Group #23760621 — subgroups

Subgroups — C₂×#451×C₇₉ #23760621

Order 10112.

740 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 248 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	C₂³×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Q₁₆×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
4	#451×C₇₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#103×C₇₉	C₂	1	2	yes	maximal, complemented
6	C₂×C₂²⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₇₉	—	2	8	no	—
8	C₂²×Q₈×C₇₉	—	2	2	no	—
9	C₂²×Q₈×C₇₉	—	2	1	no	—
10	C₂²×Q₈×C₇₉	C₂²	1	4	yes	—
11	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₇₉	C₂²	1	2	yes	—
13	C₂³×C₄×C₇₉	—	2	1	no	—
14	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₇₉	—	2	8	no	—
16	C₂×Q₁₆×C₇₉	C₂²	1	8	yes	complemented
17	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
18	C₂²⋊Q₈×C₇₉	—	2	2	no	—
19	C₂²⋊Q₈×C₇₉	C₂²	1	4	yes	—
20	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
21	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
23	#103×C₇₉	C₂²	1	8	yes	complemented
24	C₂²⋊C₈×C₇₉	C₂²	1	4	yes	—
25	C₂⁴×C₇₉	D₄	1	1	yes	characteristic
26	C₂×Q₈×C₇₉	—	2	16	no	—
27	C₂×Q₈×C₇₉	—	2	8	no	—
28	C₂×Q₈×C₇₉	—	2	16	no	—
29	C₂×Q₈×C₇₉	—	2	4	no	—
30	C₂×Q₈×C₇₉	—	2	4	no	—
31	C₂×Q₈×C₇₉	—	2	2	no	—
32	C₂×Q₈×C₇₉	—	2	1	no	—
33	C₂×Q₈×C₇₉	—	2	4	no	—
34	C₂×Q₈×C₇₉	D₄	1	8	yes	—
35	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
36	C₂×Q₈×C₇₉	C₂³	1	4	yes	—
37	C₂²×C₄×C₇₉	—	2	8	no	—
38	C₂²×C₄×C₇₉	—	2	4	no	—
39	C₂²×C₄×C₇₉	—	2	2	no	—
40	C₂²×C₄×C₇₉	—	2	4	no	—
41	C₂²×C₄×C₇₉	—	2	1	no	—
42	C₂²×C₄×C₇₉	—	2	1	no	—
43	C₂²×C₄×C₇₉	D₄	1	2	yes	—
44	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
45	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
46	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
47	Q₁₆×C₇₉	—	2	16	no	—
48	C₂×C₈×C₇₉	—	2	4	no	—
49	C₂×C₈×C₇₉	C₂³	1	4	yes	—
50	C₄⋊C₄×C₇₉	—	2	4	no	—
51	C₄⋊C₄×C₇₉	—	2	1	no	—
52	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
53	C₂²⋊C₄×C₇₉	—	2	4	no	—
54	C₂³×C₇₉	—	2	2	no	—
55	C₂³×C₇₉	—	2	2	no	—
56	C₂³×C₇₉	Q₁₆	1	4	yes	complemented
57	C₂³×C₇₉	C₂×D₄	1	2	yes	—
58	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
59	Q₈×C₇₉	—	2	16	no	—
60	Q₈×C₇₉	—	2	8	no	—
61	Q₈×C₇₉	—	2	4	no	—
62	Q₈×C₇₉	—	2	4	no	—
63	Q₈×C₇₉	—	4	2	no	—
64	Q₈×C₇₉	C₂×D₄	1	8	yes	—
65	C₂×C₄×C₇₉	—	2	16	no	—
66	C₂×C₄×C₇₉	—	2	8	no	—
67	C₂×C₄×C₇₉	—	2	2	no	—
68	C₂×C₄×C₇₉	—	2	4	no	—
69	C₂×C₄×C₇₉	—	2	4	no	—
70	C₂×C₄×C₇₉	—	2	4	no	—
71	C₂×C₄×C₇₉	—	2	2	no	—
72	C₂×C₄×C₇₉	—	2	2	no	—
73	C₂×C₄×C₇₉	—	4	2	no	—
74	C₂×C₄×C₇₉	—	4	2	no	—
75	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
78	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
79	C₈×C₇₉	—	2	4	no	—
80	C₂²×C₇₉	—	2	2	no	—
81	C₂²×C₇₉	—	2	2	no	—
82	C₂²×C₇₉	—	2	8	no	—
83	C₂²×C₇₉	#120	1	2	yes	—
84	C₂²×C₇₉	C₂×Q₁₆	1	2	yes	—
85	C₂²×C₇₉	C₂×Q₁₆	1	4	yes	complemented
86	C₂²×C₇₉	#137	1	2	yes	—
87	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
88	C₄×C₇₉	—	2	8	no	—
89	C₄×C₇₉	—	2	2	no	—
90	C₄×C₇₉	—	4	2	no	—
91	C₄×C₇₉	—	4	2	no	—
92	C₄×C₇₉	#120	1	2	yes	—
