Group #13115958 — subgroups

Subgroups — #13115958

Order 1664.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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	C₂×#88163	C₂	1	2	yes	maximal
2	C₂²×Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88064	C₂	1	2	yes	maximal, complemented
4	#11718771	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#6127	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₆	C₂²	1	2	yes	—
8	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#6099	C₂²	1	1	yes	characteristic
11	#88163	—	2	4	no	—
12	#88163	—	2	4	no	—
13	C₂×Dic₅₂	—	2	4	no	—
14	C₂×Dic₅₂	—	2	2	no	—
15	C₂×Dic₅₂	—	2	2	no	—
16	C₂×#6095	—	2	2	no	—
17	#88064	—	2	4	no	—
18	#88060	—	2	2	no	—
19	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₂²⋊D₁₃	—	2	1	no	—
21	C₂²×Dic₁₃	—	2	2	no	—
22	#6127	—	2	2	no	—
23	#6127	—	2	2	no	—
24	C₂×D₅₂	D₄	1	1	yes	characteristic
25	C₂×C₄×D₁₃	—	2	1	no	—
26	C₂×Dic₂₆	—	2	2	no	—
27	C₂×Dic₂₆	—	2	2	no	—
28	C₂×Dic₂₆	—	2	2	no	—
29	C₂×Dic₂₆	—	2	2	no	—
30	C₂×Dic₂₆	—	2	2	no	—
31	C₂×Dic₂₆	D₄	1	1	yes	characteristic
32	C₂×Dic₂₆	D₄	1	4	yes	—
33	C₁₃×M₁₆	—	2	2	no	—
34	C₁₃×M₁₆	D₄	1	4	yes	—
35	C₂×C₈×C₁₃	—	2	2	no	—
36	C₂×C₈×C₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	D₄	1	2	yes	—
38	#6099	—	2	2	no	—
39	C₂×#1055	—	2	1	no	—
40	Dic₅₂	—	2	8	no	—
41	Dic₅₂	—	2	8	no	—
42	#6095	—	2	8	no	—
43	#2020	—	13	1	no	maximal, Sylow
44	C₂³×C₁₃	#41	1	1	yes	characteristic
45	C₂²×D₁₃	—	2	1	no	—
46	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
50	C₂²⋊D₁₃	—	4	2	no	—
51	C₂×Dic₁₃	—	2	4	no	—
52	C₂×Dic₁₃	—	2	1	no	—
53	C₂×Dic₁₃	—	4	2	no	—
54	C₂×Dic₁₃	—	4	2	no	—
55	D₅₂	—	2	2	no	—
56	C₄×D₁₃	—	4	1	no	—
57	C₄×D₁₃	—	4	1	no	—
58	Dic₂₆	—	2	4	no	—
59	Dic₂₆	—	2	4	no	—
60	Dic₂₆	—	2	2	no	—
61	Dic₂₆	—	4	2	no	—
62	Dic₂₆	—	4	2	no	—
63	C₈×C₁₃	—	2	4	no	—
64	C₈×C₁₃	—	2	2	no	—
65	#1055	—	4	1	no	—
66	C₂×#137	—	13	2	no	—
67	C₂²×Q₁₆	—	13	1	no	—
68	C₂×#101	—	13	2	no	—
69	#408	—	13	1	no	—
70	#341	D₁₃	1	1	yes	characteristic, complemented
71	C₂²×C₁₃	—	2	2	no	—
72	C₂²×C₁₃	#121	1	2	yes	—
73	C₂²×C₁₃	#121	1	1	yes	characteristic
74	C₂×D₁₃	—	4	1	no	—
75	C₂×D₁₃	—	4	2	no	—
76	C₄×C₁₃	#120	1	1	yes	characteristic
77	C₄×C₁₃	#120	1	2	yes	—
78	C₄×C₁₃	#127	1	1	yes	characteristic
79	Dic₁₃	—	4	4	no	—
80	Dic₁₃	—	4	1	no	—
81	C₂×#41	—	13	1	no	—
82	C₂²×Q₈	—	13	2	no	—
83	#137	—	26	4	no	—
84	#137	—	26	4	no	—
85	C₂×Q₁₆	—	26	4	no	—
86	C₂×Q₁₆	—	26	2	no	—
87	C₂×Q₁₆	—	26	2	no	—
88	C₂×SD₁₆	—	26	2	no	—
89	C₂×M₁₆	—	13	1	no	—
90	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
91	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
92	#101	—	26	4	no	—
93	C₂²⋊C₈	—	26	2	no	—
94	C₂×C₁₃	—	2	2	no	—
95	C₂×C₁₃	#392	1	1	yes	characteristic
96	C₂×C₁₃	#473	1	2	yes	—
97	D₁₃	—	8	1	no	—
98	#41	—	26	2	no	—
99	#41	—	26	2	no	—
100	C₂×Q₈	—	13	1	no	—
101	C₂×Q₈	—	13	4	no	—
102	C₂×Q₈	—	26	2	no	—
103	C₂×Q₈	—	26	2	no	—
104	C₂×Q₈	—	26	2	no	—
105	C₂×Q₈	—	26	2	no	—
106	C₂×Q₈	—	26	2	no	—
107	C₂×D₄	—	13	1	no	—
108	C₂×D₄	—	26	1	no	—
109	C₂²×C₄	—	26	2	no	—
110	C₂²×C₄	—	26	1	no	—
111	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
112	Q₁₆	—	26	8	no	—
113	Q₁₆	—	26	8	no	—
114	SD₁₆	—	26	8	no	—
115	M₁₆	—	2	2	no	—
116	M₁₆	—	26	2	no	—
117	M₁₆	D₅₂	1	4	yes	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	26	1	no	—
121	C₂×C₈	D₅₂	1	2	yes	—
122	C₁₃	#2020	1	1	yes	characteristic, complemented, Sylow
123	C₂³	—	26	1	no	—
124	C₂³	#6131	1	1	yes	characteristic
125	Q₈	—	26	4	no	—
126	Q₈	—	26	4	no	—
127	Q₈	—	26	2	no	—
128	Q₈	—	52	2	no	—
129	Q₈	—	52	2	no	—
130	D₄	—	26	2	no	—
131	D₄	—	52	2	no	—
132	C₂×C₄	—	26	4	no	—
133	C₂×C₄	—	26	1	no	—
134	C₂×C₄	—	52	2	no	—
135	C₂×C₄	—	52	2	no	—
136	C₂×C₄	—	52	1	no	—
137	C₂×C₄	—	52	1	no	—
138	C₂×C₄	C₂×D₅₂	1	2	yes	—
139	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
140	C₂×C₄	D₄×D₁₃	1	2	yes	—
141	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	2	4	no	—
144	C₈	—	52	1	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	52	2	no	—
147	C₂²	—	52	1	no	—
148	C₂²	#88149	1	2	yes	—
149	C₂²	#88149	1	1	yes	characteristic
150	C₄	—	52	1	no	—
151	C₄	—	52	4	no	—
152	C₄	#88128	1	1	yes	characteristic
153	C₄	#88136	1	1	yes	characteristic
154	C₄	#88136	1	2	yes	—
155	C₂	—	2	2	no	—
156	C₂	—	104	1	no	—
157	C₂	#11718332	1	1	yes	characteristic
158	C₂	#11718557	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88163

