Group #20308440 — subgroups

Subgroups — C₂₉×#13540 #20308440

Order 7424.

234 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 102 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	C₂₉×#1946	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1849	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1389	C₂	1	2	yes	maximal
4	C₂₉×#1388	C₂	1	2	yes	maximal
5	C₂₉×#1375	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×M₃₂	C₂²	1	2	yes	—
7	C₂×C₂₉×#108	—	2	1	no	—
8	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
9	C₂×C₂₉×#108	C₂²	1	2	yes	—
10	C₂₉×#427	C₂²	1	1	yes	characteristic
11	C₂₉×#424	—	2	1	no	—
12	C₂₉×#423	—	2	1	no	—
13	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
14	C₂₉×#339	—	2	1	no	—
15	C₂×M₁₆×C₂₉	—	2	2	no	—
16	C₂×M₁₆×C₂₉	—	2	1	no	—
17	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
19	C₂₉×#117	—	2	1	no	—
20	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
21	C₂₉×M₃₂	—	2	2	no	—
22	C₂₉×M₃₂	—	2	2	no	—
23	C₂×C₁₆×C₂₉	—	2	2	no	—
24	C₂₉×#108	—	2	2	no	—
25	C₂₉×#108	—	2	4	no	—
26	C₂₉×#108	—	4	2	no	—
27	C₂₉×#107	—	2	1	no	—
28	C₂₉×#106	Q₈	1	2	yes	—
29	C₂₉×C₄⋊C₈	—	4	2	no	—
30	C₂₉×C₄⋊C₈	—	4	2	no	—
31	C₂₉×#97	—	2	2	no	—
32	C₂²×C₄×C₂₉	—	2	1	no	—
33	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	M₁₆×C₂₉	—	4	1	no	—
35	M₁₆×C₂₉	—	4	2	no	—
36	M₁₆×C₂₉	—	4	2	no	—
37	M₁₆×C₂₉	—	4	1	no	—
38	C₂×C₈×C₂₉	—	2	1	no	—
39	C₂×C₈×C₂₉	—	2	1	no	—
40	C₂×C₈×C₂₉	—	4	1	no	—
41	C₂×C₈×C₂₉	—	4	2	no	—
42	C₂×C₈×C₂₉	D₈	1	2	yes	—
43	C₂×C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₈×C₂₉	#41	1	2	yes	—
45	C₂×C₈×C₂₉	#41	1	2	yes	—
46	C₂×C₈×C₂₉	#41	1	1	yes	characteristic
47	C₄⋊C₄×C₂₉	—	2	2	no	—
48	C₂²⋊C₄×C₂₉	—	4	1	no	—
49	C₄²×C₂₉	—	2	1	no	—
50	C₄²×C₂₉	—	4	1	no	—
51	C₄²×C₂₉	SD₁₆	1	2	yes	—
52	C₁₆×C₂₉	—	4	2	no	—
53	#13540	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂³×C₂₉	#137	1	1	yes	characteristic
55	C₂×C₄×C₂₉	—	2	2	no	—
56	C₂×C₄×C₂₉	—	4	2	no	—
57	C₂×C₄×C₂₉	—	8	1	no	—
58	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
60	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
61	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
62	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
63	C₂×C₄×C₂₉	#137	1	1	yes	characteristic
64	C₈×C₂₉	—	2	2	no	—
65	C₈×C₂₉	—	8	1	no	—
66	C₈×C₂₉	—	8	2	no	—
67	C₈×C₂₉	#125	1	2	yes	—
68	C₈×C₂₉	#126	1	2	yes	—
69	#1946	C₂×C₂₉	1	1	yes	characteristic
70	#1849	C₂×C₂₉	1	1	yes	characteristic
71	#1389	C₂×C₂₉	1	2	yes	—
72	#1388	C₂×C₂₉	1	2	yes	—
73	#1375	C₂×C₂₉	1	1	yes	characteristic
74	C₂²×C₂₉	—	4	1	no	—
75	C₂²×C₂₉	#474	1	1	yes	characteristic
76	C₂²×C₂₉	#483	1	1	yes	characteristic
77	C₂²×C₂₉	#491	1	1	yes	characteristic
78	C₄×C₂₉	—	4	2	no	—
