Group #28506158 — subgroups

Subgroups — #28506158

Order 15104.

454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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	#21433751	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837219	C₂	1	2	yes	maximal, complemented
3	#21424146	C₂	1	1	yes	maximal, characteristic
4	#21422211	C₂	1	2	yes	maximal, complemented
5	C₅₉×#3407	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₃₆	C₂²	1	1	yes	characteristic
7	#16837973	—	2	1	no	—
8	#16837660	C₄	1	4	yes	—
9	#16837643	—	2	2	no	—
10	C₂×#14273663	C₂²	1	2	yes	—
11	#16837440	C₂²	1	1	yes	characteristic
12	#16837412	—	2	1	no	—
13	#16837386	—	2	1	no	—
14	#16837219	—	2	4	no	—
15	C₅₉⋊#338	—	2	1	no	—
16	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#504	—	2	4	no	—
18	C₂×M₃₂×C₅₉	—	2	2	no	—
19	C₂×M₃₂×C₅₉	C₂²	1	2	yes	—
20	C₂²×Dic₁₁₈	—	2	1	no	—
21	C₂×Dic₂₃₆	—	2	2	no	—
22	C₂×Dic₂₃₆	—	2	2	no	—
23	C₂×Dic₂₃₆	—	2	1	no	—
24	C₂×Dic₂₃₆	C₂×C₄	1	2	yes	—
25	C₂×#11745664	—	2	2	no	—
26	#14273725	—	4	1	no	—
27	#14273714	—	4	1	no	—
28	#14273708	—	4	2	no	—
29	#14273706	—	2	4	no	—
30	#14273686	—	2	1	no	—
31	#14273663	—	2	2	no	—
32	#14273663	—	2	2	no	—
33	#14273661	—	2	1	no	—
34	#14273659	C₂×C₄	1	2	yes	—
35	#14273652	—	2	4	no	—
36	#14273646	—	4	1	no	—
37	#14273644	—	4	1	no	—
38	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
39	#131×C₅₉	—	2	2	no	—
40	#131×C₅₉	—	2	2	no	—
41	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₅₉	D₄	1	2	yes	—
44	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
45	M₃₂×C₅₉	—	2	4	no	—
46	M₃₂×C₅₉	—	2	2	no	—
47	M₃₂×C₅₉	D₄	1	4	yes	—
48	C₂×C₁₆×C₅₉	—	2	4	no	—
49	C₂×C₁₆×C₅₉	—	2	2	no	—
50	#41×C₅₉	—	2	2	no	—
51	#41×C₅₉	—	2	2	no	—
52	C₂×Q₈×C₅₉	D₈	1	1	yes	characteristic
53	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
54	C₂×D₄×C₅₉	SD₁₆	1	2	yes	—
55	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×Dic₅₉	—	4	1	no	—
58	C₂×Dic₁₁₈	—	2	2	no	—
59	C₂×Dic₁₁₈	—	4	2	no	—
60	C₂×Dic₁₁₈	—	4	2	no	—
61	C₂×Dic₁₁₈	—	4	1	no	—
62	M₁₆×C₅₉	—	2	2	no	—
63	M₁₆×C₅₉	—	2	4	no	—
64	C₂×C₈×C₅₉	—	2	2	no	—
65	C₂×C₈×C₅₉	—	2	2	no	—
66	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₅₉	#41	1	2	yes	—
71	C₂²⋊Dic₅₉	—	4	4	no	—
72	C₂²⋊Dic₅₉	—	4	1	no	—
73	C₄⋊Dic₅₉	—	2	2	no	—
74	Dic₅₉⋊C₄	—	4	4	no	—
75	C₄×Dic₅₉	—	4	1	no	—
76	#11745664	—	4	2	no	—
77	#11745664	—	4	2	no	—
78	C₂×C₅₉⋊C₈	—	4	2	no	—
79	Dic₂₃₆	—	2	4	no	—
80	Dic₂₃₆	—	4	1	no	—
81	Dic₂₃₆	—	4	1	no	—
82	C₁₆×C₅₉	—	2	4	no	—
83	C₂³×C₅₉	#102	1	2	yes	—
84	C₂³×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
85	Q₈×C₅₉	—	2	2	no	—
86	D₄×C₅₉	—	2	4	no	—
87	D₄×C₅₉	—	2	2	no	—
88	C₂×C₄×C₅₉	—	2	2	no	—
89	C₂×C₄×C₅₉	—	2	2	no	—
90	C₂×C₄×C₅₉	#102	1	2	yes	—
91	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₅₉	#121	1	2	yes	—
93	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₅₉	#135	1	2	yes	—
95	C₂×Dic₅₉	—	4	2	no	—
96	C₂×Dic₅₉	—	4	2	no	—
97	C₂×Dic₅₉	—	8	2	no	—
98	Dic₁₁₈	—	4	2	no	—
99	Dic₁₁₈	—	4	2	no	—
100	Dic₁₁₈	—	8	2	no	—
101	C₈×C₅₉	—	2	2	no	—
102	C₈×C₅₉	C₄×D₄	1	2	yes	—
103	C₈×C₅₉	#120	1	1	yes	characteristic
104	C₈×C₅₉	#123	1	1	yes	characteristic
105	C₅₉⋊C₈	—	8	2	no	—
106	#13078	—	59	1	no	maximal, Sylow
107	C₂²×C₅₉	—	2	2	no	—
108	C₂²×C₅₉	—	4	1	no	—
109	C₂²×C₅₉	—	4	2	no	—
110	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
111	C₂²×C₅₉	#465	1	2	yes	—
112	C₄×C₅₉	—	2	2	no	—
113	C₄×C₅₉	#386	1	1	yes	characteristic
114	C₄×C₅₉	#416	1	1	yes	characteristic
115	C₄×C₅₉	#466	1	2	yes	—
116	Dic₅₉	—	8	2	no	—
117	Dic₅₉	—	8	2	no	—
118	#3407	D₅₉	1	1	yes	characteristic
