Group #14563400 — subgroups

Subgroups — #14563400

Order 2432.

336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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	C₂×#10597318	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597272	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₁₉)⋊C₄	C₄	1	2	yes	—
13	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#10597318	—	2	2	no	—
18	#10597318	—	2	2	no	—
19	(C₂×D₁₉)⋊C₈	C₄	1	4	yes	complemented
20	(C₂×D₁₉)⋊C₈	C₄	1	4	yes	complemented
21	#10597272	—	2	2	no	—
22	C₈×Dic₁₉	—	2	2	no	—
23	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₁₉	—	2	1	no	—
29	C₂×C₄×D₁₉	—	2	1	no	—
30	C₂×C₄×D₁₉	—	2	1	no	—
31	C₂×C₄×D₁₉	—	2	1	no	—
32	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
39	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₄²×C₁₉	—	2	1	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	(C₂×D₁₉)⋊C₄	—	2	4	no	—
43	Dic₁₉⋊C₄	—	2	4	no	—
44	C₄×Dic₁₉	D₄	1	2	yes	—
45	C₄×Dic₁₉	D₄	1	2	yes	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂×C₁₉⋊C₈	—	2	1	no	—
50	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
51	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
52	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×D₁₉	—	2	1	no	—
54	C₂²×D₁₉	—	2	1	no	—
55	C₂²×D₁₉	—	2	2	no	—
56	C₂²×D₁₉	—	2	2	no	—
57	C₂²×D₁₉	C₄²	1	2	yes	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
67	C₂×Dic₁₉	—	2	1	no	—
68	C₂×Dic₁₉	—	2	1	no	—
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	2	2	no	—
71	C₂×Dic₁₉	C₄²	1	2	yes	—
72	C₂×Dic₁₉	C₂²⋊C₄	1	4	yes	—
73	C₄×D₁₉	—	2	2	no	—
74	C₄×D₁₉	—	2	2	no	—
75	C₄×D₁₉	—	2	2	no	—
76	C₄×D₁₉	—	2	2	no	—
77	C₈×C₁₉	—	2	2	no	—
78	C₈×C₁₉	—	2	2	no	—
79	C₁₉⋊C₈	—	2	2	no	—
80	C₁₉⋊C₈	—	2	2	no	—
81	#1750	—	19	1	no	maximal, Sylow
82	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
83	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₁₉	#117	1	1	yes	characteristic
85	C₂²×C₁₉	#131	1	2	yes	—
86	C₂²×C₁₉	#131	1	2	yes	—
87	C₂×D₁₉	—	2	2	no	—
88	C₂×D₁₉	—	2	2	no	—
89	C₂×D₁₉	—	2	2	no	—
90	C₂×D₁₉	—	4	2	no	—
91	C₂×D₁₉	—	4	2	no	—
92	C₄×C₁₉	—	4	2	no	—
93	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
94	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
95	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
96	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
97	Dic₁₉	—	2	2	no	—
98	Dic₁₉	—	2	4	no	—
99	C₂×#117	—	19	1	no	—
100	C₂×C₂²⋊C₈	—	19	1	no	—
101	C₂×C₂²⋊C₈	—	19	1	no	—
102	C₂×#97	—	19	1	no	—
103	C₂×C₄×C₈	—	19	1	no	—
104	#336	—	19	1	no	—
105	#336	D₁₉	1	1	yes	characteristic, complemented
106	C₂×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₁₉	#405	1	1	yes	characteristic
108	C₂×C₁₉	#405	1	1	yes	characteristic
