Group #15765672 — subgroups

Subgroups — #15765672

Order 3328.

592 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 89 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	#13126217	C₂	1	3	yes	maximal, complemented
2	#13115663	C₂	1	3	yes	maximal, complemented
3	C₁₃×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719182	C₂²	1	3	yes	—
5	C₁₃×#423	C₂²	1	3	yes	—
6	C₂×#88065	—	2	6	no	—
7	#11718796	—	2	6	no	—
8	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
9	#11718504	—	2	6	no	—
10	#11718503	—	2	6	no	—
11	C₂×#6127	—	2	3	no	—
12	C₂×C₁₃×M₁₆	D₄	1	6	yes	—
13	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
14	#88184	—	2	6	no	—
15	C₂×C₄×Dic₁₃	—	2	3	no	—
16	C₂×D₁₀₄	—	2	6	no	—
17	#88129	—	2	3	no	—
18	#88128	D₄	1	3	yes	—
19	C₄×D₅₂	—	2	6	no	—
20	#88123	D₄	1	3	yes	—
21	C₁₃×C₄⋊C₈	—	2	6	no	—
22	#88065	—	4	12	no	—
23	#88061	—	2	12	no	—
24	#88057	—	2	6	no	—
25	#10300	—	13	1	no	maximal, Sylow
26	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
27	C₂×C₂²⋊D₁₃	—	4	3	no	—
28	C₂²×Dic₁₃	—	4	1	no	—
29	#6127	—	4	6	no	—
30	#6127	—	4	6	no	—
31	C₂×D₅₂	—	2	6	no	—
32	C₂×D₅₂	—	2	3	no	—
33	C₂×C₄×D₁₃	—	4	3	no	—
34	C₂×Dic₂₆	—	2	3	no	—
35	C₁₃×M₁₆	—	4	6	no	—
36	C₂×C₈×C₁₃	—	2	6	no	—
37	C₄²×C₁₃	C₂×D₄	1	3	yes	—
38	C₄²×C₁₃	#41	1	1	yes	characteristic
39	#6103	—	4	6	no	—
40	C₄⋊Dic₁₃	—	2	6	no	—
41	C₄×Dic₁₃	—	2	6	no	—
42	C₄×Dic₁₃	—	4	3	no	—
43	D₁₀₄	—	8	6	no	—
44	#3253	—	13	3	no	—
45	#1962	—	13	3	no	—
46	#1309	D₁₃	1	1	yes	characteristic, complemented
47	C₂³×C₁₃	#127	1	1	yes	characteristic
48	C₂²×D₁₃	—	4	3	no	—
49	C₂×C₄×C₁₃	—	2	3	no	—
50	C₂×C₄×C₁₃	—	2	3	no	—
51	C₂×C₄×C₁₃	#120	1	3	yes	—
52	C₂×C₄×C₁₃	#121	1	3	yes	—
53	C₂²⋊D₁₃	—	8	6	no	—
54	C₂×Dic₁₃	—	4	6	no	—
55	C₂×Dic₁₃	—	4	3	no	—
56	D₅₂	—	4	6	no	—
57	D₅₂	—	4	6	no	—
58	D₅₂	—	4	6	no	—
59	C₄×D₁₃	—	8	3	no	—
60	C₄×D₁₃	—	8	3	no	—
61	Dic₂₆	—	4	6	no	—
62	C₈×C₁₃	—	4	6	no	—
63	#532	—	13	3	no	—
64	#476	—	26	6	no	—
65	#469	—	26	6	no	—
66	#459	—	26	6	no	—
67	#423	C₂×D₁₃	1	3	yes	—
68	C₂×#104	—	26	6	no	—
69	C₄³	—	13	1	no	—
70	C₂²×C₁₃	—	2	3	no	—
71	C₂²×C₁₃	#392	1	1	yes	characteristic
72	C₂×D₁₃	—	8	3	no	—
73	C₂×D₁₃	—	8	6	no	—
74	C₄×C₁₃	—	2	3	no	—
75	C₄×C₁₃	#453	1	3	yes	—
76	C₄×C₁₃	#454	1	3	yes	—
77	Dic₁₃	—	4	4	no	—
78	Dic₁₃	—	8	3	no	—
79	C₂×#41	—	26	3	no	—
80	C₂×D₈	—	26	6	no	—
81	C₂×M₁₆	D₅₂	1	6	yes	—
82	C₄⋊Q₈	—	13	3	no	—
83	#127	—	13	3	no	—
84	#124	—	26	3	no	—
85	#121	—	26	6	no	—
86	C₄×D₄	—	26	6	no	—
87	C₂×C₄²	—	26	3	no	—
