Group #13129719 — subgroups

Subgroups — #13129719

Order 1664.

190 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 48 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	#11719127	C₂	1	1	yes	maximal, characteristic
2	C₂×#88111	C₂	1	1	yes	maximal, characteristic
3	D₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
5	C₂²×#1057	—	2	1	no	—
6	C₂×#6118	C₄	1	2	yes	—
7	C₂×C₈×D₁₃	—	2	1	no	—
8	C₂²⋊#1057	—	2	1	no	—
9	#88111	—	2	1	no	—
10	#88111	—	2	1	no	—
11	#88111	C₄	1	2	yes	—
12	C₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
13	C₂²⋊#1055	C₄	1	1	yes	characteristic
14	#88060	—	2	1	no	—
15	C₂³×D₁₃	Q₈	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₁₃	D₄	1	1	yes	characteristic
18	C₂×C₄×D₁₃	—	4	2	no	—
19	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
22	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
23	C₂×#1057	—	2	2	no	—
24	C₂×#1057	—	2	2	no	—
25	C₂×#1057	—	4	2	no	—
26	#6118	—	4	2	no	—
27	C₂×C₈×C₁₃	—	2	1	no	—
28	C₂×#1055	—	2	1	no	—
29	C₈×D₁₃	—	4	2	no	—
30	#1298	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂²×D₁₃	—	2	1	no	—
33	C₂²×D₁₃	—	2	1	no	—
34	C₂²×D₁₃	—	2	2	no	—
35	C₂²×D₁₃	—	4	1	no	—
36	C₂²×D₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂²×D₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	—	4	1	no	—
39	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×Dic₁₃	—	2	2	no	—
42	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₄×D₁₃	—	2	2	no	—
45	C₄×D₁₃	—	2	2	no	—
46	C₄×D₁₃	—	4	1	no	—
47	C₄×D₁₃	—	4	1	no	—
48	#1057	—	4	2	no	—
49	#1057	—	4	2	no	—
50	C₈×C₁₃	—	4	1	no	—
51	#1055	—	4	1	no	—
52	#407	—	13	1	no	—
53	C₂×C₂²⋊C₈	—	13	1	no	—
54	C₂×C₂²⋊C₈	—	13	1	no	—
55	C₂²×C₁₃	—	2	1	no	—
56	C₂²×C₁₃	—	2	1	no	—
57	C₂²×C₁₃	#95	1	1	yes	characteristic
58	C₂²×C₁₃	#108	1	1	yes	characteristic
59	C₂²×C₁₃	#108	1	1	yes	characteristic
60	C₂×D₁₃	—	2	1	no	—
61	C₂×D₁₃	—	2	1	no	—
62	C₂×D₁₃	—	2	1	no	—
63	C₂×D₁₃	—	2	1	no	—
64	C₂×D₁₃	—	2	1	no	—
65	C₂×D₁₃	—	4	2	no	—
66	C₂×D₁₃	—	4	2	no	—
67	C₂×D₁₃	#108	1	2	yes	—
68	C₄×C₁₃	—	2	1	no	—
69	C₄×C₁₃	—	2	1	no	—
70	Dic₁₃	—	2	1	no	—
71	Dic₁₃	#99	1	2	yes	—
72	C₂³×C₄	—	13	1	no	—
73	C₂×M₁₆	—	13	2	no	—
74	C₂²×C₈	—	26	1	no	—
75	C₂²×C₈	—	26	1	no	—
76	C₂²⋊C₈	—	13	2	no	—
77	C₂²⋊C₈	—	13	1	no	—
78	C₂²⋊C₈	—	26	1	no	—
79	C₂²⋊C₈	—	26	1	no	—
80	C₂²⋊C₈	—	26	1	no	—
81	C₂²⋊C₈	—	26	1	no	—
82	C₂²⋊C₈	#261	1	1	yes	characteristic
83	C₂×C₁₃	—	2	1	no	—
84	C₂×C₁₃	—	2	1	no	—
85	C₂×C₁₃	#341	1	1	yes	characteristic
86	C₂×C₁₃	#341	1	1	yes	characteristic
87	C₂×C₁₃	#342	1	1	yes	characteristic
88	D₁₃	—	2	2	no	—
89	D₁₃	—	4	1	no	—
90	C₂⁴	—	13	1	no	—
91	C₂²×C₄	—	13	1	no	—
92	C₂²×C₄	—	13	1	no	—
93	C₂²×C₄	—	13	1	no	—
94	C₂²×C₄	—	13	1	no	—
95	C₂²×C₄	—	13	1	no	—
96	C₂²×C₄	—	52	2	no	—
97	C₂²×C₄	C₂×#261	1	1	yes	characteristic
98	M₁₆	—	52	2	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	26	2	no	—
101	C₂×C₈	—	26	2	no	—
102	C₂×C₈	—	26	1	no	—
103	C₂×C₈	—	52	2	no	—
104	C₂×C₈	—	52	2	no	—
105	C₁₃	#1298	1	1	yes	characteristic, complemented, Sylow
106	C₂³	—	13	1	no	—
107	C₂³	—	13	1	no	—
108	C₂³	—	26	2	no	—
109	C₂³	—	26	1	no	—
110	C₂³	—	26	1	no	—
111	C₂³	—	52	1	no	—
112	C₂³	C₄⋊#261	1	1	yes	characteristic
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	13	1	no	—
115	C₂×C₄	—	13	1	no	—
116	C₂×C₄	—	26	2	no	—
117	C₂×C₄	—	26	2	no	—
118	C₂×C₄	—	26	2	no	—
119	C₂×C₄	—	52	1	no	—
120	C₂×C₄	—	52	1	no	—
121	C₂×C₄	C₄×#261	1	1	yes	characteristic
122	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
123	C₈	—	4	1	no	—
124	C₈	—	52	1	no	—
125	C₈	—	52	2	no	—
126	C₈	—	52	2	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	—	13	2	no	—
130	C₂²	—	26	1	no	—
131	C₂²	—	26	1	no	—
132	C₂²	—	26	1	no	—
133	C₂²	—	26	1	no	—
134	C₂²	—	26	1	no	—
135	C₂²	—	52	2	no	—
136	C₂²	—	52	2	no	—
137	C₂²	#88103	1	1	yes	characteristic
138	C₂²	#88104	1	1	yes	characteristic
139	C₂²	(C₂×#261)⋊C₄	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	2	1	no	—
142	C₄	—	13	2	no	—
143	C₄	—	26	1	no	—
144	C₂	—	2	1	no	—
145	C₂	—	2	1	no	—
146	C₂	—	26	2	no	—
147	C₂	—	52	1	no	—
148	C₂	#11718238	1	1	yes	characteristic
149	C₂	#11718268	1	1	yes	characteristic
150	C₂	#11718273	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11719127