109	C₂×C₁₉	#408	1	2	yes	—
110	C₂×C₁₉	#433	1	2	yes	—
111	D₁₉	—	4	2	no	—
112	C₂³×C₄	—	19	1	no	—
113	C₂²×C₈	—	19	1	no	—
114	C₂²×C₈	—	19	1	no	—
115	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
116	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
117	#117	—	38	2	no	—
118	#117	—	38	2	no	—
119	C₂×C₄⋊C₄	—	19	2	no	—
120	C₂×C₂²⋊C₄	—	19	2	no	—
121	C₂×C₄²	—	19	1	no	—
122	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
123	C₂²⋊C₈	—	19	4	no	—
124	C₂²⋊C₈	—	19	4	no	—
125	#97	—	38	2	no	—
126	C₄×C₈	—	38	2	no	—
127	C₁₉	#1750	1	1	yes	characteristic, complemented, Sylow
128	C₂⁴	—	19	1	no	—
129	C₂²×C₄	—	19	2	no	—
130	C₂²×C₄	—	19	1	no	—
131	C₂²×C₄	—	19	2	no	—
132	C₂²×C₄	—	19	2	no	—
133	C₂²×C₄	—	38	1	no	—
134	C₂²×C₄	—	38	1	no	—
135	C₂²×C₄	—	38	1	no	—
136	C₂²×C₄	—	38	1	no	—
137	C₂²×C₄	C₄×D₁₉	1	2	yes	—
138	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	19	2	no	—
144	C₂×C₈	—	19	2	no	—
145	C₂×C₈	—	38	1	no	—
146	C₂×C₈	—	38	1	no	—
147	C₂×C₈	—	38	1	no	—
148	C₂×C₈	—	38	1	no	—
149	C₂×C₈	C₄×D₁₉	1	2	yes	—
150	C₂×C₈	C₄×D₁₉	1	2	yes	—
151	C₄⋊C₄	—	38	4	no	—
152	C₂²⋊C₄	—	38	4	no	—
153	C₄²	—	2	1	no	—
154	C₄²	—	2	1	no	—
155	C₄²	—	19	2	no	—
156	C₄²	—	19	2	no	—
157	C₂³	—	19	2	no	—
158	C₂³	—	38	1	no	—
159	C₂³	—	38	1	no	—
160	C₂³	—	38	2	no	—
161	C₂³	—	38	2	no	—
162	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	19	2	no	—
167	C₂×C₄	—	19	4	no	—
168	C₂×C₄	—	38	1	no	—
169	C₂×C₄	—	38	1	no	—
170	C₂×C₄	—	38	2	no	—
171	C₂×C₄	—	38	2	no	—
172	C₂×C₄	—	38	2	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	38	2	no	—
176	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
177	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
179	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
180	C₂×C₄	#64543	1	1	yes	characteristic
181	C₂×C₄	#64545	1	1	yes	characteristic
182	C₈	—	2	2	no	—
183	C₈	—	2	2	no	—
184	C₈	—	38	2	no	—
185	C₈	—	38	2	no	—
186	C₂²	—	38	2	no	—
187	C₂²	—	38	2	no	—
188	C₂²	—	38	2	no	—
189	C₂²	—	76	2	no	—
190	C₂²	—	76	2	no	—
191	C₂²	C₄²×D₁₉	1	1	yes	characteristic
192	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
193	C₂²	#10597338	1	1	yes	characteristic
194	C₂²	#10597347	1	2	yes	—
195	C₂²	#10597353	1	2	yes	—
196	C₄	—	4	2	no	—
197	C₄	—	38	2	no	—
198	C₄	—	38	4	no	—
199	C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
200	C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
201	C₄	#10597339	1	1	yes	characteristic
202	C₄	#10597339	1	1	yes	characteristic
203	C₂	—	76	2	no	—
204	C₂	#11926391	1	1	yes	characteristic
205	C₂	#11926498	1	1	yes	characteristic
206	C₂	#11926501	1	1	yes	characteristic
207	C₂	#11926509	1	2	yes	—
208	C₂	#11926604	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597318

