Group #28500311 — subgroups

Subgroups — #28500311

Order 15104.

232 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 99 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	#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	#16837177	—	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	C₈	1	1	yes	characteristic
24	C₂×#11745659	C₈	1	1	yes	characteristic
25	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
26	C₂×C₈×D₅₉	Q₈	1	1	yes	characteristic
27	C₄²×D₅₉	C₂×C₄	1	1	yes	characteristic
28	#14273666	—	4	2	no	—
29	C₂×C₅₉⋊C₁₆	—	2	1	no	—
30	C₂×C₅₉⋊C₁₆	—	2	1	no	—
31	Dic₅₉⋊C₈	—	2	1	no	—
32	(C₂×D₅₉)⋊C₈	—	2	1	no	—
33	#14273637	C₈	1	1	yes	characteristic
34	#14273637	C₈	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	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	2	no	—
63	#11745659	—	2	2	no	—
64	C₈×D₅₉	—	2	1	no	—
65	C₈×D₅₉	—	2	1	no	—
66	C₈×D₅₉	—	4	1	no	—
67	C₁₆×C₅₉	—	4	1	no	—
68	C₁₆×C₅₉	—	4	1	no	—
69	C₅₉⋊C₁₆	—	4	1	no	—
70	C₅₉⋊C₁₆	—	4	1	no	—
71	C₂²×D₅₉	C₄⋊C₈	1	1	yes	characteristic
72	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
75	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
76	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
77	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
78	C₄×D₅₉	—	2	1	no	—
79	C₄×D₅₉	—	2	1	no	—
80	C₄×D₅₉	—	2	1	no	—
81	C₄×D₅₉	—	2	1	no	—
82	C₄×D₅₉	—	4	1	no	—
83	C₈×C₅₉	—	2	1	no	—
84	C₈×C₅₉	—	2	1	no	—
85	C₈×C₅₉	—	4	1	no	—
86	C₈×C₅₉	M₃₂	1	2	yes	complemented
87	C₈×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₈×C₅₉	#137	1	1	yes	characteristic
89	C₅₉⋊C₈	—	2	1	no	—
90	C₅₉⋊C₈	—	2	1	no	—
91	C₅₉⋊C₈	—	2	1	no	—
92	C₅₉⋊C₈	—	4	1	no	—
93	C₅₉⋊C₈	M₃₂	1	2	yes	complemented
94	#12017	—	59	1	no	maximal, Sylow
95	C₂²×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
96	C₂×D₅₉	—	2	1	no	—
97	C₂×D₅₉	—	2	1	no	—
98	C₂×D₅₉	—	2	1	no	—
99	C₄×C₅₉	—	2	1	no	—
100	C₄×C₅₉	#428	1	1	yes	characteristic
101	C₄×C₅₉	#430	1	1	yes	characteristic
102	C₄×C₅₉	C₂×M₃₂	1	1	yes	characteristic
103	C₄×C₅₉	C₂×M₃₂	1	1	yes	characteristic
104	Dic₅₉	—	2	1	no	—
105	Dic₅₉	—	2	1	no	—
106	Dic₅₉	—	2	1	no	—
107	#2163	—	59	1	no	—
108	#2150	—	59	1	no	—
109	C₈×M₁₆	—	59	1	no	—
110	#1370	—	59	1	no	—
111	#1370	D₅₉	1	1	yes	characteristic, complemented
112	#1367	—	59	1	no	—
113	#1367	—	59	1	no	—
114	C₂×C₅₉	#1565	1	1	yes	characteristic
115	C₂×C₅₉	#2150	1	1	yes	characteristic
116	C₂×C₅₉	#2153	1	1	yes	characteristic
117	D₅₉	—	4	1	no	—
118	C₂×M₃₂	—	118	1	no	—
119	#431	—	59	1	no	—
120	C₄×M₁₆	—	59	1	no	—
121	C₂×C₄×C₈	—	59	1	no	—
122	C₄⋊C₁₆	—	59	1	no	—
123	C₄⋊C₁₆	—	59	1	no	—
124	C₄⋊C₁₆	—	118	1	no	—
125	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
126	C₄⋊C₁₆	C₂×D₅₉	1	1	yes	characteristic