93	C₄×C₇₉	C₂²×D₄	1	2	yes	—
94	C₂×C₇₉	—	2	4	no	—
95	C₂×C₇₉	#451	1	4	yes	direct product factor
96	C₂×C₇₉	C₂×#120	1	1	yes	characteristic
97	C₂×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
98	C₂×C₇₉	C₂×#137	1	1	yes	characteristic
99	C₂×#451	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₇₉	C₂×#451	1	1	yes	characteristic, direct product factor, Sylow
101	C₂³×Q₈	C₂×C₇₉	1	1	yes	characteristic
102	C₂²×Q₁₆	C₂×C₇₉	1	2	yes	complemented
103	C₂×C₂²⋊Q₈	C₂×C₇₉	1	1	yes	characteristic
104	#451	C₂×C₇₉	1	8	yes	direct product factor
105	C₂×#103	C₂×C₇₉	1	2	yes	complemented
106	C₂×C₂²⋊C₈	C₂×C₇₉	1	1	yes	characteristic
107	C₂²×Q₈	—	2	8	no	—
108	C₂²×Q₈	—	2	1	no	—
109	C₂²×Q₈	—	2	2	no	—
110	C₂²×Q₈	C₂²×C₇₉	1	1	yes	characteristic
111	C₂²×Q₈	C₂²×C₇₉	1	4	yes	—
112	C₂²×Q₈	C₂²×C₇₉	1	2	yes	—
113	C₂³×C₄	—	2	1	no	—
114	C₂³×C₄	C₂²×C₇₉	1	1	yes	characteristic
115	C₂×Q₁₆	—	2	8	no	—
116	C₂×Q₁₆	C₂²×C₇₉	1	8	yes	complemented
117	C₂²×C₈	C₂²×C₇₉	1	2	yes	—
118	C₂²⋊Q₈	—	2	2	no	—
119	C₂²⋊Q₈	C₂²×C₇₉	1	4	yes	—
120	C₂×C₄⋊C₄	—	2	1	no	—
121	C₂×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
122	C₂×C₂²⋊C₄	—	2	1	no	—
123	#103	C₂²×C₇₉	1	8	yes	complemented
124	C₂²⋊C₈	C₂²×C₇₉	1	4	yes	—
125	C₂⁴	D₄×C₇₉	1	1	yes	characteristic
126	C₂×Q₈	—	2	16	no	—
127	C₂×Q₈	—	2	8	no	—
128	C₂×Q₈	—	2	16	no	—
129	C₂×Q₈	—	2	4	no	—
130	C₂×Q₈	—	2	4	no	—
131	C₂×Q₈	—	2	2	no	—
132	C₂×Q₈	—	2	1	no	—
133	C₂×Q₈	—	2	4	no	—
134	C₂×Q₈	D₄×C₇₉	1	8	yes	—
135	C₂×Q₈	C₂³×C₇₉	1	2	yes	—
136	C₂×Q₈	C₂³×C₇₉	1	4	yes	—
137	C₂²×C₄	—	2	8	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	1	no	—
142	C₂²×C₄	—	2	1	no	—
143	C₂²×C₄	D₄×C₇₉	1	1	yes	characteristic
144	C₂²×C₄	D₄×C₇₉	1	2	yes	—
145	C₂²×C₄	C₂³×C₇₉	1	2	yes	—
146	C₂²×C₄	C₂³×C₇₉	1	1	yes	characteristic
147	Q₁₆	—	2	16	no	—
148	C₂×C₈	—	2	4	no	—
149	C₂×C₈	C₂³×C₇₉	1	4	yes	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
153	C₂²⋊C₄	—	2	4	no	—
154	C₂³	—	2	2	no	—
155	C₂³	—	2	2	no	—
156	C₂³	Q₁₆×C₇₉	1	4	yes	complemented
157	C₂³	C₂×D₄×C₇₉	1	2	yes	—
158	C₂³	C₂×D₄×C₇₉	1	1	yes	characteristic
159	Q₈	—	2	16	no	—
160	Q₈	—	2	8	no	—
161	Q₈	—	2	4	no	—
162	Q₈	—	2	4	no	—
163	Q₈	—	4	2	no	—
164	Q₈	C₂×D₄×C₇₉	1	8	yes	—
165	C₂×C₄	—	2	16	no	—
166	C₂×C₄	—	2	8	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	C₂×D₄×C₇₉	1	2	yes	—
176	C₂×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
177	C₂×C₄	C₂×D₄×C₇₉	1	4	yes	—
178	C₂×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
179	C₈	—	2	4	no	—
180	C₂²	—	2	8	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	2	no	—
183	C₂²	#120×C₇₉	1	2	yes	—
184	C₂²	C₂×Q₁₆×C₇₉	1	2	yes	—
185	C₂²	C₂×Q₁₆×C₇₉	1	4	yes	complemented
186	C₂²	#137×C₇₉	1	2	yes	—
187	C₂²	C₂²×D₄×C₇₉	1	1	yes	characteristic
188	C₄	—	2	8	no	—
189	C₄	—	2	2	no	—
190	C₄	—	4	2	no	—
191	C₄	—	4	2	no	—
192	C₄	#120×C₇₉	1	2	yes	—
193	C₄	C₂²×D₄×C₇₉	1	2	yes	—
194	C₂	—	2	4	no	—
195	C₂	#451×C₇₉	1	4	yes	direct product factor
196	C₂	C₂×#120×C₇₉	1	1	yes	characteristic
197	C₂	C₂²×Q₁₆×C₇₉	1	1	yes	characteristic
198	C₂	C₂×#137×C₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Q₈×C₇₉

