Group #18089104 — subgroups

Subgroups — #18089104

Order 4864.

2006 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 2006 conjugacy classes of subgroups — too many to draw. Only its 267 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×#10597290	C₂	1	4	yes	maximal, complemented
2	#14563329	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₂²	1	4	yes	—
5	C₂×#10597290	—	2	16	no	—
6	C₂×#10597290	—	2	8	no	—
7	#11926299	—	2	4	no	—
8	C₂³×D₄×C₁₉	C₄	1	4	yes	—
9	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#127	—	2	8	no	—
11	C₂×C₁₉×#127	—	2	4	no	—
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁵×C₁₉	C₂×C₄	1	4	yes	—
14	C₂²×D₄×C₁₉	—	2	16	no	—
15	C₂²×D₄×C₁₉	—	2	8	no	—
16	C₂²×D₄×C₁₉	—	2	4	no	—
17	C₂²×D₄×C₁₉	—	2	4	no	—
18	C₂²×D₄×C₁₉	—	2	8	no	—
19	C₂²×D₄×C₁₉	—	2	8	no	—
20	C₂²×D₄×C₁₉	—	4	16	no	—
21	C₂²×D₄×C₁₉	D₄	1	8	yes	—
22	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×#127	—	2	32	no	—
25	C₂×C₄²×C₁₉	—	2	4	no	—
26	C₂×C₄²×C₁₉	D₄	1	4	yes	—
27	C₂×#64520	—	2	4	no	—
28	C₂×#64520	—	2	8	no	—
29	C₂×#64520	—	2	8	no	—
30	C₂×#64520	D₄	1	8	yes	complemented
31	C₂²×C₁₉⋊C₈	—	2	4	no	—
32	#10597290	—	2	32	no	—
33	C₂⁴×C₁₉	—	2	4	no	—
34	C₂⁴×C₁₉	—	2	4	no	—
35	C₂⁴×C₁₉	—	2	16	no	—
36	C₂⁴×C₁₉	—	4	16	no	—
37	C₂⁴×C₁₉	C₂²⋊C₄	1	8	yes	—
38	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×D₄×C₁₉	—	2	32	no	—
40	C₂×D₄×C₁₉	—	2	16	no	—
41	C₂×D₄×C₁₉	—	2	8	no	—
42	C₂×D₄×C₁₉	—	2	16	no	—
43	C₂×D₄×C₁₉	—	2	8	no	—
44	C₂×D₄×C₁₉	—	4	64	no	—
45	C₂×D₄×C₁₉	—	4	16	no	—
46	C₂×D₄×C₁₉	—	4	16	no	—
47	C₂×D₄×C₁₉	—	4	4	no	—
48	C₂×D₄×C₁₉	—	4	8	no	—
49	C₂×D₄×C₁₉	—	4	8	no	—
50	C₂×D₄×C₁₉	—	4	4	no	—
51	C₂×D₄×C₁₉	—	4	4	no	—
52	C₂×D₄×C₁₉	—	4	4	no	—
53	C₂²×C₄×C₁₉	—	2	4	no	—
54	C₂²×C₄×C₁₉	—	2	8	no	—
55	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
56	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂²×C₄×C₁₉	#41	1	4	yes	—
60	C₄²×C₁₉	—	2	8	no	—
61	#64520	—	2	16	no	—
62	#64520	—	4	8	no	—
63	C₂×C₁₉⋊C₈	—	2	8	no	—
64	C₂×C₁₉⋊C₈	—	4	4	no	—
65	C₂×C₁₉⋊C₈	—	4	4	no	—
66	#10981	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	—	2	4	no	—
