Group #28500294 — subgroups

Subgroups — #28500294

Order 15104.

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

normal subgroups only

This group has 220 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	#21425898	C₂	1	1	yes	maximal, characteristic
2	#21425894	C₂	1	1	yes	maximal, characteristic
3	#21422378	C₂	1	1	yes	maximal, characteristic
4	#21422165	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422165	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1367	C₂	1	1	yes	maximal, characteristic, complemented
8	#16837453	C₄	1	1	yes	characteristic
9	#16837453	C₄	1	1	yes	characteristic
10	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
11	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
12	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
13	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
14	(C₂×D₅₉)⋊C₁₆	—	2	1	no	—
15	#16837177	—	2	1	no	—
16	C₁₆×Dic₅₉	—	2	1	no	—
17	#16837124	C₄	1	1	yes	characteristic
18	#16837124	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×C₈×D₅₉	D₄	1	1	yes	characteristic
24	C₂×C₈×D₅₉	Q₈	1	1	yes	characteristic
25	C₄²×D₅₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₅₉⋊C₁₆	—	2	1	no	—
27	C₂×C₅₉⋊C₁₆	—	2	1	no	—
28	Dic₅₉⋊C₈	—	2	1	no	—
29	Dic₅₉⋊C₈	C₈	1	1	yes	characteristic
30	Dic₅₉⋊C₈	C₈	1	1	yes	characteristic
31	(C₂×D₅₉)⋊C₈	—	2	1	no	—
32	(C₂×D₅₉)⋊C₈	C₈	1	1	yes	characteristic
33	(C₂×D₅₉)⋊C₈	C₈	1	1	yes	characteristic
34	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₈×Dic₅₉	D₄	1	1	yes	characteristic
38	C₈×Dic₅₉	Q₈	1	1	yes	characteristic
39	C₂×C₁₆×C₅₉	—	2	1	no	—
40	C₂×C₁₆×C₅₉	—	2	1	no	—
41	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×C₄×D₅₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×D₅₉	M₁₆	1	1	yes	characteristic
47	C₂×C₈×C₅₉	—	2	1	no	—
48	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
49	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
50	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
52	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
53	C₄×Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
54	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
55	C₄×Dic₅₉	M₁₆	1	1	yes	characteristic
56	C₂×C₅₉⋊C₈	—	2	1	no	—
57	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
60	C₂×C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
61	C₈×D₅₉	—	2	1	no	—
62	C₈×D₅₉	—	2	1	no	—
63	C₈×D₅₉	—	2	2	no	—
64	C₁₆×C₅₉	—	4	1	no	—
65	C₁₆×C₅₉	—	4	1	no	—
66	C₅₉⋊C₁₆	—	4	1	no	—
67	C₅₉⋊C₁₆	—	4	1	no	—
68	C₂²×D₅₉	C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
72	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
73	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
74	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
75	C₄×D₅₉	—	2	1	no	—
76	C₄×D₅₉	—	2	1	no	—
77	C₄×D₅₉	—	2	1	no	—
78	C₄×D₅₉	—	2	1	no	—
79	C₄×D₅₉	—	4	1	no	—
80	C₈×C₅₉	—	2	1	no	—
81	C₈×C₅₉	—	2	1	no	—
82	C₈×C₅₉	—	2	1	no	—
83	C₈×C₅₉	—	4	1	no	—
84	C₈×C₅₉	#135	1	1	yes	characteristic
85	C₈×C₅₉	#135	1	1	yes	characteristic
86	C₅₉⋊C₈	—	2	1	no	—
87	C₅₉⋊C₈	—	2	1	no	—
88	C₅₉⋊C₈	—	2	1	no	—
89	C₅₉⋊C₈	—	4	1	no	—
90	C₅₉⋊C₈	#108	1	2	yes	—
91	#12014	—	59	1	no	maximal, Sylow
92	C₂²×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
93	C₂×D₅₉	—	2	1	no	—
94	C₂×D₅₉	—	2	1	no	—
95	C₂×D₅₉	—	2	1	no	—
96	C₄×C₅₉	—	2	1	no	—
97	C₄×C₅₉	#427	1	1	yes	characteristic
98	C₄×C₅₉	C₂×#108	1	1	yes	characteristic
99	C₄×C₅₉	#504	1	1	yes	characteristic