119	#3059	—	59	1	no	—
120	C₂×#362	—	59	2	no	—
121	#1813	—	59	1	no	—
122	#1389	—	59	2	no	—
123	C₂×C₅₉	—	2	1	no	—
124	C₂×C₅₉	—	2	2	no	—
125	C₂×C₅₉	—	4	2	no	—
126	C₂×C₅₉	#1893	1	1	yes	characteristic
127	C₂²×Q₁₆	—	59	1	no	—
128	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
129	#536	—	118	1	no	—
130	#504	—	2	4	no	—
131	C₂×M₃₂	—	2	2	no	—
132	C₂×M₃₂	C₂×D₅₉	1	2	yes	—
133	#470	—	59	4	no	—
134	#467	—	118	2	no	—
135	C₂×#108	—	59	2	no	—
136	#427	—	59	1	no	—
137	#419	—	118	1	no	—
138	#413	—	118	1	no	—
139	#362	—	118	4	no	—
140	#338	—	118	1	no	—
141	C₅₉	#13078	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	D₂₃₆	1	1	yes	characteristic
143	C₂²×Q₈	—	118	1	no	—
144	C₂×Q₁₆	—	59	2	no	—
145	C₂×Q₁₆	—	118	2	no	—
146	C₂×Q₁₆	—	118	2	no	—
147	C₂×Q₁₆	—	118	1	no	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	—	118	2	no	—
151	C₂×M₁₆	C₄×D₅₉	1	2	yes	—
152	C₂×M₁₆	D₂₃₆	1	1	yes	characteristic
153	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
154	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
155	C₄⋊Q₈	—	236	1	no	—
156	#124	—	236	1	no	—
157	#123	—	236	2	no	—
158	C₂²⋊Q₈	—	118	4	no	—
159	#117	—	118	1	no	—
160	M₃₂	—	2	4	no	—
161	M₃₂	—	2	2	no	—
162	M₃₂	C₂²⋊D₅₉	1	4	yes	—
163	C₂×C₁₆	—	2	4	no	—
164	C₂×C₁₆	—	2	2	no	—
165	#108	—	118	2	no	—
166	#108	—	118	2	no	—
167	#107	—	118	1	no	—
168	#106	—	59	2	no	—
169	#103	—	118	4	no	—
170	#101	—	236	1	no	—
171	#100	—	236	1	no	—
172	#41	—	2	2	no	—
173	#41	—	2	2	no	—
174	C₂×Q₈	—	118	2	no	—
175	C₂×Q₈	—	236	2	no	—
176	C₂×Q₈	—	236	2	no	—
177	C₂×Q₈	—	236	1	no	—
178	C₂×Q₈	D₄₇₂	1	1	yes	characteristic
179	C₂×D₄	#11745660	1	2	yes	—
180	C₂×D₄	D₄₇₂	1	1	yes	characteristic
181	C₂²×C₄	—	236	1	no	—
182	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
183	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
184	Q₁₆	—	118	4	no	—
185	Q₁₆	—	236	1	no	—
186	Q₁₆	—	236	1	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	2	4	no	—
189	M₁₆	—	236	2	no	—
190	M₁₆	—	236	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	236	2	no	—
194	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
195	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
196	C₂×C₈	#11745685	1	2	yes	—
197	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
198	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
199	C₄⋊C₄	—	118	2	no	—
200	C₄⋊C₄	—	236	4	no	—
201	C₂²⋊C₄	—	236	4	no	—
202	C₂²⋊C₄	—	236	1	no	—
203	C₄²	—	236	1	no	—
204	C₁₆	—	2	4	no	—
205	C₂³	#14273649	1	2	yes	—
206	C₂³	C₂×#11745660	1	1	yes	characteristic
207	Q₈	—	2	2	no	—
208	Q₈	—	472	2	no	—
209	Q₈	—	236	2	no	—
210	Q₈	—	236	2	no	—
211	D₄	—	2	4	no	—
212	D₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	472	2	no	—
216	C₂×C₄	—	236	2	no	—
217	C₂×C₄	—	236	2	no	—
218	C₂×C₄	#14273649	1	2	yes	—
219	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
220	C₂×C₄	#14273701	1	2	yes	—
221	C₂×C₄	C₂×D₄₇₂	1	1	yes	characteristic
222	C₂×C₄	#14273749	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	—	472	2	no	—
225	C₈	C₄×C₂²⋊D₅₉	1	2	yes	—
226	C₈	#14273696	1	1	yes	characteristic
227	C₈	#14273710	1	1	yes	characteristic
228	C₂²	—	2	2	no	—
229	C₂²	—	4	1	no	—
230	C₂²	—	4	2	no	—
231	C₂²	C₂×#14273649	1	1	yes	characteristic
232	C₂²	#16837631	1	2	yes	—
233	C₄	—	2	2	no	—
234	C₄	—	472	2	no	—
235	C₄	—	472	2	no	—
236	C₄	#16837281	1	1	yes	characteristic
237	C₄	#16837399	1	1	yes	characteristic
238	C₄	#16837638	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#21424524	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21433751