C₂

yes

maximal, characteristic

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal, characteristic

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597272

C₂

yes

maximal, characteristic, complemented

C₂×C₈×Dic₁₉

C₂

yes

maximal, characteristic, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#336

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₄

yes

—

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597318

—

#10597318

—

(C₂×D₁₉)⋊C₈

C₄

yes

complemented

(C₂×D₁₉)⋊C₈

C₄

yes

complemented

#10597272

—

C₈×Dic₁₉

—

C₂³×D₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₄²

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄²

yes

—

C₂×Dic₁₉

C₂²⋊C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1750

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄²

yes

characteristic

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#131

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×#117

—

100

C₂×C₂²⋊C₈

—

101

C₂×C₂²⋊C₈

—

102

C₂×#97

—

103

C₂×C₄×C₈

—

104

#336

—

105

#336

D₁₉

yes

characteristic, complemented

106

C₂×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

107

C₂×C₁₉

#405

yes

characteristic

108

C₂×C₁₉

#405

yes

characteristic

109

C₂×C₁₉

#408

yes

—

110

C₂×C₁₉

#433

yes

—

111

D₁₉

—

112

C₂³×C₄

—

113

C₂²×C₈

—

114

C₂²×C₈

—

115

C₂²×C₈

C₂×D₁₉

yes

characteristic

116

C₂²×C₈

C₂×D₁₉

yes

characteristic

117

#117

—

118

#117

—

119

C₂×C₄⋊C₄

—

120

C₂×C₂²⋊C₄

—

121

C₂×C₄²

—

122

C₂×C₄²

C₂×D₁₉

yes

characteristic

123

C₂²⋊C₈

—

124

C₂²⋊C₈

—

125

#97

—

126

C₄×C₈

—

127

C₁₉

#1750

yes

characteristic, complemented, Sylow

128

C₂⁴

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₄×D₁₉

yes

—

138

C₂²×C₄

C₂²×D₁₉

yes

characteristic

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

C₄×D₁₉

yes

—

150

C₂×C₈

C₄×D₁₉

yes

—

151

C₄⋊C₄

—

152

C₂²⋊C₄

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

C₂×C₄×D₁₉

yes

characteristic

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

177

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

178

C₂×C₄

D₄×D₁₉

yes

characteristic

179

C₂×C₄

D₄×D₁₉

yes

characteristic

180

C₂×C₄

#64543

yes

characteristic

181

C₂×C₄

#64545

yes

characteristic

182

C₈

—

183

C₈

—

184

C₈

—

185

C₈

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

C₄²×D₁₉

yes

characteristic

192

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

193

C₂²

#10597338

yes

characteristic

194

C₂²

#10597347

yes

—

195

C₂²

#10597353

yes

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

200

C₄

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

201

C₄

#10597339

yes

characteristic

202

C₄

#10597339

yes

characteristic

203

C₂

—

204

C₂

#11926391

yes

characteristic

205

C₂

#11926498

yes

characteristic

206

C₂

#11926501

yes

characteristic

207

C₂

#11926509

yes

—

208

C₂

#11926604

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄²
Fitting	C₁₉×#336	C₂
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂³×D₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#336	D₁₉
hypocenter	C₁₉	#1750
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂×C₄²

Fitting

C₁₉×#336

C₂

socle

C₂³×C₁₉

C₂²×C₄

prime radical

C₂³×D₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
4. C₂×#10597272	C₂	semidirect
5. C₂×C₈×Dic₁₉	C₂	semidirect
6. #11926299	C₂	semidirect
7. C₁₉×#336	C₂	semidirect
19. (C₂×D₁₉)⋊C₈	C₄	semidirect
20. (C₂×D₁₉)⋊C₈	C₄	semidirect
105. #336	D₁₉	semidirect
127. C₁₉	#1750	semidirect

H ≅ G/N

type

4. C₂×#10597272

C₂

semidirect

5. C₂×C₈×Dic₁₉

C₂

semidirect

6. #11926299

C₂

semidirect

7. C₁₉×#336

C₂

semidirect

19. (C₂×D₁₉)⋊C₈

C₄

semidirect

20. (C₂×D₁₉)⋊C₈

C₄

semidirect

105. #336

D₁₉

semidirect

127. C₁₉

#1750

semidirect

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

subgroup	index
C₂×#10597318	2
C₂×(C₂×D₁₉)⋊C₈	2
C₂×#10597272	2
C₂×C₈×Dic₁₉	2
#11926299	2
C₁₉×#336	2
#1750	19

subgroup

index

C₂×(C₂×D₁₉)⋊C₈

C₂×C₈×Dic₁₉

C₁₉×#336

Subgroups — #14563400

Conjugacy classes of subgroups

Complements

Maximal subgroups