Group #28500316 — subgroups

Subgroups — #28500316

Order 15104.

236 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 95 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	#21425894	C₂	1	1	yes	maximal, characteristic
2	#21425850	C₂	1	1	yes	maximal, characteristic
3	C₈×#11745659	C₂	1	1	yes	maximal, characteristic
4	#21422165	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422160	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422159	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1370	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14273666	—	2	1	no	—
9	#16837453	C₄	1	1	yes	characteristic
10	C₄×#11745659	C₄	1	1	yes	characteristic
11	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
12	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
14	Dic₅₉⋊C₁₆	—	2	1	no	—
15	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
16	C₁₆×Dic₅₉	—	2	1	no	—
17	#16837124	C₄	1	1	yes	characteristic
18	#16837123	C₄	1	1	yes	characteristic
19	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₅₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₅₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₈²×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#11745659	—	2	1	no	—
24	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
25	C₂×C₈×D₅₉	Q₈	1	1	yes	characteristic
26	C₄²×D₅₉	C₂×C₄	1	1	yes	characteristic
27	#14273666	—	4	2	no	—
28	C₂×C₅₉⋊C₁₆	—	2	1	no	—
29	C₂×C₅₉⋊C₁₆	—	2	1	no	—
30	Dic₅₉⋊C₈	C₈	1	1	yes	characteristic
31	Dic₅₉⋊C₈	C₈	1	1	yes	characteristic
32	(C₂×D₅₉)⋊C₈	C₈	1	1	yes	characteristic
33	(C₂×D₅₉)⋊C₈	C₈	1	1	yes	characteristic
34	#14273637	—	2	1	no	—
35	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₅₉	D₄	1	1	yes	characteristic
39	C₈×Dic₅₉	Q₈	1	1	yes	characteristic
40	C₂×C₁₆×C₅₉	—	2	1	no	—
41	C₂×C₁₆×C₅₉	—	2	1	no	—
42	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₅₉	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
47	C₂×C₄×D₅₉	M₁₆	1	1	yes	characteristic
48	C₂×C₈×C₅₉	—	2	1	no	—
49	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
50	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
51	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
53	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
54	C₄×Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
55	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
56	C₄×Dic₅₉	M₁₆	1	1	yes	characteristic
57	C₂×C₅₉⋊C₈	—	2	1	no	—
58	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
61	C₂×C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
62	#11745659	—	2	4	no	—
63	C₈×D₅₉	—	2	1	no	—
64	C₈×D₅₉	—	2	1	no	—
65	C₈×D₅₉	—	4	1	no	—
66	C₁₆×C₅₉	—	4	1	no	—
67	C₁₆×C₅₉	—	4	1	no	—
68	C₅₉⋊C₁₆	—	4	1	no	—
69	C₅₉⋊C₁₆	—	4	1	no	—
70	C₂²×D₅₉	C₄⋊C₈	1	1	yes	characteristic
71	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
74	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
75	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
76	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
77	C₄×D₅₉	—	2	1	no	—
78	C₄×D₅₉	—	2	1	no	—
79	C₄×D₅₉	—	2	1	no	—
80	C₄×D₅₉	—	2	1	no	—
81	C₄×D₅₉	—	2	2	no	—
82	C₈×C₅₉	—	2	2	no	—
83	C₈×C₅₉	—	2	1	no	—
84	C₈×C₅₉	—	2	1	no	—
85	C₈×C₅₉	—	2	1	no	—
86	C₈×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₈×C₅₉	#137	1	1	yes	characteristic
88	C₅₉⋊C₈	—	2	2	no	—
89	C₅₉⋊C₈	—	2	1	no	—
90	C₅₉⋊C₈	—	2	1	no	—
91	C₅₉⋊C₈	—	2	1	no	—
92	C₅₉⋊C₈	—	2	1	no	—
93	#12018	—	59	1	no	maximal, Sylow
94	C₂²×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
95	C₂×D₅₉	—	2	1	no	—
96	C₂×D₅₉	—	2	1	no	—
97	C₂×D₅₉	—	2	1	no	—
98	C₄×C₅₉	—	2	1	no	—
