Group #23773744 — subgroups

Subgroups — #23773744

Order 10112.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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	#19099119	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099111	C₂	1	1	yes	maximal, characteristic
3	#19098933	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098932	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098927	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098921	C₂	1	4	yes	maximal, complemented
7	#19098556	C₂	1	4	yes	maximal, complemented
8	#97×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#490×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11929623	C₂²	1	2	yes	—
11	C₂×C₈×D₇₉	C₂²	1	2	yes	—
12	#14579161	C₂²	1	1	yes	characteristic
13	#14579160	C₂²	1	2	yes	—
14	#14579153	C₂²	1	1	yes	characteristic
15	#14579148	C₂²	1	2	yes	—
16	#14579139	—	2	2	no	—
17	#14579132	—	2	2	no	—
18	#14579126	—	2	2	no	—
19	D₄×Dic₇₉	—	2	2	no	—
20	#14579119	C₂²	1	2	yes	—
21	C₄²×D₇₉	C₂²	1	1	yes	characteristic
22	#14579086	C₂²	1	4	yes	—
23	#14579084	C₂²	1	4	yes	—
24	#14579082	C₂²	1	4	yes	—
25	#14579072	C₂²	1	1	yes	characteristic
26	#14579071	C₂²	1	2	yes	—
27	#127×C₇₉	C₂²	1	1	yes	characteristic
28	#125×C₇₉	C₂²	1	1	yes	characteristic
29	#102×C₇₉	C₂²	1	4	yes	—
30	#97×C₇₉	C₂²	1	1	yes	characteristic
31	#11929623	—	2	8	no	—
32	C₂×Dic₁₅₈	—	2	2	no	—
33	C₂×Dic₁₅₈	C₂³	1	2	yes	—
34	C₂×C₂²⋊D₇₉	—	2	2	no	—
35	C₂²×Dic₇₉	—	2	2	no	—
36	C₂×C₄×D₇₉	D₄	1	2	yes	—
37	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
38	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
39	C₈×D₇₉	—	2	4	no	—
40	C₄⋊Dic₇₉	—	2	2	no	—
41	C₄⋊Dic₇₉	C₂³	1	2	yes	—
42	Dic₇₉⋊C₄	—	2	2	no	—
43	Dic₇₉⋊C₄	—	2	2	no	—
44	C₂²⋊Dic₇₉	—	2	4	no	—
45	(C₂×D₇₉)⋊C₄	—	2	2	no	—
46	C₄×Dic₇₉	—	2	2	no	—
47	C₄×Dic₇₉	D₄	1	2	yes	—
48	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
49	C₂×D₄×C₇₉	—	2	2	no	—
50	C₂×D₄×C₇₉	C₂³	1	2	yes	—
51	C₂×C₈×C₇₉	C₂³	1	2	yes	—
52	C₄⋊C₄×C₇₉	—	2	2	no	—
53	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
54	C₄²×C₇₉	C₂³	1	1	yes	characteristic
55	C₂³×C₇₉	—	2	2	no	—
56	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
57	D₄×C₇₉	—	2	4	no	—
58	D₄×C₇₉	—	4	4	no	—
59	C₂×C₄×C₇₉	—	2	2	no	—
60	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
62	C₂²⋊D₇₉	—	4	4	no	—
63	C₂×Dic₇₉	—	2	2	no	—
64	C₂×Dic₇₉	—	2	2	no	—
65	C₂×Dic₇₉	—	4	4	no	—
66	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
67	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
68	C₄×D₇₉	—	4	2	no	—
69	C₄×D₇₉	#41	1	4	yes	—
70	Dic₁₅₈	—	2	4	no	—
71	Dic₁₅₈	—	4	4	no	—
72	C₈×C₇₉	—	2	2	no	—
73	C₇₉⋊C₈	—	2	2	no	—
74	C₂²×C₇₉	—	4	2	no	—
75	C₂²×C₇₉	—	4	4	no	—
