

234

C₂²

#10597328

yes

characteristic

235

C₂²

#10597330

yes

characteristic

236

C₂²

SD₁₆×D₁₉

yes

—

237

C₂²

#10597364

yes

—

238

C₂²

#10597386

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

#10597328

yes

characteristic

244

C₄

#10597330

yes

characteristic

245

C₄

#10597376

yes

characteristic

246

C₄

#10597383

yes

characteristic

247

C₂

—

152

—

248

C₂

#11926453

yes

characteristic

249

C₂

#11926684

yes

—

250

C₂

#11926748

yes

—

251

C₂

#11926915

yes

characteristic

252

C₂

#11926937

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#103	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₇₆	C₂²
hypercenter	C₂×#103	D₁₉
hypocenter	C₁₉	#2013
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#103

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#103

N	H ≅ G/N	type
3. C₂×#10597390	C₂	semidirect
4. C₂×#10597267	C₂	semidirect
6. #11926298	C₂	semidirect
7. C₂×C₁₉×#103	C₂	semidirect
91. C₂×Dic₁₉	SD₁₆	semidirect
125. C₂×#103	D₁₉	semidirect
153. C₁₉	#2013	semidirect

H ≅ G/N

type

3. C₂×#10597390

C₂

semidirect

4. C₂×#10597267

C₂

semidirect

6. #11926298

C₂

semidirect

7. C₂×C₁₉×#103

C₂

semidirect

91. C₂×Dic₁₉

SD₁₆

semidirect

125. C₂×#103

D₁₉

semidirect

153. C₁₉

#2013

semidirect

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

subgroup	index
C₂²×#64516	2
C₂²×#64527	2
C₂×#10597390	2
C₂×#10597267	2
#11926445	2
#11926298	2
C₂×C₁₉×#103	2
#2013	19

subgroup

index

C₂²×#64516

C₂²×#64527

C₂×C₁₉×#103

Subgroups — #14564719

Conjugacy classes of subgroups

Complements

Maximal subgroups