Group #32922835 — subgroups

Subgroups — C₇₃×#13431 #32922835

Order 18688.

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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	C₇₃×#3202	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2135	C₂	1	2	yes	maximal
3	C₇₃×#1915	C₂	1	2	yes	maximal
4	C₇₃×#1858	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#1392	C₂	1	1	yes	maximal, characteristic
6	#568×C₇₃	C₂²	1	1	yes	characteristic
7	#536×C₇₃	C₂²	1	2	yes	—
8	#485×C₇₃	—	2	2	no	—
9	#470×C₇₃	—	2	1	no	—
10	#467×C₇₃	—	2	1	no	—
11	#451×C₇₃	—	2	2	no	—
12	#430×C₇₃	—	2	1	no	—
13	#413×C₇₃	C₂²	1	2	yes	—
14	#413×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#101×C₇₃	—	2	2	no	—
16	#408×C₇₃	C₂²	1	1	yes	characteristic
17	#356×C₇₃	—	2	4	no	—
18	#344×C₇₃	—	2	2	no	—
19	#341×C₇₃	—	2	1	no	—
20	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
21	C₂²×Q₈×C₇₃	D₄	1	2	yes	—
22	C₂×Q₁₆×C₇₃	—	2	1	no	—
23	C₂×Q₁₆×C₇₃	—	2	1	no	—
24	#131×C₇₃	—	4	2	no	—
25	C₂×M₁₆×C₇₃	—	2	2	no	—
26	C₂×M₁₆×C₇₃	—	2	1	no	—
27	C₂×M₁₆×C₇₃	—	2	1	no	—
28	C₂×M₁₆×C₇₃	—	2	2	no	—
29	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₇₃	—	2	2	no	—
32	#124×C₇₃	—	2	2	no	—
33	#123×C₇₃	—	2	2	no	—
34	#123×C₇₃	—	2	2	no	—
35	C₂²⋊Q₈×C₇₃	—	2	2	no	—
36	C₂²⋊Q₈×C₇₃	—	2	2	no	—
37	#117×C₇₃	D₄	1	2	yes	—
38	#108×C₇₃	—	4	2	no	—
39	#107×C₇₃	—	2	1	no	—
40	#106×C₇₃	—	2	1	no	—
41	#103×C₇₃	—	2	2	no	—
42	#103×C₇₃	—	2	2	no	—
43	#101×C₇₃	—	2	2	no	—
44	#101×C₇₃	—	4	4	no	—
45	#101×C₇₃	D₄	1	2	yes	—
46	#100×C₇₃	—	2	1	no	—
47	#100×C₇₃	—	2	2	no	—
48	C₂²⋊C₈×C₇₃	—	2	2	no	—
49	#41×C₇₃	—	4	1	no	—
50	#41×C₇₃	—	4	1	no	—
51	C₂×Q₈×C₇₃	—	2	2	no	—
52	C₂×Q₈×C₇₃	—	2	2	no	—
53	C₂×Q₈×C₇₃	—	4	2	no	—
54	C₂×Q₈×C₇₃	—	4	2	no	—
55	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
56	C₂×D₄×C₇₃	#41	1	1	yes	characteristic
57	C₂×D₄×C₇₃	#41	1	2	yes	—
58	C₂²×C₄×C₇₃	—	2	2	no	—
59	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₇₃	—	8	1	no	—
62	Q₁₆×C₇₃	—	8	1	no	—
63	M₁₆×C₇₃	—	2	4	no	—
64	M₁₆×C₇₃	—	2	2	no	—
65	M₁₆×C₇₃	—	2	2	no	—
66	M₁₆×C₇₃	—	4	1	no	—
67	M₁₆×C₇₃	—	4	1	no	—
68	M₁₆×C₇₃	—	4	1	no	—
69	M₁₆×C₇₃	—	4	2	no	—
70	M₁₆×C₇₃	—	4	2	no	—
71	C₂×C₈×C₇₃	—	2	1	no	—
72	C₂×C₈×C₇₃	—	2	1	no	—
73	C₂×C₈×C₇₃	—	4	1	no	—
74	C₂×C₈×C₇₃	—	4	1	no	—
75	C₂×C₈×C₇₃	—	4	2	no	—
76	C₂×C₈×C₇₃	—	4	1	no	—
77	C₂×C₈×C₇₃	—	4	2	no	—
78	C₄⋊C₄×C₇₃	—	2	2	no	—
79	C₄⋊C₄×C₇₃	—	4	2	no	—
80	C₄⋊C₄×C₇₃	—	4	2	no	—
81	C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂²⋊C₄×C₇₃	—	4	2	no	—
83	C₂²⋊C₄×C₇₃	—	4	2	no	—
84	C₄²×C₇₃	—	2	2	no	—
85	C₂³×C₇₃	#123	1	2	yes	—
86	C₂³×C₇₃	#124	1	1	yes	characteristic
87	Q₈×C₇₃	—	4	1	no	—
88	Q₈×C₇₃	—	4	2	no	—
89	Q₈×C₇₃	—	4	2	no	—
90	Q₈×C₇₃	—	8	2	no	—
91	D₄×C₇₃	—	4	1	no	—
92	D₄×C₇₃	—	4	2	no	—
93	C₂×C₄×C₇₃	—	2	1	no	—
94	C₂×C₄×C₇₃	—	2	2	no	—
95	C₂×C₄×C₇₃	—	2	1	no	—
96	C₂×C₄×C₇₃	—	2	2	no	—
97	C₂×C₄×C₇₃	—	4	4	no	—
98	C₂×C₄×C₇₃	—	4	2	no	—
99	C₂×C₄×C₇₃	—	4	2	no	—
100	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
101	C₂×C₄×C₇₃	#121	1	2	yes	—
102	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
103	C₈×C₇₃	—	4	2	no	—
104	C₈×C₇₃	—	4	1	no	—
105	C₈×C₇₃	—	4	2	no	—
106	C₈×C₇₃	—	4	1	no	—
107	C₈×C₇₃	—	8	2	no	—
108	C₂²×C₇₃	—	2	2	no	—
109	C₂²×C₇₃	—	2	1	no	—
110	C₂²×C₇₃	—	4	2	no	—
111	C₂²×C₇₃	—	4	1	no	—
112	C₂²×C₇₃	#394	1	1	yes	characteristic
