Group #23764865 — subgroups

Subgroups — #23764865

Order 10112.

184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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	#19098573	C₂	1	1	yes	maximal, characteristic
2	#19098573	C₂	1	1	yes	maximal, characteristic
3	C₂×#14579079	C₂	1	1	yes	maximal, characteristic
4	#19098335	C₂	1	1	yes	maximal, characteristic
5	#19098334	C₂	1	1	yes	maximal, characteristic
6	#19098320	C₂	1	1	yes	maximal, characteristic
7	#430×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
9	C₂×#11929608	C₂²	1	1	yes	characteristic
10	#14579120	C₂²	1	1	yes	characteristic
11	#14579120	C₂²	1	1	yes	characteristic
12	#14579086	—	2	2	no	—
13	#14579086	—	2	2	no	—
14	#14579079	—	2	2	no	—
15	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	#108×C₇₉	—	2	2	no	—
19	C₂×Dic₁₅₈	—	2	1	no	—
20	C₂×Dic₁₅₈	—	2	1	no	—
21	C₂×Dic₁₅₈	—	2	1	no	—
22	C₂×Dic₁₅₈	—	2	1	no	—
23	C₂×Dic₁₅₈	—	2	1	no	—
24	C₂×Dic₁₅₈	D₄	1	2	yes	—
25	C₂²×Dic₇₉	—	2	1	no	—
26	#11929608	—	2	1	no	—
27	#11929608	—	2	1	no	—
28	C₂×C₇₉⋊C₈	—	2	1	no	—
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	C₂²⋊Dic₇₉	—	2	1	no	—
32	C₂²⋊Dic₇₉	—	2	1	no	—
33	C₄×Dic₇₉	—	2	1	no	—
34	C₄×Dic₇₉	—	2	1	no	—
35	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
36	M₁₆×C₇₉	—	2	1	no	—
37	M₁₆×C₇₉	—	2	1	no	—
38	M₁₆×C₇₉	—	2	1	no	—
39	M₁₆×C₇₉	—	2	1	no	—
40	M₁₆×C₇₉	—	2	1	no	—
41	M₁₆×C₇₉	—	2	1	no	—
42	C₂×C₈×C₇₉	—	2	1	no	—
43	C₂×C₈×C₇₉	—	2	1	no	—
44	C₂×C₈×C₇₉	D₄	1	2	yes	—
45	C₂³×C₇₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
49	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
50	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
51	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
52	C₂×Dic₇₉	—	2	2	no	—
53	C₂×Dic₇₉	—	4	1	no	—
54	C₂×Dic₇₉	—	4	1	no	—
55	C₂×Dic₇₉	—	4	1	no	—
56	C₂×Dic₇₉	—	4	1	no	—
57	Dic₁₅₈	—	2	2	no	—
58	Dic₁₅₈	—	2	2	no	—
59	Dic₁₅₈	—	4	1	no	—
60	Dic₁₅₈	—	4	1	no	—
61	C₈×C₇₉	—	2	2	no	—
62	C₈×C₇₉	—	4	1	no	—
63	C₈×C₇₉	—	4	1	no	—
64	C₇₉⋊C₈	—	4	1	no	—
65	C₂²×C₇₉	—	4	1	no	—
66	C₂²×C₇₉	#123	1	1	yes	characteristic
67	C₂²×C₇₉	#124	1	1	yes	characteristic
68	C₂²×C₇₉	#126	1	1	yes	characteristic
69	C₄×C₇₉	#121	1	1	yes	characteristic
70	C₄×C₇₉	#123	1	1	yes	characteristic
71	C₄×C₇₉	#123	1	1	yes	characteristic
72	C₄×C₇₉	#126	1	1	yes	characteristic
73	Dic₇₉	—	4	2	no	—
74	Dic₇₉	—	8	1	no	—
75	Dic₇₉	—	8	1	no	—
76	C₂×C₇₉	—	2	1	no	—
77	C₂×C₇₉	—	2	1	no	—
78	C₂×C₇₉	—	2	1	no	—
79	C₂×C₇₉	#397	1	1	yes	characteristic
80	#2082	—	79	1	no	maximal, Sylow
81	C₇₉	#2082	1	1	yes	characteristic, complemented, Sylow
82	#430	D₇₉	1	1	yes	characteristic
83	#419	—	79	1	no	—
84	#419	—	79	1	no	—
85	C₂×#101	—	79	1	no	—
86	#344	—	79	1	no	—
87	#344	—	79	1	no	—
88	H(3,ℤ/4)	—	79	1	no	—
89	C₂²×Q₈	—	79	1	no	—
90	C₂×M₁₆	—	79	1	no	—
91	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
92	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
93	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic
94	#117	—	79	1	no	—
95	#117	—	79	1	no	—
96	#108	—	2	2	no	—
97	#103	—	158	2	no	—
98	#103	—	158	2	no	—
99	#101	—	158	2	no	—
100	C₂×Q₈	—	79	2	no	—
101	C₂×Q₈	—	158	1	no	—
102	C₂×Q₈	—	158	1	no	—
103	C₂×Q₈	—	158	1	no	—
104	C₂×Q₈	—	158	1	no	—
105	C₂×Q₈	—	158	1	no	—
106	C₂²×C₄	—	158	1	no	—
107	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
108	M₁₆	—	2	1	no	—
109	M₁₆	—	2	1	no	—
110	M₁₆	—	2	1	no	—
111	M₁₆	—	2	1	no	—
112	M₁₆	—	2	1	no	—
113	M₁₆	—	2	1	no	—
114	M₁₆	—	158	1	no	—
115	M₁₆	—	158	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	2	1	no	—
118	C₂×C₈	—	158	1	no	—
119	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
120	C₄⋊C₄	—	158	1	no	—
121	C₄⋊C₄	—	158	1	no	—
122	C₂²⋊C₄	—	158	1	no	—
123	C₂²⋊C₄	—	158	1	no	—
124	C₄²	—	158	1	no	—
125	C₄²	—	158	1	no	—
126	C₂³	#11929625	1	1	yes	characteristic
127	Q₈	—	316	1	no	—
128	Q₈	—	316	1	no	—
129	Q₈	—	158	2	no	—
130	Q₈	—	158	2	no	—
131	C₂×C₄	—	316	1	no	—
132	C₂×C₄	—	316	1	no	—
133	C₂×C₄	—	316	1	no	—
134	C₂×C₄	—	316	1	no	—
135	C₂×C₄	—	158	2	no	—
136	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
137	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
138	C₂×C₄	#11929623	1	1	yes	characteristic
139	C₂×C₄	#11929624	1	1	yes	characteristic
140	C₂×C₄	#11929624	1	1	yes	characteristic
141	C₂×C₄	#11929625	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	4	1	no	—
144	C₈	—	4	1	no	—
145	C₈	—	316	1	no	—
146	C₂²	—	4	1	no	—
147	C₂²	#14579146	1	1	yes	characteristic
148	C₂²	#14579150	1	1	yes	characteristic
149	C₂²	#14579156	1	1	yes	characteristic
150	C₄	—	316	2	no	—
151	C₄	—	632	1	no	—
152	C₄	—	632	1	no	—
153	C₄	#14579132	1	1	yes	characteristic
154	C₄	#14579144	1	1	yes	characteristic
155	C₄	#14579146	1	1	yes	characteristic
156	C₄	#14579156	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	#19098489	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098573