79	C₄×C₂₉	—	8	2	no	—
80	C₄×C₂₉	#400	1	1	yes	characteristic
81	C₄×C₂₉	#475	1	1	yes	characteristic
82	C₄×C₂₉	#480	1	1	yes	characteristic
83	C₄×C₂₉	#486	1	1	yes	characteristic
84	C₂×M₃₂	C₂²×C₂₉	1	2	yes	—
85	C₂×#108	—	2	1	no	—
86	C₂×#108	C₂²×C₂₉	1	2	yes	—
87	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
88	#427	C₂²×C₂₉	1	1	yes	characteristic
89	#424	—	2	1	no	—
90	#423	—	2	1	no	—
91	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
92	#339	—	2	1	no	—
93	C₂×C₂₉	—	2	1	no	—
94	C₂×C₂₉	—	2	1	no	—
95	C₂×C₂₉	—	2	1	no	—
96	C₂×C₂₉	#2099	1	1	yes	characteristic
97	C₂×M₁₆	—	2	1	no	—
98	C₂×M₁₆	—	2	2	no	—
99	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
100	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
101	#117	—	2	1	no	—
102	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
103	M₃₂	—	2	2	no	—
104	M₃₂	—	2	2	no	—
105	C₂×C₁₆	—	2	2	no	—
106	#108	—	2	2	no	—
107	#108	—	2	4	no	—
108	#108	—	4	2	no	—
109	#107	—	2	1	no	—
110	#106	Q₈×C₂₉	1	2	yes	—
111	C₄⋊C₈	—	4	2	no	—
112	C₄⋊C₈	—	4	2	no	—
113	#97	—	2	2	no	—
114	C₂₉	#13540	1	1	yes	characteristic, direct product factor, Sylow
115	C₂²×C₄	—	2	1	no	—
116	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
117	M₁₆	—	4	1	no	—
118	M₁₆	—	4	2	no	—
119	M₁₆	—	4	2	no	—
120	M₁₆	—	4	1	no	—
121	C₂×C₈	—	2	1	no	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	4	1	no	—
124	C₂×C₈	—	4	2	no	—
125	C₂×C₈	D₈×C₂₉	1	2	yes	—
126	C₂×C₈	C₂×Q₈×C₂₉	1	1	yes	characteristic
127	C₂×C₈	#41×C₂₉	1	2	yes	—
128	C₂×C₈	#41×C₂₉	1	2	yes	—
129	C₂×C₈	#41×C₂₉	1	1	yes	characteristic
130	C₄⋊C₄	—	2	2	no	—
131	C₂²⋊C₄	—	4	1	no	—
132	C₄²	—	2	1	no	—
133	C₄²	—	4	1	no	—
134	C₄²	SD₁₆×C₂₉	1	2	yes	—
135	C₁₆	—	4	2	no	—
136	C₂³	C₂₉×#137	1	1	yes	characteristic
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	4	2	no	—
139	C₂×C₄	—	8	1	no	—
140	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
142	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
143	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
144	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
145	C₂×C₄	C₂₉×#137	1	1	yes	characteristic
146	C₈	—	2	2	no	—
147	C₈	—	8	1	no	—
148	C₈	—	8	2	no	—
149	C₈	C₂₉×#125	1	2	yes	—
150	C₈	C₂₉×#126	1	2	yes	—
151	C₂²	—	4	1	no	—
152	C₂²	C₂₉×#474	1	1	yes	characteristic
153	C₂²	C₂₉×#483	1	1	yes	characteristic
154	C₂²	C₂₉×#491	1	1	yes	characteristic
155	C₄	—	4	2	no	—
156	C₄	—	8	2	no	—
157	C₄	C₂₉×#400	1	1	yes	characteristic
158	C₄	C₂₉×#475	1	1	yes	characteristic
159	C₄	C₂₉×#480	1	1	yes	characteristic
160	C₄	C₂₉×#486	1	1	yes	characteristic
161	C₂	—	2	1	no	—
162	C₂	—	2	1	no	—
163	C₂	—	2	1	no	—
164	C₂	C₂₉×#2099	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#1946