113	C₄×C₇₃	—	2	1	no	—
114	C₄×C₇₃	—	2	2	no	—
115	C₄×C₇₃	—	8	2	no	—
116	C₄×C₇₃	—	8	2	no	—
117	C₄×C₇₃	B(4,𝔽₂)	1	1	yes	characteristic
118	C₄×C₇₃	#458	1	1	yes	characteristic
119	#13431	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇₃	—	2	1	no	—
121	C₂×C₇₃	—	4	2	no	—
122	C₂×C₇₃	—	4	1	no	—
123	C₂×C₇₃	#2044	1	1	yes	characteristic
124	#3202	C₂×C₇₃	1	1	yes	characteristic
125	#2135	C₂×C₇₃	1	2	yes	—
126	#1915	C₂×C₇₃	1	2	yes	—
127	#1858	C₂×C₇₃	1	1	yes	characteristic
128	#1392	C₂×C₇₃	1	1	yes	characteristic
129	C₇₃	#13431	1	1	yes	characteristic, direct product factor, Sylow
130	#568	C₂²×C₇₃	1	1	yes	characteristic
131	#536	C₂²×C₇₃	1	2	yes	—
132	#485	—	2	2	no	—
133	#470	—	2	1	no	—
134	#467	—	2	1	no	—
135	#451	—	2	2	no	—
136	#430	—	2	1	no	—
137	#413	C₂²×C₇₃	1	2	yes	—
138	#413	C₂²×C₇₃	1	1	yes	characteristic
139	C₂×#101	—	2	2	no	—
140	#408	C₂²×C₇₃	1	1	yes	characteristic
141	#356	—	2	4	no	—
142	#344	—	2	2	no	—
143	#341	—	2	1	no	—
144	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
145	C₂²×Q₈	D₄×C₇₃	1	2	yes	—
146	C₂×Q₁₆	—	2	1	no	—
147	C₂×Q₁₆	—	2	1	no	—
148	#131	—	4	2	no	—
149	C₂×M₁₆	—	2	1	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	D₄×C₇₃	1	1	yes	characteristic
154	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
155	C₄⋊Q₈	—	2	2	no	—
156	#124	—	2	2	no	—
157	#123	—	2	2	no	—
158	#123	—	2	2	no	—
159	C₂²⋊Q₈	—	2	2	no	—
160	C₂²⋊Q₈	—	2	2	no	—
161	#117	D₄×C₇₃	1	2	yes	—
162	#108	—	4	2	no	—
163	#107	—	2	1	no	—
164	#106	—	2	1	no	—
165	#103	—	2	2	no	—
166	#103	—	2	2	no	—
167	#101	—	2	2	no	—
168	#101	—	4	4	no	—
169	#101	D₄×C₇₃	1	2	yes	—
170	#100	—	2	1	no	—
171	#100	—	2	2	no	—
172	C₂²⋊C₈	—	2	2	no	—
173	#41	—	4	1	no	—
174	#41	—	4	1	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×Q₈	—	4	2	no	—
179	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
180	C₂×D₄	#41×C₇₃	1	1	yes	characteristic
181	C₂×D₄	#41×C₇₃	1	2	yes	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
184	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
185	Q₁₆	—	8	1	no	—
186	Q₁₆	—	8	1	no	—
187	M₁₆	—	2	4	no	—
188	M₁₆	—	2	2	no	—
189	M₁₆	—	2	2	no	—
190	M₁₆	—	4	1	no	—
191	M₁₆	—	4	1	no	—
192	M₁₆	—	4	1	no	—
193	M₁₆	—	4	2	no	—
194	M₁₆	—	4	2	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	4	2	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₂²⋊C₄	—	2	2	no	—
206	C₂²⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₄²	—	2	2	no	—
209	C₂³	#123×C₇₃	1	2	yes	—
210	C₂³	#124×C₇₃	1	1	yes	characteristic
211	Q₈	—	4	1	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	8	2	no	—
215	D₄	—	4	1	no	—
216	D₄	—	4	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
225	C₂×C₄	#121×C₇₃	1	2	yes	—
226	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
227	C₈	—	4	2	no	—
228	C₈	—	4	1	no	—
229	C₈	—	4	2	no	—
230	C₈	—	4	1	no	—
231	C₈	—	8	2	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	4	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	#394×C₇₃	1	1	yes	characteristic
237	C₄	—	2	1	no	—
238	C₄	—	2	2	no	—
239	C₄	—	8	2	no	—
240	C₄	—	8	2	no	—
241	C₄	B(4,𝔽₂)×C₇₃	1	1	yes	characteristic
242	C₄	#458×C₇₃	1	1	yes	characteristic
243	C₂	—	2	1	no	—
244	C₂	—	4	2	no	—
245	C₂	—	4	1	no	—
246	C₂	C₇₃×#2044	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#3202