76	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
77	C₂×D₇₉	—	2	2	no	—
78	C₂×D₇₉	#124	1	2	yes	—
79	C₄×C₇₉	—	2	2	no	—
80	C₄×C₇₉	—	4	2	no	—
81	C₄×C₇₉	C₂×#41	1	2	yes	—
82	Dic₇₉	—	2	2	no	—
83	Dic₇₉	—	4	2	no	—
84	Dic₇₉	—	4	2	no	—
85	Dic₇₉	#124	1	2	yes	—
86	C₂×C₇₉	—	8	2	no	—
87	C₂×C₇₉	C₂×#124	1	1	yes	characteristic
88	C₂×C₇₉	#575	1	2	yes	—
89	D₇₉	—	2	2	no	—
90	#3135	—	79	1	no	maximal, Sylow
91	C₇₉	#3135	1	1	yes	characteristic, complemented, Sylow
92	#533	—	79	1	no	—
93	#532	—	79	1	no	—
94	#491	—	79	1	no	—
95	#491	—	79	1	no	—
96	#490	—	79	1	no	—
97	#490	D₇₉	1	1	yes	characteristic, complemented
98	#489	—	79	4	no	—
99	#416	—	79	4	no	—
100	C₂×#97	—	79	1	no	—
101	C₂×#41	—	79	2	no	—
102	C₂²×C₈	—	79	2	no	—
103	C₄⋊Q₈	—	79	2	no	—
104	C₄⋊Q₈	—	79	1	no	—
105	#127	C₂×D₇₉	1	1	yes	characteristic
106	#125	—	79	1	no	—
107	#125	C₂×D₇₉	1	1	yes	characteristic
108	#124	—	79	2	no	—
109	C₂²⋊Q₈	—	158	2	no	—
110	#121	—	158	2	no	—
111	C₄×Q₈	—	158	2	no	—
112	C₄×D₄	—	158	2	no	—
113	#117	—	79	2	no	—
114	C₂×C₄²	—	79	1	no	—
115	#103	—	79	4	no	—
116	#103	—	79	4	no	—
117	#102	—	79	4	no	—
118	#102	C₂×D₇₉	1	4	yes	—
119	#97	—	79	2	no	—
120	#97	—	79	1	no	—
121	#97	C₂×D₇₉	1	1	yes	characteristic
122	#41	—	158	8	no	—
123	C₂×Q₈	—	79	2	no	—
124	C₂×Q₈	—	158	2	no	—
125	C₂×D₄	—	2	2	no	—
126	C₂×D₄	—	158	2	no	—
127	C₂×D₄	C₂²×D₇₉	1	2	yes	—
128	C₂²×C₄	—	79	2	no	—
129	C₂²×C₄	—	79	1	no	—
130	C₂²×C₄	—	158	2	no	—
131	C₂×C₈	—	79	2	no	—
132	C₂×C₈	—	158	4	no	—
133	C₂×C₈	C₂²×D₇₉	1	2	yes	—
134	C₄⋊C₄	—	2	2	no	—
135	C₄⋊C₄	—	79	2	no	—
136	C₄⋊C₄	—	158	2	no	—
137	C₄⋊C₄	—	158	2	no	—
138	C₄⋊C₄	—	158	2	no	—
139	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
140	C₂²⋊C₄	—	158	2	no	—
141	C₂²⋊C₄	—	158	4	no	—
142	C₄²	—	79	2	no	—
143	C₄²	—	79	1	no	—
144	C₄²	—	158	2	no	—
145	C₄²	C₂²×D₇₉	1	1	yes	characteristic
146	C₂³	—	2	2	no	—
147	C₂³	—	79	1	no	—
148	Q₈	—	316	4	no	—
149	Q₈	—	158	4	no	—
150	D₄	—	2	4	no	—
151	D₄	—	4	4	no	—
152	D₄	—	316	4	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	316	2	no	—
155	C₂×C₄	—	316	4	no	—
156	C₂×C₄	—	79	1	no	—
157	C₂×C₄	—	79	4	no	—
158	C₂×C₄	—	79	2	no	—
159	C₂×C₄	—	158	2	no	—
160	C₂×C₄	—	158	2	no	—
161	C₂×C₄	D₄×D₇₉	1	2	yes	—
162	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
163	C₈	—	2	2	no	—
164	C₈	—	158	2	no	—
165	C₂²	—	4	2	no	—
166	C₂²	—	4	4	no	—
167	C₂²	—	79	2	no	—
168	C₂²	—	158	2	no	—
169	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
170	C₄	—	2	2	no	—
171	C₄	—	4	2	no	—
172	C₄	—	316	2	no	—
173	C₄	—	316	2	no	—
174	C₄	—	79	2	no	—
175	C₄	—	158	2	no	—
176	C₄	#41×D₇₉	1	2	yes	—
177	C₂	—	8	2	no	—
178	C₂	—	158	2	no	—
179	C₂	#124×D₇₉	1	1	yes	characteristic
180	C₂	#19099359	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099119

