Group #13118134 — subgroups

Subgroups — #13118134

Order 1664.

432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 141 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	C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#6103	C₂	1	3	yes	maximal
3	C₄×#6101	C₂	1	3	yes	maximal, complemented
4	#11718337	C₂	1	1	yes	maximal, characteristic
5	#11718336	C₂	1	3	yes	maximal
6	C₁₃⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
7	#11718319	C₂	1	3	yes	maximal, complemented
8	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₃	C₂²	1	3	yes	—
10	C₂×#6103	C₂²	1	3	yes	—
11	C₂×#6103	C₂²	1	3	yes	—
12	C₂×#6101	C₂²	1	3	yes	—
13	C₂×#6101	C₂²	1	3	yes	—
14	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
15	C₁₃×#95	C₂²	1	3	yes	—
16	C₁₃×#95	C₂²	1	1	yes	characteristic
17	#88071	C₂²	1	3	yes	—
18	#88071	C₂²	1	3	yes	—
19	#88071	C₂²	1	3	yes	—
20	#88071	C₂²	1	3	yes	—
21	C₂³×D₁₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
23	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₃	C₂³	1	3	yes	—
27	C₂²×Dic₁₃	C₂³	1	3	yes	—
28	C₂×C₄×D₁₃	—	2	6	no	—
29	C₄²×C₁₃	—	2	6	no	—
30	#6103	—	2	6	no	—
31	#6103	—	2	6	no	—
32	#6101	—	2	6	no	—
33	#6101	—	2	6	no	—
34	C₄×Dic₁₃	—	2	6	no	—
35	#2401	—	13	1	no	maximal, Sylow
36	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
37	C₂²×D₁₃	—	2	3	no	—
38	C₂²×D₁₃	—	2	3	no	—
39	C₂²×D₁₃	#41	1	2	yes	—
40	C₂×C₄×C₁₃	—	2	3	no	—
41	C₂×C₄×C₁₃	—	2	3	no	—
42	C₂×C₄×C₁₃	—	2	3	no	—
43	C₂×C₄×C₁₃	—	2	3	no	—
44	C₂×C₄×C₁₃	—	2	3	no	—
45	C₂×C₄×C₁₃	—	2	3	no	—
46	C₂×C₄×C₁₃	#41	1	6	yes	—
47	C₂×Dic₁₃	—	2	3	no	—
48	C₂×Dic₁₃	—	2	3	no	—
49	C₂×Dic₁₃	—	2	3	no	—
50	C₂×Dic₁₃	—	2	3	no	—
51	C₂×Dic₁₃	—	2	3	no	—
52	C₂×Dic₁₃	—	2	3	no	—
53	C₂×Dic₁₃	#41	1	6	yes	—
54	C₄×D₁₃	—	4	4	no	—
55	#401	—	13	1	no	—
56	#400	—	13	3	no	—
57	#397	—	13	3	no	—
58	#396	—	13	1	no	—
59	C₄×C₄⋊C₄	—	13	3	no	—
60	C₄×C₂²⋊C₄	—	13	3	no	—
61	#376	D₁₃	1	1	yes	characteristic, complemented
62	C₂²×C₁₃	C₂×#41	1	3	yes	—
63	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
64	C₂²×C₁₃	C₂×#41	1	3	yes	—
65	C₂×D₁₃	—	2	6	no	—
66	C₂×D₁₃	—	4	1	no	—
67	C₂×D₁₃	—	4	3	no	—
68	C₄×C₁₃	—	4	3	no	—
69	C₄×C₁₃	—	4	3	no	—
70	C₄×C₁₃	#126	1	4	yes	—
71	Dic₁₃	—	2	6	no	—
72	Dic₁₃	—	4	1	no	—
73	Dic₁₃	—	4	3	no	—
74	C₂³×C₄	—	13	1	no	—
75	C₂×C₄⋊C₄	—	13	3	no	—
76	C₂×C₄⋊C₄	—	13	3	no	—
77	C₂×C₂²⋊C₄	—	13	3	no	—
78	C₂×C₂²⋊C₄	—	13	3	no	—
79	C₂×C₄²	—	13	3	no	—
80	C₂×C₄²	C₂×D₁₃	1	3	yes	—
81	#95	—	13	3	no	—
82	#95	—	13	3	no	—
83	#95	—	13	3	no	—
84	#95	—	13	3	no	—
85	#95	C₂×D₁₃	1	1	yes	characteristic
86	#95	C₂×D₁₃	1	3	yes	—
87	C₂×C₁₃	C₂×#126	1	1	yes	characteristic
88	C₂×C₁₃	#529	1	3	yes	—
89	C₂×C₁₃	#529	1	3	yes	—
90	D₁₃	—	4	2	no	—
91	C₂⁴	—	13	1	no	—
92	C₂²×C₄	—	13	3	no	—
93	C₂²×C₄	—	13	1	no	—
94	C₂²×C₄	—	13	3	no	—
95	C₂²×C₄	—	26	6	no	—
96	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
97	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
98	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
99	C₄⋊C₄	—	26	6	no	—
100	C₄⋊C₄	—	26	6	no	—
101	C₂²⋊C₄	—	26	6	no	—
102	C₂²⋊C₄	—	26	6	no	—
103	C₄²	—	2	6	no	—
104	C₄²	—	26	6	no	—
105	C₁₃	#2401	1	1	yes	characteristic, complemented, Sylow
106	C₂³	—	13	2	no	—
107	C₂³	—	26	3	no	—
108	C₂³	—	26	3	no	—
109	C₂³	C₂³×D₁₃	1	1	yes	characteristic
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	2	3	no	—
116	C₂×C₄	—	13	6	no	—
117	C₂×C₄	—	26	3	no	—
118	C₂×C₄	—	26	3	no	—
119	C₂×C₄	—	26	3	no	—
120	C₂×C₄	—	26	3	no	—
121	C₂×C₄	—	26	3	no	—
122	C₂×C₄	—	26	3	no	—
123	C₂×C₄	—	52	4	no	—
124	C₂×C₄	#6127	1	6	yes	—
125	C₂²	—	26	6	no	—
126	C₂²	—	52	1	no	—
127	C₂²	—	52	3	no	—
128	C₂²	C₂×#6127	1	3	yes	—
129	C₂²	#41×D₁₃	1	3	yes	—
130	C₂²	#41×D₁₃	1	1	yes	characteristic
131	C₄	—	4	3	no	—
132	C₄	—	4	3	no	—
133	C₄	—	26	6	no	—
134	C₄	—	52	1	no	—
135	C₄	—	52	3	no	—
136	C₄	#88130	1	4	yes	—
137	C₂	—	52	2	no	—
138	C₂	C₂×#88130	1	1	yes	characteristic
139	C₂	#11719233	1	3	yes	—
140	C₂	#11719233	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#376