68	C₂³×C₁₉	—	2	8	no	—
69	C₂³×C₁₉	—	2	16	no	—
70	C₂³×C₁₉	—	4	16	no	—
71	C₂³×C₁₉	—	4	16	no	—
72	C₂³×C₁₉	—	4	8	no	—
73	C₂³×C₁₉	—	4	8	no	—
74	C₂³×C₁₉	—	4	16	no	—
75	C₂³×C₁₉	—	8	32	no	—
76	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
77	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂³×C₁₉	C₄×D₄	1	4	yes	—
79	D₄×C₁₉	—	4	64	no	—
80	D₄×C₁₉	—	4	16	no	—
81	D₄×C₁₉	—	4	16	no	—
82	C₂×C₄×C₁₉	—	2	16	no	—
83	C₂×C₄×C₁₉	—	2	4	no	—
84	C₂×C₄×C₁₉	—	2	4	no	—
85	C₂×C₄×C₁₉	#100	1	8	yes	complemented
86	C₂×C₄×C₁₉	#120	1	4	yes	—
87	C₂×C₄×C₁₉	#120	1	4	yes	—
88	C₂×C₄×C₁₉	#121	1	4	yes	—
89	C₂×C₄×C₁₉	#121	1	8	yes	—
90	C₂×C₄×C₁₉	#123	1	4	yes	—
91	C₂×C₄×C₁₉	#124	1	2	yes	—
92	C₂×C₄×C₁₉	#127	1	2	yes	—
93	C₁₉⋊C₈	—	4	8	no	—
94	C₂²×#127	D₁₉	1	1	yes	characteristic
95	C₂²×#100	—	19	4	no	—
96	#1728	—	19	2	no	—
97	C₂²×C₁₉	—	2	8	no	—
98	C₂²×C₁₉	—	2	4	no	—
99	C₂²×C₁₉	—	4	8	no	—
100	C₂²×C₁₉	—	4	16	no	—
101	C₂²×C₁₉	—	8	16	no	—
102	C₂²×C₁₉	—	8	16	no	—
103	C₂²×C₁₉	—	8	16	no	—
104	C₂²×C₁₉	#379	1	1	yes	characteristic
105	C₂²×C₁₉	#386	1	4	yes	—
106	C₂²×C₁₉	#390	1	2	yes	—
107	C₂²×C₁₉	C₂×#100	1	4	yes	—
108	C₄×C₁₉	—	2	8	no	—
109	C₄×C₁₉	#392	1	4	yes	—
110	C₄×C₁₉	#394	1	4	yes	—
111	C₂³×D₄	Dic₁₉	1	4	yes	—
112	C₂³×D₄	C₂×D₁₉	1	2	yes	—
113	C₂²×M₁₆	—	19	4	no	—
114	C₂×#127	—	2	8	no	—
115	C₂×#127	—	2	4	no	—
116	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
117	C₂×#100	—	38	16	no	—
118	C₂×#100	—	38	8	no	—
119	#336	—	38	4	no	—
120	C₂×C₁₉	—	2	4	no	—
121	C₂×C₁₉	—	8	8	no	—
122	C₂×C₁₉	#1438	1	1	yes	characteristic
123	C₂×C₁₉	#1783	1	2	yes	—
124	C₂×C₁₉	#1965	1	4	yes	—
125	C₂⁵	C₂×Dic₁₉	1	4	yes	—
126	C₂²×D₄	—	2	16	no	—
127	C₂²×D₄	—	2	8	no	—
128	C₂²×D₄	—	2	8	no	—
129	C₂²×D₄	—	2	8	no	—
130	C₂²×D₄	—	2	4	no	—
131	C₂²×D₄	—	2	4	no	—
132	C₂²×D₄	—	4	16	no	—
133	C₂²×D₄	C₂²⋊D₁₉	1	8	yes	—
134	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
135	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
136	C₂×M₁₆	—	19	8	no	—
137	C₂×M₁₆	—	38	4	no	—
138	C₂×M₁₆	—	38	8	no	—
139	C₂×M₁₆	—	38	8	no	—
140	C₂²×C₈	—	38	4	no	—
141	#127	—	2	32	no	—
142	C₂×C₄²	—	2	4	no	—
143	C₂×C₄²	C₂²⋊D₁₉	1	4	yes	—