100	C₄×C₅₉	#504	1	1	yes	characteristic
101	Dic₅₉	—	2	1	no	—
102	Dic₅₉	—	2	1	no	—
103	Dic₅₉	—	2	1	no	—
104	#2163	—	59	1	no	—
105	#2162	—	59	1	no	—
106	#1450	—	59	1	no	—
107	#1370	—	59	1	no	—
108	#1370	—	59	1	no	—
109	#1367	—	59	1	no	—
110	#1367	D₅₉	1	1	yes	characteristic, complemented
111	C₂×C₅₉	#1564	1	1	yes	characteristic
112	C₂×C₅₉	#2151	1	1	yes	characteristic
113	C₂×C₅₉	#2153	1	1	yes	characteristic
114	D₅₉	—	4	1	no	—
115	#431	—	59	1	no	—
116	#431	—	59	1	no	—
117	C₂×C₄×C₈	—	59	1	no	—
118	C₄⋊C₁₆	—	59	1	no	—
119	C₄⋊C₁₆	—	59	1	no	—
120	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
121	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
122	C₂²⋊C₁₆	—	118	1	no	—
123	C₂²⋊C₁₆	—	118	1	no	—
124	#346	—	118	1	no	—
125	C₄×C₁₆	—	118	1	no	—
126	#322	—	59	1	no	—
127	#322	—	59	1	no	—
128	C₈²	—	59	1	no	—
129	C₈²	C₂×D₅₉	1	1	yes	characteristic
130	C₅₉	#12014	1	1	yes	characteristic, complemented, Sylow
131	C₂²×C₈	—	59	1	no	—
132	C₂²×C₈	—	59	1	no	—
133	C₂×C₄²	—	59	1	no	—
134	C₂×C₁₆	—	2	1	no	—
135	C₂×C₁₆	—	2	1	no	—
136	C₂×C₁₆	—	118	1	no	—
137	C₂×C₁₆	—	118	1	no	—
138	C₄⋊C₈	—	59	1	no	—
139	C₄⋊C₈	—	59	1	no	—
140	C₄⋊C₈	—	118	1	no	—
141	C₂²⋊C₈	—	59	1	no	—
142	C₂²⋊C₈	—	59	1	no	—
143	C₂²⋊C₈	—	118	1	no	—
144	C₄×C₈	—	59	1	no	—
145	C₄×C₈	—	59	1	no	—
146	C₄×C₈	—	59	1	no	—
147	C₄×C₈	—	59	1	no	—
148	C₄×C₈	—	59	1	no	—
149	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
150	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
151	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
152	C₂²×C₄	—	59	1	no	—
153	C₂²×C₄	—	59	1	no	—
154	C₂²×C₄	—	59	1	no	—
155	C₂×C₈	—	2	1	no	—
156	C₂×C₈	—	59	1	no	—
157	C₂×C₈	—	59	1	no	—
158	C₂×C₈	—	59	1	no	—
159	C₂×C₈	—	59	1	no	—
160	C₂×C₈	—	118	2	no	—
161	C₂×C₈	—	118	1	no	—
162	C₂×C₈	—	118	1	no	—
163	C₂×C₈	—	118	1	no	—
164	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
165	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
166	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
167	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
168	C₄²	—	59	1	no	—
169	C₄²	—	59	1	no	—
170	C₄²	—	59	1	no	—
171	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
172	C₁₆	—	4	1	no	—
173	C₁₆	—	4	1	no	—
174	C₁₆	—	236	1	no	—
175	C₁₆	—	236	1	no	—
176	C₂³	—	59	1	no	—
177	C₂×C₄	—	59	1	no	—
178	C₂×C₄	—	59	1	no	—
179	C₂×C₄	—	59	1	no	—
180	C₂×C₄	—	118	1	no	—
181	C₂×C₄	—	118	1	no	—
182	C₂×C₄	—	118	1	no	—
183	C₂×C₄	—	118	1	no	—
184	C₂×C₄	—	236	1	no	—
185	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
186	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
187	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
188	C₈	—	2	1	no	—
189	C₈	—	2	1	no	—
190	C₈	—	2	1	no	—
191	C₈	—	4	1	no	—
192	C₈	—	59	2	no	—
193	C₈	—	118	1	no	—
194	C₈	—	118	1	no	—
195	C₈	—	118	1	no	—
196	C₈	—	236	1	no	—
197	C₈	#14273748	1	1	yes	characteristic
198	C₈	#14273748	1	1	yes	characteristic
199	C₂²	—	118	1	no	—
200	C₂²	—	118	1	no	—
201	C₂²	—	118	1	no	—
202	C₂²	C₄⋊C₈×D₅₉	1	1	yes	characteristic
203	C₄	—	2	1	no	—
204	C₄	—	118	1	no	—
205	C₄	—	118	1	no	—
206	C₄	—	118	1	no	—
207	C₄	#16837437	1	1	yes	characteristic
208	C₄	#108×D₅₉	1	1	yes	characteristic
209	C₄	#16837818	1	1	yes	characteristic
210	C₄	#16837820	1	1	yes	characteristic
211	C₂	—	236	1	no	—
212	C₂	#21422841	1	1	yes	characteristic
213	C₂	#21425853	1	1	yes	characteristic
214	C₂	#21425860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425898