C₂

yes

maximal, characteristic

C₇₃×#2135

C₂

yes

maximal

C₇₃×#1915

C₂

yes

maximal

C₇₃×#1858

C₂

yes

maximal, characteristic

C₇₃×#1392

C₂

yes

maximal, characteristic

#568×C₇₃

C₂²

yes

characteristic

#536×C₇₃

C₂²

yes

—

#485×C₇₃

—

#470×C₇₃

—

#467×C₇₃

—

#451×C₇₃

—

#430×C₇₃

—

#413×C₇₃

C₂²

yes

—

#413×C₇₃

C₂²

yes

characteristic

C₂×#101×C₇₃

—

#408×C₇₃

C₂²

yes

characteristic

#356×C₇₃

—

#344×C₇₃

—

#341×C₇₃

—

C₂×#41×C₇₃

C₂³

yes

characteristic

C₂²×Q₈×C₇₃

D₄

yes

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

#131×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₄⋊Q₈×C₇₃

—

#124×C₇₃

—

#123×C₇₃

—

#123×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₂²⋊Q₈×C₇₃

—

#117×C₇₃

D₄

yes

—

#108×C₇₃

—

#107×C₇₃

—

#106×C₇₃

—

#103×C₇₃

—

#103×C₇₃

—

#101×C₇₃

—

#101×C₇₃

—

#101×C₇₃

D₄

yes

—

#100×C₇₃

—

#100×C₇₃

—

C₂²⋊C₈×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

C₂×D₄

yes

C₂×D₄×C₇₃

yes

C₂×D₄×C₇₃

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

#123

yes

—

C₂³×C₇₃

#124

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

#120

yes

characteristic

101

C₂×C₄×C₇₃

#121

yes

—

102

C₂×C₄×C₇₃

#121

yes

characteristic

103

C₈×C₇₃

—

104

C₈×C₇₃

—

105

C₈×C₇₃

—

106

C₈×C₇₃

—

107

C₈×C₇₃

—

108

C₂²×C₇₃

—

109

C₂²×C₇₃

—

110

C₂²×C₇₃

—

111

C₂²×C₇₃

—

112

C₂²×C₇₃

#394

yes

characteristic

113

C₄×C₇₃

—

114

C₄×C₇₃

—

115

C₄×C₇₃

—

116

C₄×C₇₃

—

117

C₄×C₇₃

B(4,𝔽₂)