127	C₂²⋊C₁₆	—	118	1	no	—
128	#346	—	118	1	no	—
129	#322	—	59	1	no	—
130	#322	—	59	1	no	—
131	C₈²	—	59	1	no	—
132	C₈²	C₂×D₅₉	1	1	yes	characteristic
133	C₅₉	#12017	1	1	yes	characteristic, complemented, Sylow
134	C₂×M₁₆	—	59	1	no	—
135	C₂×M₁₆	—	59	1	no	—
136	C₂²×C₈	—	59	1	no	—
137	C₂²×C₈	—	59	1	no	—
138	C₂×C₄²	—	59	1	no	—
139	M₃₂	—	236	2	no	—
140	C₂×C₁₆	—	2	1	no	—
141	C₂×C₁₆	—	2	1	no	—
142	C₂×C₁₆	—	118	1	no	—
143	C₂×C₁₆	—	118	1	no	—
144	C₄⋊C₈	—	118	1	no	—
145	C₂²⋊C₈	—	118	1	no	—
146	#97	—	59	1	no	—
147	#97	—	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	—	59	1	no	—
153	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
154	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
155	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
156	C₂²×C₄	—	59	1	no	—
157	C₂²×C₄	—	59	1	no	—
158	C₂²×C₄	—	59	1	no	—
159	M₁₆	—	118	2	no	—
160	M₁₆	—	118	2	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	59	1	no	—
163	C₂×C₈	—	59	1	no	—
164	C₂×C₈	—	59	1	no	—
165	C₂×C₈	—	59	1	no	—
166	C₂×C₈	—	118	1	no	—
167	C₂×C₈	—	118	1	no	—
168	C₂×C₈	—	118	1	no	—
169	C₂×C₈	—	236	1	no	—
170	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
171	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
172	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
173	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
174	C₄²	—	59	1	no	—
175	C₄²	—	59	1	no	—
176	C₄²	—	59	1	no	—
177	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
178	C₁₆	—	4	1	no	—
179	C₁₆	—	4	1	no	—
180	C₁₆	—	236	1	no	—
181	C₁₆	—	236	1	no	—
182	C₂³	—	59	1	no	—
183	C₂×C₄	—	59	1	no	—
184	C₂×C₄	—	59	1	no	—
185	C₂×C₄	—	59	1	no	—
186	C₂×C₄	—	118	1	no	—
187	C₂×C₄	—	118	1	no	—
188	C₂×C₄	—	118	1	no	—
189	C₂×C₄	—	118	1	no	—
190	C₂×C₄	—	236	1	no	—
191	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
192	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
193	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	4	1	no	—
197	C₈	—	59	2	no	—
198	C₈	—	118	1	no	—
199	C₈	—	118	1	no	—
200	C₈	—	118	1	no	—
201	C₈	—	236	1	no	—
202	C₈	#14273666	1	2	yes	complemented
203	C₈	#14273751	1	1	yes	characteristic
204	C₈	#14273759	1	1	yes	characteristic
205	C₂²	—	118	1	no	—
206	C₂²	—	118	1	no	—
207	C₂²	—	118	1	no	—
208	C₂²	C₄⋊C₈×D₅₉	1	1	yes	characteristic
209	C₄	—	2	1	no	—
210	C₄	—	118	1	no	—
211	C₄	—	118	1	no	—
212	C₄	—	118	1	no	—
213	C₄	#16837443	1	1	yes	characteristic
214	C₄	#16837449	1	1	yes	characteristic
215	C₄	M₃₂×D₅₉	1	1	yes	characteristic
216	C₄	C₂×#14273666	1	1	yes	characteristic
217	C₂	—	236	1	no	—
218	C₂	#21422847	1	1	yes	characteristic
219	C₂	#21425850	1	1	yes	characteristic
220	C₂	#21425860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425898