C₂

yes

maximal, characteristic

#21425894

C₂

yes

maximal, characteristic

#21422378

C₂

yes

maximal, characteristic

#21422165

C₂

yes

maximal, characteristic, complemented

#21422165

C₂

yes

maximal, characteristic, complemented

#21422160

C₂

yes

maximal, characteristic, complemented

C₅₉×#1367

C₂

yes

maximal, characteristic, complemented

#16837453

C₄

yes

characteristic

#16837453

C₄

yes

characteristic

C₄×C₈×D₅₉

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂²

yes

characteristic

(C₂×D₅₉)⋊C₁₆

—

(C₂×D₅₉)⋊C₁₆

—

#16837177

—

C₁₆×Dic₅₉

—

#16837124

C₄

yes

characteristic

#16837124

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×C₈×D₅₉

D₄

yes

characteristic

C₂×C₈×D₅₉

Q₈

yes

characteristic

C₄²×D₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₁₆

—

C₂×C₅₉⋊C₁₆

—

Dic₅₉⋊C₈

—

Dic₅₉⋊C₈

C₈

yes

characteristic

Dic₅₉⋊C₈

C₈

yes

characteristic

(C₂×D₅₉)⋊C₈

—

(C₂×D₅₉)⋊C₈

C₈

yes

characteristic

(C₂×D₅₉)⋊C₈

C₈

yes

characteristic

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

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

#108

yes

—

#12014

—

maximal, Sylow

C₂²×C₅₉

C₂×C₄⋊C₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

100

C₄×C₅₉

#504

yes

characteristic

101

Dic₅₉

—

102

Dic₅₉

—

103

Dic₅₉

—

104

#2163

—

105

#2162

—

106

#1450

—

107

#1370

—

108

#1370

—

109

#1367

—

110

#1367

D₅₉

yes

characteristic, complemented

111

C₂×C₅₉

#1564

yes

characteristic

112

C₂×C₅₉

#2151

yes

characteristic

113

C₂×C₅₉

#2153

yes

characteristic

114

D₅₉

—

115

#431

—

116

#431

—

117

C₂×C₄×C₈

—

118

C₄⋊C₁₆

—

119

C₄⋊C₁₆

—

120

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

121

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

122

C₂²⋊C₁₆

—

118

—

123

C₂²⋊C₁₆

—

118

—

124

#346

—

118

—

125

C₄×C₁₆

—

118

—

126

#322

—

127

#322

—

128

C₈²

—

129

C₈²

C₂×D₅₉

yes

characteristic

130

C₅₉

#12014

yes

characteristic, complemented, Sylow

131

C₂²×C₈

—

132

C₂²×C₈

—

133

C₂×C₄²

—

134

C₂×C₁₆

—

135

C₂×C₁₆

—

136

C₂×C₁₆

—

118

—

137

C₂×C₁₆

—

118

—

138

C₄⋊C₈

—

139

C₄⋊C₈

—

140

C₄⋊C₈

—

118

—

141

C₂²⋊C₈

—

142

C₂²⋊C₈

—

143

C₂²⋊C₈

—

118

—

144

C₄×C₈

—

145

C₄×C₈

—

146

C₄×C₈

—

147

C₄×C₈

—

148

C₄×C₈

—

149

C₄×C₈

C₄×D₅₉

yes

characteristic

150

C₄×C₈

C₄×D₅₉

yes

characteristic

151

C₄×C₈

C₂²×D₅₉

yes

characteristic

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