C₂

yes

maximal, characteristic

C₂×#16837219

C₂

yes

maximal, complemented

#21424146

C₂

yes

maximal, characteristic

#21422211

C₂

yes

maximal, complemented

C₅₉×#3407

C₂

yes

maximal, characteristic

C₂²×Dic₂₃₆

C₂²

yes

characteristic

#16837973

—

#16837660

C₄

yes

—

#16837643

—

C₂×#14273663

C₂²

yes

—

#16837440

C₂²

yes

—

—

—

C₅₉⋊#338

—

C₂×#131×C₅₉

C₂²

yes

characteristic

C₅₉×#504

—

C₂×M₃₂×C₅₉

—

C₂×M₃₂×C₅₉

C₂²

yes

—

C₂²×Dic₁₁₈

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#14273652

—

#14273646

—

#14273644

—

C₂×#41×C₅₉

D₄

yes

characteristic

#131×C₅₉

—

#131×C₅₉

—

C₂×M₁₆×C₅₉

C₂×C₄

yes

—

C₂×M₁₆×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

—

M₃₂×C₅₉

D₄

yes

—

C₂×C₁₆×C₅₉

—

C₂×C₁₆×C₅₉

—

#41×C₅₉

—

#41×C₅₉

—

C₂×Q₈×C₅₉

D₈

yes

characteristic

C₂×D₄×C₅₉

D₈

yes

characteristic

C₂×D₄×C₅₉

SD₁₆

yes

—

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₂²⋊Dic₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

