Group #28488653 — subgroups

Subgroups — #28488653

Order 15104.

498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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	#21434524	C₂	1	1	yes	maximal, characteristic
2	#21424234	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422548	C₂	1	2	yes	maximal, complemented
4	#21422548	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14273749	—	2	2	no	—
7	#16837952	C₂²	1	2	yes	—
8	#16837786	—	2	2	no	—
9	#16837782	C₄	1	1	yes	characteristic
10	#16837779	C₄	1	1	yes	characteristic
11	#16837775	C₄	1	2	yes	—
12	#16837426	C₂²	1	2	yes	—
13	#16837167	—	2	2	no	—
14	#16837131	—	2	4	no	—
15	#16837131	—	2	4	no	—
16	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₅₉×#322	—	2	2	no	—
20	C₂×#11745685	—	2	2	no	—
21	#14273749	—	4	8	no	—
22	C₂×Dic₂₃₆	—	2	2	no	—
23	C₂×#11745660	—	2	4	no	—
24	C₂×D₄₇₂	—	2	2	no	—
25	C₂×#11745664	—	2	2	no	—
26	#14273727	C₂×C₄	1	2	yes	—
27	#14273724	C₂×C₄	1	2	yes	—
28	#14273715	—	2	2	no	—
29	#14273701	—	2	2	no	—
30	#14273701	—	2	2	no	—
31	C₄×D₂₃₆	—	2	2	no	—
32	C₄×D₂₃₆	—	2	2	no	—
33	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
34	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
35	C₂²×C₈×C₅₉	—	2	1	no	—
36	C₂²×C₈×C₅₉	—	2	1	no	—
37	C₂²×C₈×C₅₉	D₄	1	2	yes	—
38	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
39	C₄×C₈×C₅₉	—	2	1	no	—
40	C₄×C₈×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	D₄	1	2	yes	—
44	C₄×C₈×C₅₉	D₄	1	2	yes	—
45	C₄×C₈×C₅₉	D₄	1	2	yes	—
46	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
49	C₂×C₂²⋊D₅₉	—	4	2	no	—
50	#11745685	—	4	8	no	—
51	C₂×D₂₃₆	—	2	2	no	—
52	C₂×D₂₃₆	—	2	2	no	—
53	C₂×D₂₃₆	—	2	2	no	—
54	C₂×C₄×D₅₉	—	4	2	no	—
55	C₂×Dic₁₁₈	—	2	2	no	—
56	C₂×C₈×C₅₉	—	2	4	no	—
57	C₂×C₈×C₅₉	—	2	2	no	—
58	C₂×C₈×C₅₉	—	2	4	no	—
59	C₂×C₈×C₅₉	—	2	2	no	—
60	C₂×C₈×C₅₉	—	4	2	no	—
61	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
67	(C₂×D₅₉)⋊C₄	—	4	2	no	—
68	(C₂×D₅₉)⋊C₄	—	4	2	no	—
69	C₄⋊Dic₅₉	—	2	2	no	—
70	C₄⋊Dic₅₉	—	2	2	no	—
71	#11745664	—	4	4	no	—
72	C₂×C₅₉⋊C₈	—	4	2	no	—
73	Dic₂₃₆	—	4	4	no	—
74	D₄₇₂	—	4	4	no	—
75	#11745660	—	4	8	no	—
76	C₂³×C₅₉	#124	1	1	yes	characteristic
77	C₂²×D₅₉	—	4	2	no	—
78	C₂×C₄×C₅₉	—	2	2	no	—
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	4	yes	—
87	C₂²⋊D₅₉	—	8	4	no	—
88	C₂×Dic₅₉	—	4	2	no	—
89	D₂₃₆	—	4	4	no	—
90	D₂₃₆	—	4	4	no	—
91	D₂₃₆	—	4	4	no	—
92	C₄×D₅₉	—	8	4	no	—
93	Dic₁₁₈	—	4	4	no	—
94	C₈×C₅₉	—	2	4	no	—
95	C₈×C₅₉	—	2	2	no	—
96	C₈×C₅₉	—	2	2	no	—
97	C₈×C₅₉	—	4	2	no	—
98	C₅₉⋊C₈	—	8	2	no	—
99	#9860	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	—	2	1	no	—
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	#390	1	1	yes	characteristic
103	C₂²×C₅₉	#490	1	2	yes	—
104	C₂×D₅₉	—	8	2	no	—
105	C₂×D₅₉	—	8	2	no	—
106	C₂×D₅₉	—	8	2	no	—
107	C₄×C₅₉	—	2	1	no	—
108	C₄×C₅₉	—	2	1	no	—
109	C₄×C₅₉	#418	1	2	yes	—
110	C₄×C₅₉	#443	1	2	yes	—
111	C₄×C₅₉	#444	1	2	yes	—
112	C₄×C₅₉	#496	1	2	yes	—
113	Dic₅₉	—	8	2	no	—
114	#3147	—	59	1	no	—
115	#1837	—	59	1	no	—
116	#1492	—	59	2	no	—
117	#1492	—	59	2	no	—
118	C₂×#322	D₅₉	1	1	yes	characteristic, complemented
119	C₂×C₅₉	—	2	2	no	—
120	C₂×C₅₉	#1961	1	1	yes	characteristic
121	C₂×C₅₉	#1974	1	1	yes	characteristic
122	C₂×C₅₉	#1975	1	1	yes	characteristic
123	D₅₉	—	16	2	no	—