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₇₉

C₂

yes

maximal, complemented

C₂×C₂²⋊Q₈×C₇₉

C₂

yes

maximal, characteristic

#451×C₇₉

C₂

yes

maximal, direct product factor

C₂×#103×C₇₉

C₂

yes

maximal, complemented

C₂×C₂²⋊C₈×C₇₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₇₉

—

C₂²×Q₈×C₇₉

—

C₂²×Q₈×C₇₉

—

C₂²×Q₈×C₇₉

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂²×Q₈×C₇₉

C₂²

yes

—

C₂³×C₄×C₇₉

—

C₂³×C₄×C₇₉

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

—

C₂×Q₁₆×C₇₉

C₂²

yes

complemented

C₂²×C₈×C₇₉

C₂²

yes

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₇₉

—

#103×C₇₉

C₂²

yes

complemented

C₂²⋊C₈×C₇₉

C₂²

yes

—

C₂⁴×C₇₉

D₄

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

D₄

yes

—

C₂×Q₈×C₇₉

C₂³

yes

—

C₂×Q₈×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₂²⋊C₄×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

Q₁₆

yes

complemented

C₂³×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₈×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#120

yes

—

C₂²×C₇₉

C₂×Q₁₆

yes

—

C₂²×C₇₉

C₂×Q₁₆

yes

complemented

C₂²×C₇₉

#137

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#120

yes

—

C₄×C₇₉

C₂²×D₄

yes

—

C₂×C₇₉

—

C₂×C₇₉

#451

yes

direct product factor

C₂×C₇₉

C₂×#120

yes

characteristic

C₂×C₇₉

C₂²×Q₁₆

yes

C₂×C₇₉

yes

C₇₉

yes

maximal, characteristic, direct product factor, Sylow

100

C₇₉

C₂×#451

yes

characteristic, direct product factor, Sylow

101

C₂³×Q₈

C₂×C₇₉

yes

characteristic

102

C₂²×Q₁₆

C₂×C₇₉

yes

complemented

103

C₂×C₂²⋊Q₈

C₂×C₇₉

yes

characteristic

104

#451

C₂×C₇₉

yes

direct product factor

105

C₂×#103

C₂×C₇₉

yes

complemented

106

C₂×C₂²⋊C₈

C₂×C₇₉

yes

characteristic

107

C₂²×Q₈

—

108

C₂²×Q₈

—

109

C₂²×Q₈

—

110

C₂²×Q₈

C₂²×C₇₉

yes

characteristic

111

C₂²×Q₈

C₂²×C₇₉

yes

—

112

C₂²×Q₈

C₂²×C₇₉

yes

—

113

C₂³×C₄

—

114

C₂³×C₄

C₂²×C₇₉

yes

characteristic

115

C₂×Q₁₆

—

116

C₂×Q₁₆

C₂²×C₇₉

yes

complemented

117

C₂²×C₈

C₂²×C₇₉

yes

—

118

C₂²⋊Q₈

—

119

C₂²⋊Q₈

C₂²×C₇₉

yes

—

120

C₂×C₄⋊C₄

—

121

C₂×C₄⋊C₄

C₂²×C₇₉

yes

characteristic

122

C₂×C₂²⋊C₄

—

123

#103

C₂²×C₇₉

yes

complemented

124

C₂²⋊C₈

C₂²×C₇₉

yes

—

125

C₂⁴

D₄×C₇₉

yes

characteristic

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

D₄×C₇₉

yes

—

135

C₂×Q₈

C₂³×C₇₉

yes

—

136

C₂×Q₈

C₂³×C₇₉

yes

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

D₄×C₇₉

yes

characteristic

144

C₂²×C₄

D₄×C₇₉

yes

—

145

C₂²×C₄

C₂³×C₇₉

yes

—

146

C₂²×C₄

C₂³×C₇₉

yes

characteristic

147

Q₁₆

—

148

C₂×C₈

—

149

C₂×C₈

C₂³×C₇₉

yes

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

C₂³×C₇₉

yes

—

153

C₂²⋊C₄