C₁₆×C₅₉

—

C₂³×C₅₉

#102

yes

—

C₂³×C₅₉

C₂×SD₁₆

yes

characteristic

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

C₂×D₈

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

100

Dic₁₁₈

—

101

C₈×C₅₉

—

102

C₈×C₅₉

C₄×D₄

yes

—

103

C₈×C₅₉

#120

yes

characteristic

104

C₈×C₅₉

#123

yes

characteristic

105

C₅₉⋊C₈

—

106

#13078

—

maximal, Sylow

107

C₂²×C₅₉

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

C₂×#102

yes

characteristic

111

C₂²×C₅₉

#465

yes

—

112

C₄×C₅₉

—

113

C₄×C₅₉

#386

yes

characteristic

114

C₄×C₅₉

#416

yes

characteristic

115

C₄×C₅₉

#466

yes

—

116

Dic₅₉

—

117

Dic₅₉

—

118

#3407

D₅₉

yes

characteristic

119

#3059

—

120

C₂×#362

—

121

#1813

—

122

#1389

—

123

C₂×C₅₉

—

124

C₂×C₅₉

—

125

C₂×C₅₉

—

126

C₂×C₅₉

#1893

yes

characteristic

127

C₂²×Q₁₆

—

128

C₂×#131

C₂×D₅₉

yes

characteristic

129

#536

—

118

—

130

#504

—

131

C₂×M₃₂

—

132

C₂×M₃₂

C₂×D₅₉

yes

—

133

#470

—

134

#467

—

118

—

135

C₂×#108

—

136

#427

—

137

#419

—

118

—

138

#413

—

118

—

139

#362

—

118

—

140

#338

—

118

—

141

C₅₉

#13078

yes

characteristic, complemented, Sylow

142

C₂×#41

D₂₃₆

yes

characteristic

143

C₂²×Q₈

—

118

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

118

—

146

C₂×Q₁₆

—

118

—

147

C₂×Q₁₆

—

118

—

148

#131

—

149

#131

—

150

C₂×M₁₆

—

118

—

151

C₂×M₁₆

C₄×D₅₉

yes

—

152

C₂×M₁₆

D₂₃₆

yes

characteristic

153

C₂²×C₈

C₂²⋊D₅₉

yes

—

154

C₂²×C₈

C₂²×D₅₉

yes

characteristic

155

C₄⋊Q₈

—

236

—

156

#124

—

236

—

157

#123

—

236

—

158

C₂²⋊Q₈

—

118

—

159

#117

—

118

—

160

M₃₂

—

161

M₃₂

—

162

M₃₂

C₂²⋊D₅₉

yes

—

163

C₂×C₁₆

—

164

C₂×C₁₆

—

165

#108

—

118

—

166

#108

—

118

—

167

#107

—

118

—

168

#106

—

169

#103

—

118

—

170

#101

—

236

—

171

#100

—

236

—

172

#41

—

173

#41

—

174

C₂×Q₈

—

118

—

175

C₂×Q₈

—

236

—

176

C₂×Q₈

—

236

—

177

C₂×Q₈

—

236

—

178

C₂×Q₈

D₄₇₂

yes

characteristic

179

C₂×D₄

#11745660

yes

—

180

C₂×D₄

D₄₇₂

yes

characteristic

181

C₂²×C₄

—

236

—

182

C₂²×C₄

(C₂×D₅₉)⋊C₄

yes

—

183

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

184

Q₁₆

—

118

—

185

Q₁₆

—

236

—

186

Q₁₆

—

236

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

236

—

190

M₁₆

—

236

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

236

—

194

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

195

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

196

C₂×C₈

#11745685

yes

—

197

C₂×C₈

C₂×C₂²⋊D₅₉

yes

—

198

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

199

C₄⋊C₄

—

118

—

200

C₄⋊C₄

—

236

—

201

C₂²⋊C₄

—

236

—

202

C₂²⋊C₄

—

236

—

203

C₄²

—

236

—

204

C₁₆

—

205

C₂³

#14273649

yes

—

206

C₂³

C₂×#11745660

yes

characteristic

207

Q₈

—

208

Q₈

—

472

—

209

Q₈

—

236

—

210

Q₈

—

236

—

211

D₄

—

212

D₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

472

—

216

C₂×C₄

—

236

—

217

C₂×C₄

—

236

—

218

C₂×C₄

#14273649

yes

—

219

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

220

C₂×C₄

#14273701

yes

—

221

C₂×C₄

C₂×D₄₇₂

yes

characteristic

222

C₂×C₄

#14273749

yes

—

223

C₈

—

224

C₈

—

472

—

225

C₈

C₄×C₂²⋊D₅₉

yes

—

226

C₈

#14273696

yes

characteristic

227

C₈

#14273710

yes

characteristic

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

C₂×#14273649

yes

characteristic

232

C₂²

#16837631

yes

—

233

C₄

—

234

C₄

—

472

—

235

C₄

—

472

—

236

C₄

#16837281

yes

characteristic

237

C₄

#16837399

yes

characteristic

238

C₄

#16837638

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#21424524

yes

characteristic

	subgroup	G/H
center	C₂	#21424524
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#3407	C₂
socle	C₂×C₅₉	#1893
prime radical	C₂×#41×C₅₉	D₄
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#3407	D₅₉
hypocenter	C₅₉	#13078
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#21424524

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#3407

C₂

socle

C₂×C₅₉

#1893

prime radical

C₂×#41×C₅₉

D₄

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. C₂×#16837219	C₂	semidirect
4. #21422211	C₂	semidirect
141. C₅₉	#13078	semidirect

H ≅ G/N

type

2. C₂×#16837219

C₂

semidirect

4. #21422211

C₂

semidirect

141. C₅₉

#13078

semidirect

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

subgroup	index
#21433751	2
C₂×#16837219	2
#21424146	2
#21422211	2
C₅₉×#3407	2
#13078	59

subgroup

index

C₅₉×#3407

Subgroups — #28506158

Conjugacy classes of subgroups

Complements

Maximal subgroups