Group #13114830 — subgroups

Subgroups — #13114830

Order 1664.

272 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 95 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×Q₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#101	C₂	1	1	yes	maximal, characteristic
3	C₂×#88076	C₂	1	1	yes	maximal, characteristic
4	#11718779	C₂	1	2	yes	maximal
5	#11718146	C₂	1	2	yes	maximal
6	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
8	Q₈×Dic₁₃	—	2	2	no	—
9	Q₈×Dic₁₃	—	2	2	no	—
10	C₂×C₄⋊Dic₁₃	C₄	1	2	yes	—
11	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₃	C₄	1	2	yes	—
13	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×#6099	C₂²	1	2	yes	—
15	C₁₃×#101	—	2	2	no	—
16	#88076	—	2	2	no	—
17	#88054	—	2	2	no	—
18	#88054	—	2	2	no	—
19	C₂×Q₈×C₁₃	—	2	2	no	—
20	C₂×Q₈×C₁₃	—	2	2	no	—
21	C₂×Q₈×C₁₃	D₄	1	2	yes	—
22	C₂×Q₈×C₁₃	Q₈	1	2	yes	—
23	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
27	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₁₃×M₁₆	—	2	2	no	—
29	C₁₃×M₁₆	—	2	2	no	—
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₄⋊Dic₁₃	—	2	2	no	—
32	C₄⋊Dic₁₃	—	2	4	no	—
33	C₄×Dic₁₃	—	2	2	no	—
34	C₄×Dic₁₃	—	2	2	no	—
35	C₄×Dic₁₃	D₄	1	2	yes	—
36	C₄×Dic₁₃	D₄	1	2	yes	—
37	#6099	—	2	2	no	—
38	#6099	—	2	2	no	—
39	C₂×#1055	—	2	2	no	—
40	#1801	—	13	1	no	maximal, Sylow
41	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	Q₈×C₁₃	—	2	4	no	—
43	Q₈×C₁₃	—	2	4	no	—
44	C₂×C₄×C₁₃	—	2	2	no	—
45	C₂×C₄×C₁₃	—	2	2	no	—
46	C₂×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
47	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	#41	1	2	yes	—
51	C₂×Dic₁₃	—	2	2	no	—
52	C₂×Dic₁₃	—	2	2	no	—
53	C₂×Dic₁₃	—	4	1	no	—
54	C₂×Dic₁₃	—	4	2	no	—
55	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Dic₁₃	C₂²⋊C₄	1	2	yes	—
57	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₈×C₁₃	—	4	2	no	—
59	#1055	—	4	2	no	—
60	C₂×C₄×Q₈	—	13	1	no	—
61	#423	—	13	2	no	—
62	C₂×#101	—	13	1	no	—
63	C₂×#101	D₁₃	1	1	yes	characteristic
64	#343	—	13	2	no	—
65	C₂²×C₁₃	—	2	1	no	—
66	C₂²×C₁₃	—	2	1	no	—
67	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₁₃	#117	1	1	yes	characteristic
70	C₄×C₁₃	—	2	4	no	—
71	C₄×C₁₃	#121	1	2	yes	—
72	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
73	Dic₁₃	—	2	1	no	—
74	Dic₁₃	—	2	2	no	—
75	Dic₁₃	—	4	2	no	—
76	Dic₁₃	#101	1	2	yes	complemented
77	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
78	C₂×M₁₆	—	13	2	no	—
79	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
80	C₄×Q₈	—	26	2	no	—
81	C₄×Q₈	—	26	2	no	—
82	C₂×C₄⋊C₄	—	13	2	no	—
83	C₂×C₄⋊C₄	—	13	1	no	—
84	C₂×C₄²	—	13	1	no	—
85	C₂×C₄²	—	13	2	no	—
86	C₄⋊C₈	—	26	2	no	—
87	C₄⋊C₈	—	26	2	no	—
88	#101	—	2	2	no	—
89	#101	—	26	2	no	—
90	C₂×C₁₃	—	2	1	no	—
91	C₂×C₁₃	—	2	1	no	—
92	C₂×C₁₃	#380	1	1	yes	characteristic
93	C₂×C₁₃	C₂×#101	1	1	yes	characteristic
94	C₂×C₁₃	#413	1	1	yes	characteristic
95	C₂×Q₈	—	2	2	no	—
96	C₂×Q₈	—	2	2	no	—
97	C₂×Q₈	Dic₂₆	1	2	yes	—
98	C₂×Q₈	C₂²⋊D₁₃	1	2	yes	—
99	C₂²×C₄	—	13	1	no	—
100	C₂²×C₄	—	13	1	no	—
101	C₂²×C₄	—	13	2	no	—
102	C₂²×C₄	C₄×D₁₃	1	2	yes	—
103	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
104	M₁₆	—	2	2	no	—
105	M₁₆	—	2	2	no	—
106	M₁₆	—	26	2	no	—
107	M₁₆	—	26	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	26	2	no	—
110	C₄⋊C₄	—	26	4	no	—
111	C₄⋊C₄	—	26	2	no	—
112	C₄²	—	13	2	no	—
113	C₄²	—	13	2	no	—
114	C₄²	—	26	2	no	—
115	C₄²	—	26	2	no	—
116	C₁₃	#1801	1	1	yes	characteristic, complemented, Sylow
117	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
118	Q₈	—	2	4	no	—
119	Q₈	—	2	4	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	13	1	no	—
123	C₂×C₄	—	13	1	no	—
124	C₂×C₄	—	13	2	no	—
125	C₂×C₄	—	26	2	no	—
126	C₂×C₄	—	26	2	no	—
127	C₂×C₄	—	52	1	no	—
128	C₂×C₄	—	52	2	no	—
129	C₂×C₄	#6101	1	4	yes	—
130	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
131	C₂×C₄	D₄×D₁₃	1	2	yes	—
132	C₂×C₄	#6129	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
134	C₈	—	4	2	no	—
135	C₈	—	52	2	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	#88131	1	1	yes	characteristic
139	C₂²	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
140	C₂²	C₂×#6101	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	13	2	no	—
143	C₄	—	26	1	no	—
144	C₄	—	26	2	no	—
145	C₄	—	52	2	no	—
146	C₄	#88132	1	2	yes	—
147	C₄	#88193	1	2	yes	—
148	C₂	—	2	1	no	—
149	C₂	—	2	1	no	—
150	C₂	D₁₃×#101	1	1	yes	characteristic
151	C₂	#11718412	1	1	yes	characteristic
152	C₂	#11718603	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₁₃