C₂

yes

maximal, characteristic

C₂×#88111

C₂

yes

maximal, characteristic

D₁₃×C₂²⋊C₈

C₂

yes

maximal, characteristic

C₂²×C₄×D₁₃

C₂²

yes

characteristic

C₂²×#1057

—

C₂×#6118

C₄

yes

—

C₂×C₈×D₁₃

—

C₂²⋊#1057

—

#88111

—

#88111

—

#88111

C₄

yes

—

C₁₃×C₂²⋊C₈

C₄

yes

characteristic

C₂²⋊#1055

C₄

yes

characteristic

#88060

—

C₂³×D₁₃

Q₈

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

D₄

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₄×D₁₃

D₄

yes

characteristic

C₂×C₄×D₁₃

D₄

yes

—

—

—

—

C₂×C₈×C₁₃

—

C₂×#1055

—

C₈×D₁₃

—

#1298

—

maximal, Sylow

C₂³×C₁₃

C₄⋊C₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

C₄⋊C₄

yes

characteristic

C₂²×D₁₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

#1057

—

#1057

—

C₈×C₁₃

—

#1055

—

#407

—

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

#108

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

#99

yes

—

C₂³×C₄

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

#261

yes

characteristic

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

D₁₃

—

D₁₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

characteristic

M₁₆

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₁₃

#1298

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

C₄⋊#261

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₄×#261

yes

characteristic

122

C₂×C₄

C₂²⋊#261

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

#88103

yes

characteristic

138

C₂²

#88104

yes

characteristic

139

C₂²

(C₂×#261)⋊C₄

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₂

—

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

#11718238

yes

characteristic

149

C₂

#11718268

yes

characteristic

150

C₂

#11718273

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#261)⋊C₄
commutator	C₂×C₄×C₁₃	C₄²
Frattini	C₂²×C₄	C₂×#261
Fitting	C₁₃×C₂²⋊C₈	C₄
socle	C₂²×C₁₃	#95
prime radical	C₂³×D₁₃	Q₈
cosocle	C₂²×C₄×D₁₃	C₂²
hypercenter	C₂²⋊C₈	#261
hypocenter	C₁₃	#1298
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center

C₂²

(C₂×#261)⋊C₄

commutator

C₂×C₄×C₁₃

C₄²

Frattini

C₂²×C₄

C₂×#261

Fitting

C₁₃×C₂²⋊C₈

C₄

socle

C₂²×C₁₃

#95

prime radical

C₂³×D₁₃

Q₈

cosocle

C₂²×C₄×D₁₃

C₂²

C₂²⋊C₈

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
105. C₁₃	#1298	semidirect

H ≅ G/N

type

105. C₁₃

#1298

semidirect

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

subgroup	index
#11719127	2
C₂×#88111	2
D₁₃×C₂²⋊C₈	2
#1298	13

subgroup

index

#11719127

C₂×#88111

D₁₃×C₂²⋊C₈

#1298

Subgroups — #13129719

Conjugacy classes of subgroups

Complements

Maximal subgroups