C₂

yes

maximal, characteristic, complemented

#19099111

C₂

yes

maximal, characteristic

#19098933

C₂

yes

maximal, characteristic, complemented

#19098932

C₂

yes

maximal, characteristic, complemented

#19098927

C₂

yes

maximal, characteristic, complemented

#19098921

C₂

yes

maximal, complemented

#19098556

C₂

yes

maximal, complemented

#97×D₇₉

C₂

yes

maximal, characteristic, complemented

#490×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929623

C₂²

yes

—

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

characteristic

#14579160

C₂²

yes

—

#14579153

C₂²

yes

characteristic

#14579148

C₂²

yes

—

#14579139

—

#14579132

—

#14579126

—

D₄×Dic₇₉

—

#14579119

C₂²

yes

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579086

C₂²

yes

—

#14579084

C₂²

yes

—

#14579082

C₂²

yes

—

#14579072

C₂²

yes

characteristic

#14579071

C₂²

yes

—

#127×C₇₉

C₂²

yes

characteristic

#125×C₇₉

C₂²

yes

characteristic

#102×C₇₉

C₂²

yes

—

#97×C₇₉

C₂²

yes

characteristic

#11929623

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂³

yes

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

—

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂³

yes

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

C₂×D₄

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

#41

yes

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

#124

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×#41

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

#124

yes

—

C₂×C₇₉

—

C₂×C₇₉

C₂×#124

yes

characteristic

C₂×C₇₉

#575

yes

—

D₇₉

—

#3135

—

maximal, Sylow

C₇₉

#3135

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic, complemented

#489

—

#416

—

100

C₂×#97

—

101

C₂×#41

—

102

C₂²×C₈

—

103

C₄⋊Q₈

—

104

C₄⋊Q₈

—

105

#127

C₂×D₇₉

yes

characteristic

106

#125

—

107

#125

C₂×D₇₉

yes

characteristic

108

#124

—

109

C₂²⋊Q₈

—

158

—

110

#121

—

158

—

111

C₄×Q₈

—

158

—

112

C₄×D₄

—

158

—

113

#117

—

114

C₂×C₄²

—

115

#103

—

116

#103

—

117

#102

—

118

#102

C₂×D₇₉

yes

—

119

#97

—

120

#97

—

121

#97

C₂×D₇₉

yes

characteristic

122

#41

—

158

—

123

C₂×Q₈

—

124

C₂×Q₈

—

158

—

125

C₂×D₄

—

126

C₂×D₄

—

158

—

127

C₂×D₄

C₂²×D₇₉

yes

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

158

—

131

C₂×C₈

—

132

C₂×C₈

—

158

—

133

C₂×C₈

C₂²×D₇₉

yes

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

158

—

137

C₄⋊C₄

—

158

—

138

C₄⋊C₄

—

158

—

139

C₄⋊C₄

C₂²×D₇₉

yes

—

140

C₂²⋊C₄

—

158

—

141

C₂²⋊C₄

—

158

—

142

C₄²

—

143

C₄²

—

144

C₄²

—

158

—

145

C₄²

C₂²×D₇₉

yes

characteristic

146

C₂³

—

147

C₂³

—

148

Q₈

—

316

—

149

Q₈

—

158

—

150

D₄

—

151

D₄

—

152

D₄

—

316

—

153

C₂×C₄

—

154

C₂×C₄

—

316

—

155

C₂×C₄

—

316

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

158

—

160

C₂×C₄

—

158

—

161

C₂×C₄

D₄×D₇₉

yes

—

162

C₂×C₄

C₂³×D₇₉

yes

characteristic

163

C₈

—

164

C₈

—

158

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

158

—

169

C₂²

C₂×D₄×D₇₉

yes

characteristic

170

C₄

—

171

C₄

—

172

C₄

—

316

—

173

C₄

—

316

—

174

C₄

—

175

C₄

—

158

—

176

C₄

#41×D₇₉

yes

—

177

C₂

—

178

C₂

—

158

—

179

C₂

#124×D₇₉

yes

characteristic

180

C₂

#19099359

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#490×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	#19099111	C₂
hypercenter	#490	D₇₉
hypocenter	C₇₉	#3135
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #490

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#490×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

C₂

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #490

N	H ≅ G/N	type
1. #19099119	C₂	semidirect
3. #19098933	C₂	semidirect
4. #19098932	C₂	semidirect
5. #19098927	C₂	semidirect
6. #19098921	C₂	semidirect
7. #19098556	C₂	semidirect
8. #97×D₇₉	C₂	semidirect
9. #490×C₇₉	C₂	semidirect
91. C₇₉	#3135	semidirect
97. #490	D₇₉	semidirect

H ≅ G/N

type

1. #19099119

C₂

semidirect

3. #19098933

C₂

semidirect

4. #19098932

C₂

semidirect

5. #19098927

C₂

semidirect

6. #19098921

C₂

semidirect

7. #19098556

C₂

semidirect

8. #97×D₇₉

C₂

semidirect

9. #490×C₇₉

C₂

semidirect

91. C₇₉

#3135

semidirect

97. #490

D₇₉

semidirect

Subgroups — #23773744

Conjugacy classes of subgroups

Complements