124	C₂×#135	—	118	2	no	—
125	#532	—	59	2	no	—
126	#495	—	118	2	no	—
127	#494	—	59	1	no	—
128	#493	—	59	1	no	—
129	#492	—	59	2	no	—
130	#423	—	59	2	no	—
131	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
132	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
134	#341	—	118	2	no	—
135	D₄⋊C₈	—	118	4	no	—
136	D₄⋊C₈	—	118	4	no	—
137	#322	—	2	2	no	—
138	C₅₉	#9860	1	1	yes	characteristic, complemented, Sylow
139	C₂×#41	—	118	2	no	—
140	#135	—	236	8	no	—
141	C₂×Q₁₆	—	118	2	no	—
142	C₂×SD₁₆	—	118	4	no	—
143	C₂×D₈	—	118	2	no	—
144	C₂×M₁₆	—	118	2	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	2	1	no	—
147	C₂²×C₈	D₂₃₆	1	2	yes	—
148	C₄⋊Q₈	—	59	2	no	—
149	#127	—	59	2	no	—
150	#124	—	118	2	no	—
151	#121	—	118	2	no	—
152	#121	—	118	2	no	—
153	C₄×D₄	—	118	2	no	—
154	C₄×D₄	—	118	2	no	—
155	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
156	C₄⋊C₈	—	118	2	no	—
157	C₄⋊C₈	—	118	2	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	—	2	1	no	—
160	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
161	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
162	C₄×C₈	D₂₃₆	1	2	yes	—
163	C₄×C₈	D₂₃₆	1	2	yes	—
164	C₄×C₈	C₂²⋊D₅₉	1	2	yes	—
165	#41	—	236	8	no	—
166	C₂×Q₈	—	118	2	no	—
167	C₂×D₄	—	118	2	no	—
168	C₂×D₄	—	118	2	no	—
169	C₂×D₄	—	118	2	no	—
170	C₂×D₄	—	236	2	no	—
171	C₂²×C₄	—	236	2	no	—
172	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
173	C₂²×C₄	#11745685	1	1	yes	characteristic
174	C₂²×C₄	#11745685	1	1	yes	characteristic
175	Q₁₆	—	236	4	no	—
176	SD₁₆	—	236	8	no	—
177	D₈	—	236	4	no	—
178	M₁₆	—	236	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	236	2	no	—
185	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
186	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
187	C₄⋊C₄	—	118	2	no	—
188	C₄⋊C₄	—	118	2	no	—
189	C₂²⋊C₄	—	236	2	no	—
190	C₂²⋊C₄	—	236	2	no	—
191	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
192	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
193	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
194	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
195	C₂³	—	236	2	no	—
196	C₂³	#14273715	1	1	yes	characteristic
197	Q₈	—	236	4	no	—
198	D₄	—	472	4	no	—
199	D₄	—	236	4	no	—
200	D₄	—	236	4	no	—
201	D₄	—	236	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	472	4	no	—
205	C₂×C₄	—	236	2	no	—
206	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
208	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
209	C₂×C₄	#14273701	1	1	yes	characteristic
210	C₂×C₄	#14273701	1	1	yes	characteristic
211	C₂×C₄	#14273724	1	1	yes	characteristic
212	C₂×C₄	#14273755	1	4	yes	—
213	C₈	—	2	4	no	—
214	C₈	—	2	2	no	—
215	C₈	—	2	2	no	—
216	C₈	—	4	2	no	—
217	C₈	—	472	2	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	472	2	no	—
221	C₂²	—	472	2	no	—
222	C₂²	—	472	2	no	—
223	C₂²	#16837304	1	1	yes	characteristic
224	C₂²	#16837767	1	2	yes	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	472	2	no	—
228	C₄	#16837408	1	2	yes	—
229	C₄	#16837520	1	2	yes	—
230	C₄	#16837525	1	2	yes	—
231	C₄	#16837791	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	944	2	no	—
234	C₂	#21424920	1	1	yes	characteristic
235	C₂	#21424984	1	1	yes	characteristic
236	C₂	#21424989	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21434524