C₂

yes

maximal, characteristic

C₂×C₁₃×#101

C₂

yes

maximal, characteristic

C₂×#88076

C₂

yes

maximal, characteristic

#11718779

C₂

yes

maximal

#11718146

C₂

yes

maximal

C₂²×Q₈×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×M₁₆

C₂²

yes

—

Q₈×Dic₁₃

—

Q₈×Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₄

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₄

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

C₁₃×#101

—

#88076

—

#88054

—

#88054

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

D₄

yes

—

C₂×Q₈×C₁₃

Q₈

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

D₄

yes

—

—

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

C₂²⋊C₄

yes

—

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₈×C₁₃

—

#1055

—

C₂×C₄×Q₈

—

#423

—

C₂×#101

—

C₂×#101

D₁₃

yes

characteristic

#343

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

#121

yes

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#101

yes

complemented

C₂²×Q₈

C₂×D₁₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

#101

—

#101

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₂₆

yes

—

C₂×Q₈

C₂²⋊D₁₃

yes

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₄×D₁₃

yes

—

103

C₂²×C₄

C₂²×D₁₃

yes

characteristic

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

M₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₁₃

#1801

yes

characteristic, complemented, Sylow

117

C₂³

C₂×C₄×D₁₃

yes

characteristic

118

Q₈

—

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#6101

yes

—

130

C₂×C₄

C₂×Dic₂₆

yes

characteristic

131

C₂×C₄

D₄×D₁₃

yes

—

132

C₂×C₄

#6129

yes

—

133

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

—

138

C₂²

#88131

yes

characteristic

139

C₂²

C₂²⋊C₄×D₁₃

yes

characteristic

140

C₂²

C₂×#6101

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

#88132

yes

—

147

C₄

#88193

yes

—

148

C₂

—

149

C₂

—

150

C₂

D₁₃×#101

yes

characteristic

151

C₂

#11718412

yes

characteristic

152

C₂

#11718603

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₁₃
commutator, prime radical	C₂³×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#101	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×#101	D₁₃
hypocenter	C₁₃	#1801
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₁₃

commutator, prime radical

C₂³×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#101

C₂

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
76. Dic₁₃	#101	semidirect
116. C₁₃	#1801	semidirect

H ≅ G/N

type

76. Dic₁₃

#101

semidirect

116. C₁₃

#1801

semidirect

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

subgroup	index
C₂×Q₈×Dic₁₃	2
C₂×C₁₃×#101	2
C₂×#88076	2
#11718779	2
#11718146	2
#1801	13

subgroup

index

C₂×Q₈×Dic₁₃

C₂×C₁₃×#101

Subgroups — #13114830

Conjugacy classes of subgroups

Complements

Maximal subgroups