C₂

yes

maximal, characteristic

C₂₉×#1849

C₂

yes

maximal, characteristic

C₂₉×#1389

C₂

yes

maximal

C₂₉×#1388

C₂

yes

maximal

C₂₉×#1375

C₂

yes

maximal, characteristic

C₂×C₂₉×M₃₂

C₂²

yes

—

C₂×C₂₉×#108

—

C₂×C₂₉×#108

C₂²

yes

characteristic

C₂×C₂₉×#108

C₂²

yes

—

C₂₉×#427

C₂²

yes

characteristic

C₂₉×#424

—

C₂₉×#423

—

C₂×C₂₉×#97

C₂²

yes

characteristic

C₂₉×#339

—

C₂×M₁₆×C₂₉

—

C₂×M₁₆×C₂₉

—

C₂²×C₈×C₂₉

D₄

yes

characteristic

C₂²×C₈×C₂₉

C₂³

yes

characteristic

C₂₉×#117

—

C₂×C₄²×C₂₉

D₄

yes

characteristic

C₂₉×M₃₂

—

C₂₉×M₃₂

—

C₂×C₁₆×C₂₉

—

C₂₉×#108

—

C₂₉×#108

—

C₂₉×#108

—

C₂₉×#107

—

C₂₉×#106

Q₈

yes

—

C₂₉×C₄⋊C₈

—

C₂₉×C₄⋊C₈

—

C₂₉×#97

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×D₄

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₈

yes

—

C₂×C₈×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₂₉

#41

yes

—

C₂×C₈×C₂₉

#41

yes

—

C₂×C₈×C₂₉

#41

yes

characteristic

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

SD₁₆

yes

—

C₁₆×C₂₉

—

#13540

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

#137

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

C₂×D₈

yes

characteristic

C₂×C₄×C₂₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₂₉

#137

yes

characteristic

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

#125

yes

—

C₈×C₂₉

#126

yes

—

#1946

C₂×C₂₉

yes

characteristic

#1849

C₂×C₂₉

yes

characteristic

#1389

C₂×C₂₉

yes

—

#1388

C₂×C₂₉

yes

—

#1375

C₂×C₂₉

yes

characteristic

C₂²×C₂₉

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₂×M₃₂

C₂²×C₂₉

yes

—

C₂×#108

—

C₂×#108

C₂²×C₂₉

yes

—

C₂×#108

C₂²×C₂₉

yes

characteristic

#427

C₂²×C₂₉

yes

characteristic

#424

—

#423

—

C₂×#97

C₂²×C₂₉

yes

characteristic

#339

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#2099

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

D₄×C₂₉

yes

characteristic

100

C₂²×C₈

C₂³×C₂₉

yes

characteristic

101

#117

—

102

C₂×C₄²

D₄×C₂₉

yes

characteristic

103

M₃₂

—

104

M₃₂

—

105

C₂×C₁₆

—

106

#108

—

107

#108

—

108

#108

—

109

#107

—

110

#106

Q₈×C₂₉

yes

—

111

C₄⋊C₈

—

112

C₄⋊C₈

—

113

#97

—

114

C₂₉

#13540

yes

characteristic, direct product factor, Sylow

115

C₂²×C₄

—

116

C₂²×C₄

C₂×D₄×C₂₉

yes

characteristic

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

D₈×C₂₉

yes

—

126

C₂×C₈

C₂×Q₈×C₂₉

yes

characteristic

127

C₂×C₈

#41×C₂₉

yes

—

128

C₂×C₈

#41×C₂₉

yes

—

129

C₂×C₈

#41×C₂₉

yes

characteristic

130

C₄⋊C₄

—

131

C₂²⋊C₄

—

132

C₄²

—

133

C₄²

—

134

C₄²

SD₁₆×C₂₉

yes

—

135

C₁₆

—

136

C₂³

C₂₉×#137

yes

characteristic

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

C₂₉×C₂²⋊Q₈

yes

characteristic

141

C₂×C₄

C₂₉×#123

yes

characteristic

142

C₂×C₄

C₂₉×#124

yes

characteristic

143

C₂×C₄

C₂×D₈×C₂₉

yes

characteristic

144

C₂×C₄

C₂×SD₁₆×C₂₉

yes

characteristic

145

C₂×C₄

C₂₉×#137

yes

characteristic

146

C₈

—

147

C₈

—

148

C₈

—

149

C₈

C₂₉×#125

yes

—

150

C₈

C₂₉×#126

yes

—

151

C₂²

—

152

C₂²

C₂₉×#474

yes

characteristic

153

C₂²

C₂₉×#483

yes

characteristic

154

C₂²

C₂₉×#491

yes

characteristic

155

C₄

—

156

C₄

—

157

C₄

C₂₉×#400

yes

characteristic

158

C₄

C₂₉×#475

yes

characteristic

159

C₄

C₂₉×#480

yes

characteristic

160

C₄

C₂₉×#486

yes

characteristic

161

C₂

—

162

C₂

—

163

C₂

—

164

C₂

C₂₉×#2099

yes

characteristic

	subgroup	G/H
center	C₄×C₂₉	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₂₉
socle	C₂×C₂₉	#2099
prime radical	C₂³×C₂₉	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₂₉×#97 ◁ G

subgroup

G/H

center

C₄×C₂₉

#486

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₂₉

C₂×C₂₉

C₂³×C₂₉

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₂₉×#97 ◁ G

N	H ≅ G/N	type
53. #13540	C₂₉	direct (N × H)
114. C₂₉	#13540	direct (N × H)

H ≅ G/N

type

53. #13540

C₂₉

direct (N × H)

114. C₂₉

#13540

direct (N × H)

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

subgroup	index
C₂₉×#1946	2
C₂₉×#1849	2
C₂₉×#1389	2
C₂₉×#1388	2
C₂₉×#1375	2
#13540	29

subgroup

index

C₂₉×#1946

C₂₉×#1849

C₂₉×#1389

C₂₉×#1388

C₂₉×#1375

#13540

Subgroups — C₂₉×#13540 #20308440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#13540 #20308440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#13540 #20308440