C₂

yes

maximal

C₂²×Dic₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#88064

C₂

yes

maximal, complemented

#11718771

C₂

yes

maximal, characteristic

C₁₃×#341

C₂

yes

maximal, characteristic, complemented

C₂×#6127

C₂²

yes

characteristic

C₂²×Dic₂₆

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

characteristic

#88163

—

#88163

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×#6095

—

#88064

—

#88060

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₂²⋊D₁₃

—

C₂²×Dic₁₃

—

#6127

—

#6127

—

C₂×D₅₂

D₄

yes

characteristic

C₂×C₄×D₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

D₄

yes

characteristic

C₂×Dic₂₆

D₄

yes

—

C₁₃×M₁₆

—

C₁₃×M₁₆

D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

#6099

—

C₂×#1055

—

Dic₅₂

—

Dic₅₂

—

—

—

C₂³×C₁₃

yes

C₂²×D₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂²⋊D₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

C₂×#137

—

C₂²×Q₁₆

—

C₂×#101

—

#408

—

#341

D₁₃

yes

characteristic, complemented

C₂²×C₁₃

—

C₂²×C₁₃

#121

yes

—

C₂²×C₁₃

#121

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

#120

yes

characteristic

C₄×C₁₃

#120

yes

—

C₄×C₁₃

#127

yes

characteristic

Dic₁₃

—

Dic₁₃

—

C₂×#41

—

C₂²×Q₈

—

#137

—

#137

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

#101

—

C₂²⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

#392

yes

characteristic

C₂×C₁₃

#473

yes

—

D₁₃

—

#41

—

#41

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²×D₁₃

yes

characteristic

112

Q₁₆

—

113

Q₁₆

—

114

SD₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

D₅₂

yes

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

D₅₂

yes

—

122

C₁₃

#2020

yes

characteristic, complemented, Sylow

123

C₂³

—

124

C₂³

#6131

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₂×D₅₂

yes

—

139

C₂×C₄

C₂×D₅₂

yes

characteristic

140

C₂×C₄

D₄×D₁₃

yes

—

141

C₂×C₄

D₄×D₁₃

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

#88149

yes

—

149

C₂²

#88149

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

#88128

yes

characteristic

153

C₄

#88136

yes

characteristic

154

C₄

#88136

yes

—

155

C₂

—

156

C₂

—

104

—

157

C₂

#11718332

yes

characteristic

158

C₂

#11718557

yes

—

	subgroup	G/H
center	C₂²	#88149
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#341	C₂
socle	C₂²×C₁₃	#121
prime radical	C₂×#6127	C₂²
hypercenter	#341	D₁₃
hypocenter	C₁₃	#2020
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#88149

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#341

C₂

C₂²×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
2. C₂²×Dic₅₂	C₂	semidirect
3. C₂×#88064	C₂	semidirect
5. C₁₃×#341	C₂	semidirect
70. #341	D₁₃	semidirect
122. C₁₃	#2020	semidirect

H ≅ G/N

type

2. C₂²×Dic₅₂

C₂

semidirect

3. C₂×#88064

C₂

semidirect

5. C₁₃×#341

C₂

semidirect

70. #341

D₁₃

semidirect

122. C₁₃

#2020

semidirect

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

subgroup	index
C₂×#88163	2
C₂²×Dic₅₂	2
C₂×#88064	2
#11718771	2
C₁₃×#341	2
#2020	13

subgroup

index

C₂²×Dic₅₂

C₁₃×#341

Subgroups — #13115958

Conjugacy classes of subgroups

Complements

Maximal subgroups