yes

characteristic

118

C₄×C₇₃

#458

yes

characteristic

119

#13431

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

120

C₂×C₇₃

—

121

C₂×C₇₃

—

122

C₂×C₇₃

—

123

C₂×C₇₃

#2044

yes

characteristic

124

#3202

C₂×C₇₃

yes

characteristic

125

#2135

C₂×C₇₃

yes

—

126

#1915

C₂×C₇₃

yes

—

127

#1858

C₂×C₇₃

yes

characteristic

128

#1392

C₂×C₇₃

yes

characteristic

129

C₇₃

#13431

yes

characteristic, direct product factor, Sylow

130

#568

C₂²×C₇₃

yes

characteristic

131

#536

C₂²×C₇₃

yes

—

132

#485

—

133

#470

—

134

#467

—

135

#451

—

136

#430

—

137

#413

C₂²×C₇₃

yes

—

138

#413

C₂²×C₇₃

yes

characteristic

139

C₂×#101

—

140

#408

C₂²×C₇₃

yes

characteristic

141

#356

—

142

#344

—

143

#341

—

144

C₂×#41

C₂³×C₇₃

yes

characteristic

145

C₂²×Q₈

D₄×C₇₃

yes

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

#131

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

D₄×C₇₃

yes

characteristic

154

C₂²×C₈

D₄×C₇₃

yes

characteristic

155

C₄⋊Q₈

—

156

#124

—

157

#123

—

158

#123

—

159

C₂²⋊Q₈

—

160

C₂²⋊Q₈

—

161

#117

D₄×C₇₃

yes

—

162

#108

—

163

#107

—

164

#106

—

165

#103

—

166

#103

—

167

#101

—

168

#101

—

169

#101

D₄×C₇₃

yes

—

170

#100

—

171

#100

—

172

C₂²⋊C₈

—

173

#41

—

174

#41

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

C₂×D₄×C₇₃

yes

characteristic

180

C₂×D₄

#41×C₇₃

yes

characteristic

181

C₂×D₄

#41×C₇₃

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

C₂×D₄×C₇₃

yes

—

184

C₂²×C₄

C₂×D₄×C₇₃

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

193

M₁₆

—

194

M₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

—

209

C₂³

#123×C₇₃

yes

—

210

C₂³

#124×C₇₃

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#120×C₇₃

yes

characteristic

225

C₂×C₄

#121×C₇₃

yes

—

226

C₂×C₄

#121×C₇₃

yes

characteristic

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

#394×C₇₃

yes

characteristic

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

B(4,𝔽₂)×C₇₃

yes

characteristic

242

C₄

#458×C₇₃

yes

characteristic

243

C₂

—

244

C₂

—

245

C₂

—

246

C₂

C₇₃×#2044

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₇₃	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₇₃
prime radical	C₂×#41×C₇₃	C₂³
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#41×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂×C₇₃

#2044

commutator, Frattini, cosocle

C₂×#41

C₂³×C₇₃

prime radical

C₂×#41×C₇₃

C₂³

LCS

G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#41×C₇₃ ◁ G

N	H ≅ G/N	type
119. #13431	C₇₃	direct (N × H)
129. C₇₃	#13431	direct (N × H)

H ≅ G/N

type

119. #13431

C₇₃

direct (N × H)

129. C₇₃

#13431

direct (N × H)

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

subgroup	index
C₇₃×#3202	2
C₇₃×#2135	2
C₇₃×#1915	2
C₇₃×#1858	2
C₇₃×#1392	2
#13431	73

subgroup

index

C₇₃×#3202

C₇₃×#2135

C₇₃×#1915

C₇₃×#1858

C₇₃×#1392

#13431

Subgroups — C₇₃×#13431 #32922835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#13431 #32922835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#13431 #32922835