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

—

#16837177

—

#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

C₈

yes

characteristic

C₂×#11745659

C₈

yes

characteristic

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

—

(C₂×D₅₉)⋊C₈

—

#14273637

C₈

yes

characteristic

#14273637

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

#11745659

—

#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

M₃₂

yes

C₈×C₅₉

yes

C₈×C₅₉

yes

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

M₃₂

yes

complemented

#12017

—

maximal, Sylow

C₂²×C₅₉

C₂×C₄⋊C₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

100

C₄×C₅₉

#428

yes

characteristic

101

C₄×C₅₉

#430

yes

characteristic

102

C₄×C₅₉

C₂×M₃₂

yes

characteristic

103

C₄×C₅₉

C₂×M₃₂

yes

characteristic

104

Dic₅₉

—

105

Dic₅₉

—

106

Dic₅₉

—

107

#2163

—

108

#2150

—

109

C₈×M₁₆

—

110

#1370

—

111

#1370

D₅₉

yes

characteristic, complemented

112

#1367

—

113

#1367

—

114

C₂×C₅₉

#1565

yes

characteristic

115

C₂×C₅₉

#2150

yes

characteristic

116

C₂×C₅₉

#2153

yes

characteristic

117

D₅₉

—

118

C₂×M₃₂

—

118

—

119

#431

—

120

C₄×M₁₆

—

121

C₂×C₄×C₈

—

122

C₄⋊C₁₆

—

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

118

—

125

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

126

C₄⋊C₁₆

C₂×D₅₉

yes

characteristic

127

C₂²⋊C₁₆

—

118

—

128

#346

—

118

—

129

#322

—

130

#322

—

131

C₈²

—

132

C₈²

C₂×D₅₉

yes

characteristic

133

C₅₉

#12017

yes

characteristic, complemented, Sylow

134

C₂×M₁₆

—

135

C₂×M₁₆

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂×C₄²

—

139

M₃₂

—

236

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

C₂×C₁₆

—

118

—

143

C₂×C₁₆

—

118

—

144

C₄⋊C₈

—

118

—

145

C₂²⋊C₈

—

118

—

146

#97

—

147

#97

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₄×C₈

C₄×D₅₉

yes

characteristic

154

C₄×C₈

C₄×D₅₉

yes

characteristic

155

C₄×C₈

C₂²×D₅₉

yes

characteristic

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

M₁₆

—

118

—

160

M₁₆

—

118

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

118

—

167

C₂×C₈

—

118

—

168

C₂×C₈

—

118

—

169

C₂×C₈

—

236

—

170

C₂×C₈

C₈×D₅₉

yes

characteristic

171

C₂×C₈

C₈×D₅₉

yes

characteristic

172

C₂×C₈

D₄×D₅₉

yes

characteristic

173

C₂×C₈

Q₈×D₅₉

yes

characteristic

174

C₄²

—

175

C₄²

—

176

C₄²

—

177

C₄²

C₂×C₄×D₅₉

yes

characteristic

178

C₁₆

—

179

C₁₆

—

180

C₁₆

—

236

—

181

C₁₆

—

236

—

182

C₂³

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

118

—

187

C₂×C₄

—

118

—

188

C₂×C₄

—

118

—

189

C₂×C₄

—

118

—

190

C₂×C₄

—

236

—

191

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

192

C₂×C₄

C₂×C₈×D₅₉

yes

characteristic

193

C₂×C₄

M₁₆×D₅₉

yes

characteristic

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

—

198

C₈

—

118

—

199

C₈

—

118

—

200

C₈

—

118

—

201

C₈

—

236

—

202

C₈

#14273666

yes

complemented

203

C₈

#14273751

yes

characteristic

204

C₈

#14273759

yes

characteristic

205

C₂²

—

118

—

206

C₂²

—

118

—

207

C₂²

—

118

—

208

C₂²

C₄⋊C₈×D₅₉

yes

characteristic

209

C₄

—

210

C₄

—

118

—

211

C₄

—

118

—

212

C₄

—

118

—

213

C₄

#16837443

yes

characteristic

214

C₄

#16837449

yes

characteristic

215

C₄

M₃₂×D₅₉

yes

characteristic

216

C₄

C₂×#14273666

yes

characteristic

217

C₂

—

236

—

218

C₂

#21422847

yes

characteristic

219

C₂

#21425850

yes

characteristic

220

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×#1370	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₈
prime radical	C₂²×D₅₉	C₄⋊C₈
cosocle	C₄×C₈×C₅₉	C₂³
hypercenter	#1370	D₅₉
hypocenter	C₅₉	#12017
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
86. C₈×C₅₉	M₃₂	semidirect
93. C₅₉⋊C₈	M₃₂	semidirect
111. #1370	D₅₉	semidirect
133. C₅₉	#12017	semidirect
202. C₈	#14273666	semidirect

H ≅ G/N

type

4. #21422165

C₂

semidirect

5. #21422160

C₂

semidirect

6. #21422159

C₂

semidirect

7. C₅₉×#1370

C₂

semidirect

86. C₈×C₅₉

M₃₂

semidirect

93. C₅₉⋊C₈

M₃₂

semidirect

111. #1370

D₅₉

semidirect

133. C₅₉

#12017

semidirect

202. C₈

#14273666

semidirect

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

subgroup	index
#21425898	2
#21425850	2
C₈×#11745659	2
#21422165	2
#21422160	2
#21422159	2
C₅₉×#1370	2
#12017	59

subgroup

index

C₅₉×#1370

Subgroups — #28500311

Conjugacy classes of subgroups

Complements

Maximal subgroups