C₂

yes

maximal, characteristic

#19098573

C₂

yes

maximal, characteristic

C₂×#14579079

C₂

yes

maximal, characteristic

#19098335

C₂

yes

maximal, characteristic

#19098334

C₂

yes

maximal, characteristic

#19098320

C₂

yes

maximal, characteristic

#430×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

characteristic

#14579120

C₂²

yes

characteristic

#14579120

C₂²

yes

—

—

—

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

C₂×M₁₆×C₇₉

C₂²

yes

characteristic

#108×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

D₄

yes

—

C₂²×Dic₇₉

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₂³×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#430

D₇₉

yes

—

—

—

—

—

—

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂×M₁₆

C₂×D₇₉

yes

characteristic

C₂×M₁₆

C₂×D₇₉

yes

—

—

—

—

158

—

#103

—

158

—

#101

—

158

—

100

C₂×Q₈

—

101

C₂×Q₈

—

158

—

102

C₂×Q₈

—

158

—

103

C₂×Q₈

—

158

—

104

C₂×Q₈

—

158

—

105

C₂×Q₈

—

158

—

106

C₂²×C₄

—

158

—

107

C₂²×C₄

C₂²×D₇₉

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

158

—

115

M₁₆

—

158

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

158

—

119

C₂×C₈

C₂²⋊D₇₉

yes

—

120

C₄⋊C₄

—

158

—

121

C₄⋊C₄

—

158

—

122

C₂²⋊C₄

—

158

—

123

C₂²⋊C₄

—

158

—

124

C₄²

—

158

—

125

C₄²

—

158

—

126

C₂³

#11929625

yes

characteristic

127

Q₈

—

316

—

128

Q₈

—

316

—

129

Q₈

—

158

—

130

Q₈

—

158

—

131

C₂×C₄

—

316

—

132

C₂×C₄

—

316

—

133

C₂×C₄

—

316

—

134

C₂×C₄

—

316

—

135

C₂×C₄

—

158

—

136

C₂×C₄

D₄×D₇₉

yes

characteristic

137

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

138

C₂×C₄

#11929623

yes

characteristic

139

C₂×C₄

#11929624

yes

characteristic

140

C₂×C₄

#11929624

yes

characteristic

141

C₂×C₄

#11929625

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

316

—

146

C₂²

—

147

C₂²

#14579146

yes

characteristic

148

C₂²

#14579150

yes

characteristic

149

C₂²

#14579156

yes

characteristic

150

C₄

—

316

—

151

C₄

—

632

—

152

C₄

—

632

—

153

C₄

#14579132

yes

characteristic

154

C₄

#14579144

yes

characteristic

155

C₄

#14579146

yes

characteristic

156

C₄

#14579156

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#19098489

yes

characteristic

	subgroup	G/H
center	C₂	#19098489
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#430×C₇₉	C₂
socle	C₂×C₇₉	#397
prime radical	C₂³×C₇₉	#41
hypercenter	#430	D₇₉
hypocenter	C₇₉	#2082
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₂

#19098489

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#430×C₇₉

C₂

C₂×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
81. C₇₉	#2082	semidirect

H ≅ G/N

type

81. C₇₉

#2082

semidirect

Subgroups — #23764865

Conjugacy classes of subgroups

Complements