C₂

yes

maximal, characteristic

#21424234

C₂

yes

maximal, characteristic, complemented

#21422548

C₂

yes

maximal, complemented

#21422548

C₂

yes

maximal, complemented

C₂×C₅₉×#322

C₂

yes

maximal, characteristic, complemented

C₂×#14273749

—

#16837952

C₂²

yes

—

#16837786

—

#16837782

C₄

yes

characteristic

#16837779

C₄

yes

characteristic

#16837775

C₄

yes

—

#16837426

C₂²

yes

—

#16837167

—

#16837131

—

#16837131

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#322

—

C₂×#11745685

—

#14273749

—

C₂×Dic₂₃₆

—

C₂×#11745660

—

C₂×D₄₇₂

—

C₂×#11745664

—

#14273727

C₂×C₄

yes

—

#14273724

C₂×C₄

yes

—

#14273715

—

#14273701

—

#14273701

—

C₄×D₂₃₆

—

C₄×D₂₃₆

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₂²×C₈×C₅₉

—

C₂²×C₈×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄×C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

—

C₄×C₈×C₅₉

D₄

yes

—

C₄×C₈×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂×C₂²⋊D₅₉

—

#11745685

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

Dic₂₃₆

—

D₄₇₂

—

#11745660

—

C₂³×C₅₉

#124

yes

characteristic

C₂²×D₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

—

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

C₄×D₅₉

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

#9860

—

maximal, Sylow

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

#390

yes

characteristic

103

C₂²×C₅₉

#490

yes

—

104

C₂×D₅₉

—

105

C₂×D₅₉

—

106

C₂×D₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

#418

yes

—

110

C₄×C₅₉

#443

yes

—

111

C₄×C₅₉

#444

yes

—

112

C₄×C₅₉

#496

yes

—

113

Dic₅₉

—

114

#3147

—

115

#1837

—

116

#1492

—

117

#1492

—

118

C₂×#322

D₅₉

yes

characteristic, complemented

119

C₂×C₅₉

—

120

C₂×C₅₉

#1961

yes

characteristic

121

C₂×C₅₉

#1974

yes

characteristic

122

C₂×C₅₉

#1975

yes

characteristic

123

D₅₉

—

124

C₂×#135

—

118

—

125

#532

—

126

#495

—

118

—

127

#494

—

128

#493

—

129

#492

—

130

#423

—

131

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

132

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

133

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

134

#341

—

118

—

135

D₄⋊C₈

—

118

—

136

D₄⋊C₈

—

118

—

137

#322

—

138

C₅₉

#9860

yes

characteristic, complemented, Sylow

139

C₂×#41

—

118

—

140

#135

—

236

—

141

C₂×Q₁₆

—

118

—

142

C₂×SD₁₆

—

118

—

143

C₂×D₈

—

118

—

144

C₂×M₁₆

—

118

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

D₂₃₆

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

118

—

151

#121

—

118

—

152

#121

—

118

—

153

C₄×D₄

—

118

—

154

C₄×D₄

—

118

—

155

C₂×C₄²

C₂²×D₅₉

yes

characteristic

156

C₄⋊C₈

—

118

—

157

C₄⋊C₈

—

118

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

C₄×D₅₉

yes

characteristic

161

C₄×C₈

C₄×D₅₉

yes

characteristic

162

C₄×C₈

D₂₃₆

yes

—

163

C₄×C₈

D₂₃₆

yes

—

164

C₄×C₈

C₂²⋊D₅₉

yes

—

165