99	C₄×C₅₉	#428	1	1	yes	characteristic
100	C₄×C₅₉	#430	1	1	yes	characteristic
101	C₄×C₅₉	#504	1	1	yes	characteristic
102	C₄×C₅₉	#504	1	1	yes	characteristic
103	Dic₅₉	—	2	1	no	—
104	Dic₅₉	—	2	1	no	—
105	Dic₅₉	#364	1	2	yes	—
106	#2162	—	59	1	no	—
107	#2150	—	59	1	no	—
108	C₈×M₁₆	—	59	1	no	—
109	#1370	—	59	1	no	—
110	#1370	D₅₉	1	1	yes	characteristic, complemented
111	#1367	—	59	1	no	—
112	#1367	—	59	1	no	—
113	C₂×C₅₉	#1565	1	1	yes	characteristic
114	C₂×C₅₉	#2151	1	1	yes	characteristic
115	C₂×C₅₉	C₂×#364	1	1	yes	characteristic
116	D₅₉	—	4	1	no	—
117	C₂×M₃₂	—	118	1	no	—
118	#431	—	59	1	no	—
119	C₄×M₁₆	—	59	1	no	—
120	C₂×C₄×C₈	—	59	1	no	—
121	C₄⋊C₁₆	—	59	1	no	—
122	C₄⋊C₁₆	—	59	1	no	—
123	C₄⋊C₁₆	—	118	1	no	—
124	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
125	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
126	C₂²⋊C₁₆	—	118	1	no	—
127	C₄×C₁₆	—	118	1	no	—
128	#322	—	59	1	no	—
129	#322	—	59	1	no	—
130	C₈²	—	59	1	no	—
131	C₈²	C₂×D₅₉	1	1	yes	characteristic
132	C₅₉	#12018	1	1	yes	characteristic, complemented, Sylow
133	C₂×M₁₆	—	118	1	no	—
134	C₂²×C₈	—	59	1	no	—
135	C₂²×C₈	—	59	1	no	—
136	C₂×C₄²	—	59	1	no	—
137	M₃₂	—	236	2	no	—
138	C₂×C₁₆	—	2	1	no	—
139	C₂×C₁₆	—	2	1	no	—
140	C₂×C₁₆	—	118	1	no	—
141	C₂×C₁₆	—	118	1	no	—
142	C₄⋊C₈	—	59	1	no	—
143	C₄⋊C₈	—	59	1	no	—
144	C₂²⋊C₈	—	59	1	no	—
145	C₂²⋊C₈	—	59	1	no	—
146	#97	—	118	1	no	—
147	C₄×C₈	—	59	1	no	—
148	C₄×C₈	—	59	1	no	—
149	C₄×C₈	—	59	1	no	—
150	C₄×C₈	—	59	1	no	—
151	C₄×C₈	—	59	1	no	—
152	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
153	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
154	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
155	C₂²×C₄	—	59	1	no	—
156	C₂²×C₄	—	59	1	no	—
157	C₂²×C₄	—	59	1	no	—
158	M₁₆	—	118	4	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	59	1	no	—
161	C₂×C₈	—	59	1	no	—
162	C₂×C₈	—	59	1	no	—
163	C₂×C₈	—	59	1	no	—
164	C₂×C₈	—	118	1	no	—
165	C₂×C₈	—	118	1	no	—
166	C₂×C₈	—	118	1	no	—
167	C₂×C₈	—	236	1	no	—
168	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
169	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
170	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
171	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
172	C₄²	—	59	1	no	—
173	C₄²	—	59	1	no	—
174	C₄²	—	59	1	no	—
175	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
176	C₁₆	—	4	1	no	—
177	C₁₆	—	4	1	no	—
178	C₁₆	—	236	1	no	—
179	C₁₆	—	236	1	no	—
180	C₂³	—	59	1	no	—
181	C₂×C₄	—	59	1	no	—
182	C₂×C₄	—	59	1	no	—
183	C₂×C₄	—	59	1	no	—
184	C₂×C₄	—	118	2	no	—
185	C₂×C₄	—	118	1	no	—
186	C₂×C₄	—	118	1	no	—
187	C₂×C₄	—	118	1	no	—
188	C₂×C₄	—	118	1	no	—
189	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
190	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
191	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
192	C₈	—	2	2	no	—
193	C₈	—	2	1	no	—
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	118	2	no	—
197	C₈	—	118	1	no	—
198	C₈	—	118	1	no	—
199	C₈	—	118	1	no	—
200	C₈	—	118	1	no	—
201	C₈	#14273751	1	1	yes	characteristic
202	C₈	#14273759	1	1	yes	characteristic
203	C₂²	—	118	1	no	—
204	C₂²	—	118	1	no	—
205	C₂²	—	118	1	no	—
206	C₂²	C₄⋊C₈×D₅₉	1	1	yes	characteristic
207	C₄	—	2	1	no	—
208	C₄	—	59	2	no	—
209	C₄	—	118	1	no	—
210	C₄	—	118	1	no	—
211	C₄	#16837443	1	1	yes	characteristic
212	C₄	#16837449	1	1	yes	characteristic
213	C₄	#16837818	1	1	yes	characteristic
214	C₄	#16837820	1	1	yes	characteristic
215	C₂	—	236	1	no	—
216	C₂	#21422847	1	1	yes	characteristic
217	C₂	#21425853	1	1	yes	characteristic
218	C₂	#364×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425894

