Group #13123025 — subgroups

Subgroups — #13123025

Order 1664.

380 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 115 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×#395	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718892	C₂	1	1	yes	maximal, characteristic
3	#11718890	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718650	C₂	1	3	yes	maximal
5	#11718643	C₂	1	3	yes	maximal, complemented
6	#11718336	C₂	1	3	yes	maximal
7	#11718319	C₂	1	3	yes	maximal, complemented
8	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
11	C₂×#6103	C₂²	1	3	yes	—
12	C₂×#6103	C₂²	1	3	yes	—
13	C₂×#6101	C₂²	1	3	yes	—
14	C₂×#6101	C₂²	1	3	yes	—
15	C₁₃×#95	C₂²	1	3	yes	—
16	#88071	C₂²	1	3	yes	—
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	C₂×Q₈×C₁₃	—	4	3	no	—
23	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
25	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
26	C₂²×Dic₁₃	C₂³	1	3	yes	—
27	C₂²×Dic₁₃	C₂³	1	3	yes	—
28	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄×D₁₃	—	4	3	no	—
30	C₁₃×C₄⋊C₄	—	4	3	no	—
31	#6103	—	2	6	no	—
32	#6103	—	4	3	no	—
33	#6101	—	4	3	no	—
34	#6101	—	4	3	no	—
35	#2835	—	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	Q₈×C₁₃	—	4	4	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	—	2	3	no	—
47	C₂×C₄×C₁₃	—	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	—	2	6	no	—
54	C₄×D₁₃	—	4	4	no	—
55	#400	—	13	3	no	—
56	#400	—	13	3	no	—
57	#397	—	13	3	no	—
58	#395	—	13	1	no	—
59	#395	D₁₃	1	1	yes	characteristic, complemented
60	#393	—	13	1	no	—
61	#385	—	13	3	no	—
62	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
63	C₂²×C₁₃	H(5,𝔽₂)	1	3	yes	—
64	C₂²×C₁₃	2₋¹⁺⁴	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	1	no	—
70	C₄×C₁₃	—	4	3	no	—
71	Dic₁₃	—	4	3	no	—
72	Dic₁₃	—	4	1	no	—
73	Dic₁₃	—	4	3	no	—
74	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
75	C₂³×C₄	—	13	1	no	—
76	C₂×C₄⋊C₄	—	13	3	no	—
77	C₂×C₄⋊C₄	—	13	3	no	—
78	C₂×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
79	C₂×C₂²⋊C₄	—	13	3	no	—
80	C₂×C₂²⋊C₄	—	13	3	no	—
81	#95	—	13	3	no	—
82	#95	—	13	3	no	—
83	#95	—	13	3	no	—
84	#95	—	13	3	no	—
85	#95	—	13	3	no	—
86	#95	C₂×D₁₃	1	3	yes	—
87	C₂×C₁₃	#539	1	3	yes	—
88	C₂×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
89	C₂×C₁₃	#563	1	3	yes	—
90	D₁₃	—	4	2	no	—
91	C₂⁴	—	13	1	no	—
92	C₂×Q₈	—	4	3	no	—
93	C₂²×C₄	—	13	3	no	—
94	C₂²×C₄	—	13	3	no	—
95	C₂²×C₄	—	13	1	no	—
96	C₂²×C₄	—	52	3	no	—
97	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
99	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
100	C₄⋊C₄	—	4	3	no	—
101	C₄⋊C₄	—	52	3	no	—
102	C₄⋊C₄	—	52	3	no	—
103	C₂²⋊C₄	—	26	6	no	—
104	C₂²⋊C₄	—	52	3	no	—
105	C₁₃	#2835	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	Q₈	—	4	4	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	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	26	3	no	—
119	C₂×C₄	—	26	3	no	—
120	C₂×C₄	—	26	3	no	—
121	C₂×C₄	—	26	6	no	—
122	C₂×C₄	—	26	3	no	—
123	C₂×C₄	—	26	3	no	—
124	C₂×C₄	—	52	4	no	—
125	C₂²	—	26	6	no	—
126	C₂²	—	52	3	no	—
127	C₂²	—	52	1	no	—
128	C₂²	#88251	1	3	yes	—
129	C₂²	#88254	1	3	yes	—
130	C₂²	#41×D₁₃	1	1	yes	characteristic
131	C₄	—	4	1	no	—
132	C₄	—	4	3	no	—
133	C₄	—	4	3	no	—
134	C₄	—	52	3	no	—
135	C₄	—	52	1	no	—
136	C₄	—	52	3	no	—
137	C₂	—	52	2	no	—
138	C₂	#11719299	1	1	yes	characteristic
139	C₂	#11719343	1	3	yes	—
140	C₂	#11719440	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#395

C₂

yes

maximal, characteristic, complemented

#11718892

C₂

yes

maximal, characteristic

#11718890

C₂

yes

maximal, characteristic, complemented

#11718650

C₂

yes

maximal

#11718643

C₂

yes

maximal, complemented

#11718336

C₂

yes

maximal

#11718319

C₂

yes

maximal, complemented

C₂²×Q₈×C₁₃

C₂²

yes

characteristic

C₂²×C₄×D₁₃

C₂²

yes

characteristic

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×#6103

C₂²

yes

—

C₂×#6103

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂³×D₁₃

C₂³

yes

characteristic

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂×C₄×D₁₃

—

C₁₃×C₄⋊C₄

—

—

—

—

—

—

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

#41

yes

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₄×D₁₃

—

—

—

—

—

D₁₃

yes

characteristic, complemented

#393

—

#385

—

C₂²×C₁₃

C₂×#41

yes

characteristic

C₂²×C₁₃

H(5,𝔽₂)

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

C₂×D₁₃

yes

characteristic

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

—

—

C₂×D₁₃

yes

—

C₂×C₁₃

#539

yes

—

C₂×C₁₃

H(3,𝔽₄)

yes

characteristic

C₂×C₁₃

#563

yes

—

D₁₃

—

C₂⁴

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₁₃

#2835

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₂³×D₁₃

yes

characteristic

110

Q₈

—

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

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

#88251

yes

—

129

C₂²

#88254

yes

—

130

C₂²

#41×D₁₃

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₂

—

138

C₂

#11719299

yes

characteristic

139

C₂

#11719343

yes

—

140

C₂

#11719440

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#395	C₂
prime radical	C₂³×D₁₃	C₂³
hypercenter	#395	D₁₃
hypocenter	C₁₃	#2835
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#395

C₂

prime radical

C₂³×D₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
1. C₁₃×#395	C₂	semidirect
3. #11718890	C₂	semidirect
5. #11718643	C₂	semidirect
7. #11718319	C₂	semidirect
59. #395	D₁₃	semidirect
105. C₁₃	#2835	semidirect

H ≅ G/N

type

1. C₁₃×#395

C₂

semidirect

3. #11718890

C₂

semidirect

5. #11718643

C₂

semidirect

7. #11718319

C₂

semidirect

59. #395

D₁₃

semidirect

105. C₁₃

#2835

semidirect

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

subgroup	index
C₁₃×#395	2
#11718892	2
#11718890	2
#11718650	2
#11718643	2
#11718336	2
#11718319	2
#2835	13

subgroup

index

C₁₃×#395

Subgroups — #13123025

Conjugacy classes of subgroups

Complements

Maximal subgroups