118

—

161

C₂×C₈

—

118

—

162

C₂×C₈

—

118

—

163

C₂×C₈

—

118

—

164

C₂×C₈

C₈×D₅₉

yes

characteristic

165

C₂×C₈

C₈×D₅₉

yes

characteristic

166

C₂×C₈

D₄×D₅₉

yes

characteristic

167

C₂×C₈

Q₈×D₅₉

yes

characteristic

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₄²

C₂×C₄×D₅₉

yes

characteristic

172

C₁₆

—

173

C₁₆

—

174

C₁₆

—

236

—

175

C₁₆

—

236

—

176

C₂³

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

118

—

181

C₂×C₄

—

118

—

182

C₂×C₄

—

118

—

183

C₂×C₄

—

118

—

184

C₂×C₄

—

236

—

185

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

186

C₂×C₄

C₂×C₈×D₅₉

yes

characteristic

187

C₂×C₄

M₁₆×D₅₉

yes

characteristic

188

C₈

—

189

C₈

—

190

C₈

—

191

C₈

—

192

C₈

—

193

C₈

—

118

—

194

C₈

—

118

—

195

C₈

—

118

—

196

C₈

—

236

—

197

C₈

#14273748

yes

characteristic

198

C₈

#14273748

yes

characteristic

199

C₂²

—

118

—

200

C₂²

—

118

—

201

C₂²

—

118

—

202

C₂²

C₄⋊C₈×D₅₉

yes

characteristic

203

C₄

—

204

C₄

—

118

—

205

C₄

—

118

—

206

C₄

—

118

—

207

C₄

#16837437

yes

characteristic

208

C₄

#108×D₅₉

yes

characteristic

209

C₄

#16837818

yes

characteristic

210

C₄

#16837820

yes

characteristic

211

C₂

—

236

—

212

C₂

#21422841

yes

characteristic

213

C₂

#21425853

yes

characteristic

214

C₂

#21425860

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₅₉
Fitting	C₅₉×#1367	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₈
prime radical	C₂²×D₅₉	C₄⋊C₈
cosocle	C₄×C₈×C₅₉	C₂³
hypercenter	#1367	D₅₉
hypocenter	C₅₉	#12014
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1367

subgroup

G/H

center

C₂×C₈

D₄×D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₅₉

Fitting

C₅₉×#1367

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 ◁ #1367

N	H ≅ G/N	type
4. #21422165	C₂	semidirect
5. #21422165	C₂	semidirect
6. #21422160	C₂	semidirect
7. C₅₉×#1367	C₂	semidirect
110. #1367	D₅₉	semidirect
130. C₅₉	#12014	semidirect

H ≅ G/N

type

4. #21422165

C₂

semidirect

5. #21422165

C₂

semidirect

6. #21422160

C₂

semidirect

7. C₅₉×#1367

C₂

semidirect

110. #1367

D₅₉

semidirect

130. C₅₉

#12014

semidirect

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

subgroup	index
#21425898	2
#21425894	2
#21422378	2
#21422165	2
#21422160	2
C₅₉×#1367	2
#12014	59

subgroup

index

C₅₉×#1367

Subgroups — #28500294

Conjugacy classes of subgroups

Complements

Maximal subgroups