144	#100	—	38	32	no	—
145	C₁₉	#10981	1	1	yes	characteristic, complemented, Sylow
146	C₂⁴	—	2	4	no	—
147	C₂⁴	—	2	4	no	—
148	C₂⁴	—	2	16	no	—
149	C₂⁴	—	4	16	no	—
150	C₂⁴	C₂²⋊Dic₁₉	1	8	yes	—
151	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
152	C₂×D₄	—	2	32	no	—
153	C₂×D₄	—	2	8	no	—
154	C₂×D₄	—	2	8	no	—
155	C₂×D₄	—	2	16	no	—
156	C₂×D₄	—	2	16	no	—
157	C₂×D₄	—	4	64	no	—
158	C₂×D₄	—	4	16	no	—
159	C₂×D₄	—	4	4	no	—
160	C₂×D₄	—	4	4	no	—
161	C₂×D₄	—	4	4	no	—
162	C₂×D₄	—	4	8	no	—
163	C₂×D₄	—	4	8	no	—
164	C₂×D₄	—	4	4	no	—
165	C₂×D₄	—	4	16	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
169	C₂²×C₄	D₄×D₁₉	1	4	yes	—
170	C₂²×C₄	#64543	1	4	yes	—
171	C₂²×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
173	M₁₆	—	38	16	no	—
174	M₁₆	—	76	8	no	—
175	C₂×C₈	—	38	8	no	—
176	C₂×C₈	—	76	4	no	—
177	C₂×C₈	—	76	4	no	—
178	C₄²	—	2	8	no	—
179	C₂³	—	2	4	no	—
180	C₂³	—	2	8	no	—
181	C₂³	—	2	16	no	—
182	C₂³	—	4	16	no	—
183	C₂³	—	4	16	no	—
184	C₂³	—	4	8	no	—
185	C₂³	—	4	8	no	—
186	C₂³	—	4	16	no	—
187	C₂³	—	8	32	no	—
188	C₂³	D₄×Dic₁₉	1	4	yes	—
189	C₂³	C₂×C₂²⋊Dic₁₉	1	2	yes	—
190	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
191	D₄	—	4	64	no	—
192	D₄	—	4	16	no	—
193	D₄	—	4	16	no	—
194	C₂×C₄	—	2	16	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	#10597290	1	8	yes	complemented
198	C₂×C₄	#10597381	1	4	yes	—
199	C₂×C₄	#10597382	1	2	yes	—
200	C₂×C₄	#10597383	1	4	yes	—
201	C₂×C₄	#10597384	1	4	yes	—
202	C₂×C₄	#10597385	1	8	yes	—
203	C₂×C₄	#10597386	1	2	yes	—
204	C₂×C₄	#10597399	1	4	yes	—
205	C₈	—	76	8	no	—
206	C₂²	—	2	8	no	—
207	C₂²	—	2	4	no	—
208	C₂²	—	4	8	no	—
209	C₂²	—	4	16	no	—
210	C₂²	—	8	16	no	—
211	C₂²	—	8	16	no	—
212	C₂²	—	8	16	no	—
213	C₂²	#11926400	1	1	yes	characteristic
214	C₂²	#11926424	1	4	yes	—
215	C₂²	#11926447	1	2	yes	—
216	C₂²	C₂×#10597290	1	4	yes	—
217	C₄	—	2	8	no	—
218	C₄	#11926452	1	4	yes	—
219	C₄	#11926458	1	4	yes	—
220	C₂	—	2	4	no	—
221	C₂	—	8	8	no	—
222	C₂	#14561876	1	1	yes	characteristic
223	C₂	#14563556	1	2	yes	—
224	C₂	#14564476	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10597290