#41

—

236

—

166

C₂×Q₈

—

118

—

167

C₂×D₄

—

118

—

168

C₂×D₄

—

118

—

169

C₂×D₄

—

118

—

170

C₂×D₄

—

236

—

171

C₂²×C₄

—

236

—

172

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

173

C₂²×C₄

#11745685

yes

characteristic

174

C₂²×C₄

#11745685

yes

characteristic

175

Q₁₆

—

236

—

176

SD₁₆

—

236

—

177

D₈

—

236

—

178

M₁₆

—

236

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

236

—

185

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

186

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

187

C₄⋊C₄

—

118

—

188

C₄⋊C₄

—

118

—

189

C₂²⋊C₄

—

236

—

190

C₂²⋊C₄

—

236

—

191

C₄²

C₂×C₄×D₅₉

yes

characteristic

192

C₄²

C₂×D₂₃₆

yes

characteristic

193

C₄²

C₂×D₂₃₆

yes

characteristic

194

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

195

C₂³

—

236

—

196

C₂³

#14273715

yes

characteristic

197

Q₈

—

236

—

198

D₄

—

472

—

199

D₄

—

236

—

200

D₄

—

236

—

201

D₄

—

236

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

472

—

205

C₂×C₄

—

236

—

206

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

207

C₂×C₄

C₄×D₂₃₆

yes

characteristic

208

C₂×C₄

C₄×D₂₃₆

yes

characteristic

209

C₂×C₄

#14273701

yes

characteristic

210

C₂×C₄

#14273701

yes

characteristic

211

C₂×C₄

#14273724

yes

characteristic

212

C₂×C₄

#14273755

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

—

472

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

472

—

221

C₂²

—

472

—

222

C₂²

—

472

—

223

C₂²

#16837304

yes

characteristic

224

C₂²

#16837767

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

472

—

228

C₄

#16837408

yes

—

229

C₄

#16837520

yes

—

230

C₄

#16837525

yes

—

231

C₄

#16837791

yes

—

232

C₂

—

233

C₂

—

944

—

234

C₂

#21424920

yes

characteristic

235

C₂

#21424984

yes

characteristic

236

C₂

#21424989

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273724
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₂×C₅₉×#322	C₂
socle	C₂²×C₅₉	#390
prime radical	#21434524	C₂
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₂×#322	D₅₉
hypocenter	C₅₉	#9860
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

#14273724

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₂×C₅₉×#322

C₂

C₂²×C₅₉

C₂

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#322

N	H ≅ G/N	type
2. #21424234	C₂	semidirect
3. #21422548	C₂	semidirect
4. #21422548	C₂	semidirect
5. C₂×C₅₉×#322	C₂	semidirect
118. C₂×#322	D₅₉	semidirect
138. C₅₉	#9860	semidirect

H ≅ G/N

type

2. #21424234

C₂

semidirect

3. #21422548

C₂

semidirect

4. #21422548

C₂

semidirect

5. C₂×C₅₉×#322

C₂

semidirect

118. C₂×#322

D₅₉

semidirect

138. C₅₉

#9860

semidirect

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

subgroup	index
#21434524	2
#21424234	2
#21422548	2
C₂×C₅₉×#322	2
#9860	59

subgroup

index

C₂×C₅₉×#322

Subgroups — #28488653

Conjugacy classes of subgroups

Complements

Maximal subgroups