C₂

yes

maximal, characteristic

#21425850

C₂

yes

maximal, characteristic

C₈×#11745659

C₂

yes

maximal, characteristic

#21422165

C₂

yes

maximal, characteristic, complemented

#21422160

C₂

yes

maximal, characteristic, complemented

#21422159

C₂

yes

maximal, characteristic, complemented

C₅₉×#1370

C₂

yes

maximal, characteristic, complemented

C₂×#14273666

—

#16837453

C₄

yes

characteristic

C₄×#11745659

C₄

yes

characteristic

C₄×C₈×D₅₉

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂²

yes

characteristic

Dic₅₉⋊C₁₆

—

(C₂×D₅₉)⋊C₁₆

—

C₁₆×Dic₅₉

—

#16837124

C₄

yes

characteristic

#16837123

C₄

yes

characteristic

C₈×C₅₉⋊C₈

C₂²

yes

characteristic

C₅₉×C₄⋊C₁₆

C₂²

yes

characteristic

C₅₉×C₄⋊C₁₆

C₂²

yes

characteristic

C₈²×C₅₉

C₂²

yes

characteristic

C₂×#11745659

—

C₂×C₈×D₅₉

D₄

yes

characteristic

C₂×C₈×D₅₉

Q₈

yes

characteristic

C₄²×D₅₉

C₂×C₄

yes

characteristic

#14273666

—

C₂×C₅₉⋊C₁₆

—

C₂×C₅₉⋊C₁₆

—

Dic₅₉⋊C₈

C₈

yes

characteristic

Dic₅₉⋊C₈

C₈

yes

characteristic

(C₂×D₅₉)⋊C₈

C₈

yes

characteristic

(C₂×D₅₉)⋊C₈

C₈

yes

characteristic

#14273637

—

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₅₉

D₄

yes

characteristic

C₈×Dic₅₉

Q₈

yes

characteristic

C₂×C₁₆×C₅₉

—

C₂×C₁₆×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₄×D₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×D₅₉