C₂

yes

maximal, complemented

#14563329

C₂

yes

maximal, complemented

C₂²×C₁₉×#127

C₂

yes

maximal, characteristic

C₂²×#64520

C₂²

yes

—

C₂×#10597290

—

C₂×#10597290

—

#11926299

—

C₂³×D₄×C₁₉

C₄

yes

—

C₂³×D₄×C₁₉

C₂²

yes

—

C₂×C₁₉×#127

—

C₂×C₁₉×#127

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂⁵×C₁₉

C₂×C₄

yes

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₁₉×#127

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

—

—

—

D₄

yes

complemented

C₂²×C₁₉⋊C₈

—

#10597290

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₄²×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10981

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₄×D₄

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

complemented

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#127

yes

—

C₁₉⋊C₈

—

C₂²×#127

D₁₉

yes

characteristic

C₂²×#100

—

#1728

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

#379

yes

characteristic

105

C₂²×C₁₉

#386

yes

—

106

C₂²×C₁₉

#390

yes

—

107

C₂²×C₁₉

C₂×#100

yes

—

108

C₄×C₁₉

—

109

C₄×C₁₉

#392

yes

—

110

C₄×C₁₉

#394

yes

—

111

C₂³×D₄

Dic₁₉

yes

—

112

C₂³×D₄

C₂×D₁₉

yes

—

113

C₂²×M₁₆

—

114

C₂×#127

—

115

C₂×#127

—

116

C₂²×C₄²

C₂×D₁₉

yes

characteristic

117

C₂×#100

—

118

C₂×#100

—

119

#336

—

120

C₂×C₁₉

—

121

C₂×C₁₉

—

122

C₂×C₁₉

#1438

yes

characteristic

123

C₂×C₁₉

#1783

yes

—

124

C₂×C₁₉

#1965

yes

—

125

C₂⁵

C₂×Dic₁₉

yes

—

126

C₂²×D₄

—

127

C₂²×D₄

—

128

C₂²×D₄

—

129

C₂²×D₄

—

130

C₂²×D₄

—

131

C₂²×D₄

—

132

C₂²×D₄

—

133

C₂²×D₄

C₂²⋊D₁₉

yes

—

134

C₂³×C₄

C₂×Dic₁₉

yes

—

135

C₂³×C₄

C₂²×D₁₉

yes

characteristic

136

C₂×M₁₆

—

137

C₂×M₁₆

—

138

C₂×M₁₆

—

139

C₂×M₁₆

—

140

C₂²×C₈

—

141

#127

—

142

C₂×C₄²

—

143

C₂×C₄²

C₂²⋊D₁₉

yes

—

144

#100

—

145

C₁₉

#10981

yes

characteristic, complemented, Sylow

146

C₂⁴

—

147

C₂⁴

—

148

C₂⁴

—

149

C₂⁴

—

150

C₂⁴

C₂²⋊Dic₁₉

yes

—

151

C₂⁴

C₂²×Dic₁₉

yes

characteristic

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

169

C₂²×C₄

D₄×D₁₉

yes

—

170

C₂²×C₄

#64543

yes

—

171

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

173

M₁₆

—

174

M₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄²

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

D₄×Dic₁₉

yes

—

189

C₂³

C₂×C₂²⋊Dic₁₉

yes

—

190

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

191

D₄

—

192

D₄

—

193

D₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

#10597290

yes

complemented

198

C₂×C₄

#10597381

yes

—

199

C₂×C₄

#10597382

yes

—

200

C₂×C₄

#10597383

yes

—

201

C₂×C₄

#10597384

yes

—

202

C₂×C₄

#10597385

yes

—

203

C₂×C₄

#10597386

yes

—

204

C₂×C₄

#10597399

yes

—

205

C₈

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

#11926400

yes

characteristic

214

C₂²

#11926424

yes

—

215

C₂²

#11926447

yes

—

216

C₂²

C₂×#10597290

yes

—

217

C₄

—

218

C₄

#11926452

yes

—

219

C₄

#11926458

yes

—

220

C₂

—

221

C₂

—

222

C₂

#14561876

yes

characteristic

223

C₂

#14563556

yes

—

224

C₂

#14564476

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₂²×C₁₉×#127	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#127	D₁₉
hypocenter	C₁₉	#10981
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂⁴×C₁₉

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₁₉

Fitting, prime radical

C₂²×C₁₉×#127

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂³×C₄×C₁₉

C₂³

hypercenter

C₂²×#127

D₁₉

hypocenter

C₁₉

#10981

LCS

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂²×#127

N	H ≅ G/N	type
1. C₂²×#10597290	C₂	semidirect
2. #14563329	C₂	semidirect
30. C₂×#64520	D₄	semidirect
85. C₂×C₄×C₁₉	#100	semidirect
145. C₁₉	#10981	semidirect
197. C₂×C₄	#10597290	semidirect

H ≅ G/N

type

1. C₂²×#10597290

C₂

semidirect

2. #14563329

C₂

semidirect

30. C₂×#64520

D₄

semidirect

85. C₂×C₄×C₁₉

#100

semidirect

145. C₁₉

#10981

semidirect

197. C₂×C₄

#10597290

semidirect

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

subgroup	index
C₂²×#10597290	2
#14563329	2
C₂²×C₁₉×#127	2
#10981	19

subgroup

index

C₂²×#10597290

#14563329

C₂²×C₁₉×#127

#10981

Subgroups — #18089104

Conjugacy classes of subgroups

Complements

Maximal subgroups