C₂

yes

maximal, characteristic, complemented

C₄×#6103

C₂

yes

maximal

C₄×#6101

C₂

yes

maximal, complemented

#11718337

C₂

yes

maximal, characteristic

#11718336

C₂

yes

maximal

C₁₃⋊#401

C₂

yes

maximal, characteristic, complemented

#11718319

C₂

yes

maximal, complemented

C₂²×C₄×D₁₃

C₂²

yes

characteristic

C₂×C₄²×C₁₃

C₂²

yes

—

C₂×#6103

C₂²

yes

—

C₂×#6103

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

C₁₃×#95

C₂²

yes

characteristic

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂³×D₁₃

C₂³

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂×C₄×D₁₃

—

C₄²×C₁₃

—

—

—

—

—

C₄×Dic₁₃

—

#2401

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

#41

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#41

yes

—

C₄×D₁₃

—

—

—

—

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

D₁₃

yes

characteristic, complemented

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

C₂×#41

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#126

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

—

—

C₂×D₁₃

yes

characteristic

#95

C₂×D₁₃

yes

—

C₂×C₁₃

C₂×#126

yes

characteristic

C₂×C₁₃

#529

yes

—

C₂×C₁₃

#529

yes

—

D₁₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₁₃

#2401

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₂³×D₁₃

yes

characteristic

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

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

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#6127

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

C₂×#6127

yes

—

129

C₂²

#41×D₁₃

yes

—

130

C₂²

#41×D₁₃

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#88130

yes

—

137

C₂

—

138

C₂

C₂×#88130

yes

characteristic

139

C₂

#11719233

yes

—

140

C₂

#11719233

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Frattini	C₂³	C₂³×D₁₃
Fitting	C₁₃×#376	C₂
prime radical	C₂³×D₁₃	C₂³
hypercenter	#376	D₁₃
hypocenter	C₁₃	#2401
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₁₃

commutator, socle, cosocle

C₂³×C₁₃

C₂⁴

Frattini

C₂³

C₂³×D₁₃

Fitting

C₁₃×#376

C₂

prime radical

C₂³×D₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
1. C₁₃×#376	C₂	semidirect
3. C₄×#6101	C₂	semidirect
6. C₁₃⋊#401	C₂	semidirect
7. #11718319	C₂	semidirect
61. #376	D₁₃	semidirect
105. C₁₃	#2401	semidirect

H ≅ G/N

type

1. C₁₃×#376

C₂

semidirect

3. C₄×#6101

C₂

semidirect

6. C₁₃⋊#401

C₂

semidirect

7. #11718319

C₂

semidirect

61. #376

D₁₃

semidirect

105. C₁₃

#2401

semidirect

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

subgroup	index
C₁₃×#376	2
C₄×#6103	2
C₄×#6101	2
#11718337	2
#11718336	2
C₁₃⋊#401	2
#11718319	2
#2401	13

subgroup

index

C₁₃×#376

C₁₃⋊#401

Subgroups — #13118134

Conjugacy classes of subgroups

Complements

Maximal subgroups