—

154

C₂³

—

155

C₂³

—

156

C₂³

Q₁₆×C₇₉

yes

complemented

157

C₂³

C₂×D₄×C₇₉

yes

—

158

C₂³

C₂×D₄×C₇₉

yes

characteristic

159

Q₈

—

160

Q₈

—

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

Q₈

C₂×D₄×C₇₉

yes

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₂×D₄×C₇₉

yes

—

176

C₂×C₄

C₂×D₄×C₇₉

yes

characteristic

177

C₂×C₄

C₂×D₄×C₇₉

yes

—

178

C₂×C₄

C₂⁴×C₇₉

yes

characteristic

179

C₈

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

#120×C₇₉

yes

—

184

C₂²

C₂×Q₁₆×C₇₉

yes

—

185

C₂²

C₂×Q₁₆×C₇₉

yes

complemented

186

C₂²

#137×C₇₉

yes

—

187

C₂²

C₂²×D₄×C₇₉

yes

characteristic

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

#120×C₇₉

yes

—

193

C₄

C₂²×D₄×C₇₉

yes

—

194

C₂

—

195

C₂

#451×C₇₉

yes

direct product factor

196

C₂

C₂×#120×C₇₉

yes

characteristic

197

C₂

C₂²×Q₁₆×C₇₉

yes

characteristic

198

C₂

C₂×#137×C₇₉

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₇₉

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₇₉

prime radical

C₂⁴×C₇₉

D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ G

N	H ≅ G/N	type
2. C₂²×Q₁₆×C₇₉	C₂	semidirect
4. #451×C₇₉	C₂	direct (N × H)
5. C₂×#103×C₇₉	C₂	semidirect
16. C₂×Q₁₆×C₇₉	C₂²	semidirect
23. #103×C₇₉	C₂²	semidirect
56. C₂³×C₇₉	Q₁₆	semidirect
85. C₂²×C₇₉	C₂×Q₁₆	semidirect
95. C₂×C₇₉	#451	direct (N × H)
99. C₂×#451	C₇₉	direct (N × H)
100. C₇₉	C₂×#451	direct (N × H)
102. C₂²×Q₁₆	C₂×C₇₉	semidirect
104. #451	C₂×C₇₉	direct (N × H)
105. C₂×#103	C₂×C₇₉	semidirect
116. C₂×Q₁₆	C₂²×C₇₉	semidirect
123. #103	C₂²×C₇₉	semidirect
156. C₂³	Q₁₆×C₇₉	semidirect
185. C₂²	C₂×Q₁₆×C₇₉	semidirect
195. C₂	#451×C₇₉	direct (N × H)

H ≅ G/N

type

2. C₂²×Q₁₆×C₇₉

C₂

semidirect

4. #451×C₇₉

C₂

direct (N × H)

5. C₂×#103×C₇₉

C₂

semidirect

16. C₂×Q₁₆×C₇₉

C₂²

semidirect

23. #103×C₇₉

C₂²

semidirect

56. C₂³×C₇₉

Q₁₆

semidirect

85. C₂²×C₇₉

C₂×Q₁₆

semidirect

95. C₂×C₇₉

#451

direct (N × H)

99. C₂×#451

C₇₉

direct (N × H)

100. C₇₉

C₂×#451

direct (N × H)

102. C₂²×Q₁₆

C₂×C₇₉

semidirect

104. #451

C₂×C₇₉

direct (N × H)

105. C₂×#103

C₂×C₇₉

semidirect

116. C₂×Q₁₆

C₂²×C₇₉

semidirect

123. #103

C₂²×C₇₉

semidirect

156. C₂³

Q₁₆×C₇₉

semidirect

185. C₂²

C₂×Q₁₆×C₇₉

semidirect

195. C₂

#451×C₇₉

direct (N × H)

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

subgroup	index
C₂³×Q₈×C₇₉	2
C₂²×Q₁₆×C₇₉	2
C₂×C₂²⋊Q₈×C₇₉	2
#451×C₇₉	2
C₂×#103×C₇₉	2
C₂×C₂²⋊C₈×C₇₉	2
C₂×#451	79

subgroup

index

C₂³×Q₈×C₇₉

C₂²×Q₁₆×C₇₉

C₂×C₂²⋊Q₈×C₇₉

#451×C₇₉

C₂×#103×C₇₉

C₂×C₂²⋊C₈×C₇₉

C₂×#451

Subgroups — C₂×#451×C₇₉ #23760621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#451×C79 #23760621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#451×C₇₉ #23760621