C₂×C₈

yes

characteristic

C₂×C₄×D₅₉

M₁₆

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₈

yes

characteristic

C₂×C₈×C₅₉

C₂×C₈

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×Q₈

yes

characteristic

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄×Dic₅₉

C₄⋊C₄

yes

characteristic

C₄×Dic₅₉

C₂×C₈

yes

characteristic

C₄×Dic₅₉

M₁₆

yes

characteristic

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₈

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₈

yes

characteristic

#11745659

—

C₈×D₅₉

—

C₈×D₅₉

—

C₈×D₅₉

—

C₁₆×C₅₉

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×M₁₆

yes

characteristic

C₂×Dic₅₉

C₄⋊C₈

yes

characteristic

C₂×Dic₅₉

C₄⋊C₈

yes

characteristic

C₂×Dic₅₉

C₄⋊C₈

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

yes

C₈×C₅₉

yes

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

#12018

—

maximal, Sylow

C₂²×C₅₉

C₂×C₄⋊C₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#428

yes

characteristic

100

C₄×C₅₉

#430

yes

characteristic

101

C₄×C₅₉

#504

yes

characteristic

102

C₄×C₅₉

#504

yes

characteristic

103

Dic₅₉

—

104

Dic₅₉

—

105

Dic₅₉

#364

yes

—

106

#2162

—

107

#2150

—

108

C₈×M₁₆

—

109

#1370

—

110

#1370

D₅₉

yes

characteristic, complemented

111

#1367

—

112

#1367

—

113

C₂×C₅₉

#1565

yes

characteristic

114

C₂×C₅₉

#2151

yes

characteristic

115

C₂×C₅₉

C₂×#364

yes

characteristic

116

D₅₉

—

117

C₂×M₃₂

—

118

—

118

#431

—

119

C₄×M₁₆

—

120

C₂×C₄×C₈

—

121

C₄⋊C₁₆

—

122

C₄⋊C₁₆

—

123

C₄⋊C₁₆

—

118

—

124

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

125

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

126

C₂²⋊C₁₆

—

118

—

127

C₄×C₁₆

—

118

—

128

#322

—

129

#322

—

130

C₈²

—

131

C₈²

C₂×D₅₉

yes

characteristic

132

C₅₉

#12018

yes

characteristic, complemented, Sylow

133

C₂×M₁₆

—

118

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂×C₄²

—

137

M₃₂

—

236

—

138

C₂×C₁₆

—

139

C₂×C₁₆

—

140

C₂×C₁₆

—

118

—

141

C₂×C₁₆

—

118

—

142

C₄⋊C₈

—

143

C₄⋊C₈

—

144

C₂²⋊C₈

—

145

C₂²⋊C₈

—

146

#97

—

118

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

C₄×D₅₉

yes

characteristic

153

C₄×C₈

C₄×D₅₉

yes

characteristic

154

C₄×C₈

C₂²×D₅₉

yes

characteristic

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

M₁₆

—

118

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

118

—

165

C₂×C₈

—

118

—

166

C₂×C₈

—

118

—

167

C₂×C₈

—

236

—

168

C₂×C₈

C₈×D₅₉

yes

characteristic

169

C₂×C₈

C₈×D₅₉

yes

characteristic

170

C₂×C₈

D₄×D₅₉

yes

characteristic

171

C₂×C₈

Q₈×D₅₉

yes

characteristic

172

C₄²

—

173

C₄²

—

174

C₄²

—

175

C₄²

C₂×C₄×D₅₉

yes

characteristic

176

C₁₆

—

177

C₁₆

—

178

C₁₆

—

236

—

179

C₁₆

—

236

—

180

C₂³

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

118

—

185

C₂×C₄

—

118

—

186

C₂×C₄

—

118

—

187

C₂×C₄

—

118

—

188

C₂×C₄

—

118

—

189

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

190

C₂×C₄

C₂×C₈×D₅₉

yes

characteristic

191

C₂×C₄

M₁₆×D₅₉

yes

characteristic

192

C₈

—

193

C₈

—

194

C₈

—

195

C₈

—

196

C₈

—

118

—

197

C₈

—

118

—

198

C₈

—

118

—

199

C₈

—

118

—

200

C₈

—

118

—

201

C₈

#14273751

yes

characteristic

202

C₈

#14273759

yes

characteristic

203

C₂²

—

118

—

204

C₂²

—

118

—

205

C₂²

—

118

—

206

C₂²

C₄⋊C₈×D₅₉

yes

characteristic

207

C₄

—

208

C₄

—

209

C₄

—

118

—

210

C₄

—

118

—

211

C₄

#16837443

yes

characteristic

212

C₄

#16837449

yes

characteristic

213

C₄

#16837818

yes

characteristic

214

C₄

#16837820

yes

characteristic

215

C₂

—

236

—

216

C₂

#21422847

yes

characteristic

217

C₂

#21425853

yes

characteristic

218

C₂

#364×D₅₉

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₅₉
Fitting	C₅₉×#1370	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₈
prime radical	C₂²×D₅₉	C₄⋊C₈
cosocle	C₄×C₈×C₅₉	C₂³
hypercenter	#1370	D₅₉
hypocenter	C₅₉	#12018
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₅₉

Fitting

C₅₉×#1370

C₂

socle

C₂²×C₅₉

C₂×C₄⋊C₈

prime radical

C₂²×D₅₉

C₄⋊C₈

cosocle

C₄×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
4. #21422165	C₂	semidirect
5. #21422160	C₂	semidirect
6. #21422159	C₂	semidirect
7. C₅₉×#1370	C₂	semidirect
110. #1370	D₅₉	semidirect
132. C₅₉	#12018	semidirect

H ≅ G/N

type

4. #21422165

C₂

semidirect

5. #21422160

C₂

semidirect

6. #21422159

C₂

semidirect

7. C₅₉×#1370

C₂

semidirect

110. #1370

D₅₉

semidirect

132. C₅₉

#12018

semidirect

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

subgroup	index
#21425894	2
#21425850	2
C₈×#11745659	2
#21422165	2
#21422160	2
#21422159	2
C₅₉×#1370	2
#12018	59

subgroup

index

C₅₉×#1370

Subgroups — #28500316

Conjugacy classes of subgroups

Complements

Maximal subgroups