88	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
89	#106	—	26	6	no	—
90	C₄⋊C₈	—	2	6	no	—
91	#104	—	52	12	no	—
92	#102	—	26	12	no	—
93	C₂×C₁₃	—	4	1	no	—
94	C₂×C₁₃	#2006	1	3	yes	—
95	D₁₃	—	16	3	no	—
96	#41	—	52	6	no	—
97	#41	—	52	6	no	—
98	C₂×Q₈	—	26	3	no	—
99	C₂×D₄	—	26	6	no	—
100	C₂×D₄	—	26	3	no	—
101	C₂×D₄	—	52	3	no	—
102	C₂²×C₄	—	52	1	no	—
103	C₂²×C₄	—	52	3	no	—
104	C₂²×C₄	C₂×D₅₂	1	3	yes	—
105	D₈	—	104	6	no	—
106	M₁₆	—	4	6	no	—
107	C₂×C₈	—	2	6	no	—
108	C₄⋊C₄	—	26	6	no	—
109	C₂²⋊C₄	—	52	6	no	—
110	C₄²	—	26	6	no	—
111	C₄²	—	52	3	no	—
112	C₄²	D₄×D₁₃	1	3	yes	—
113	C₄²	#6131	1	1	yes	characteristic
114	C₁₃	#10300	1	1	yes	characteristic, complemented, Sylow
115	C₂³	—	52	3	no	—
116	C₂³	#88128	1	1	yes	characteristic
117	Q₈	—	52	6	no	—
118	D₄	—	52	6	no	—
119	D₄	—	52	6	no	—
120	D₄	—	52	6	no	—
121	D₄	—	104	6	no	—
122	C₂×C₄	—	2	3	no	—
123	C₂×C₄	—	2	3	no	—
124	C₂×C₄	—	52	6	no	—
125	C₂×C₄	—	52	3	no	—
126	C₂×C₄	—	104	3	no	—
127	C₂×C₄	—	104	3	no	—
128	C₂×C₄	#88136	1	3	yes	—
129	C₂×C₄	#88149	1	3	yes	—
130	C₈	—	4	6	no	—
131	C₂²	—	2	3	no	—
132	C₂²	—	104	3	no	—
133	C₂²	—	104	6	no	—
134	C₂²	#11718332	1	1	yes	characteristic
135	C₄	—	2	3	no	—
136	C₄	—	52	4	no	—
137	C₄	—	104	3	no	—
138	C₄	#11718408	1	3	yes	—
139	C₄	#11718414	1	3	yes	—
140	C₂	—	4	1	no	—
141	C₂	—	208	3	no	—
142	C₂	#13115880	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13126217

C₂

yes

maximal, complemented

#13115663

C₂

yes

maximal, complemented

C₁₃×#1309

C₂

yes

maximal, characteristic, complemented

#11719182

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

C₂×#88065

—

#11718796

—

C₄²×Dic₁₃

C₂²

yes

—

—

—

C₂×C₁₃×M₁₆

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

#88184

—

C₂×C₄×Dic₁₃

—

C₂×D₁₀₄

—

#88129

—

#88128

D₄

yes

—

C₄×D₅₂

—

#88123

D₄

yes

—

C₁₃×C₄⋊C₈

—

—

—

—

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₂²⋊D₁₃

—

C₂²×Dic₁₃

—

#6127

—

#6127

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×C₄×D₁₃

—

C₂×Dic₂₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

#6103

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

D₁₀₄

—

#3253

—

#1962

—

#1309

D₁₃

yes

characteristic, complemented

C₂³×C₁₃

#127

yes

characteristic

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂²⋊D₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

D₅₂

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

C₈×C₁₃

—

—

—

—

—

C₂×D₁₃

yes

—

C₂×#104

—

C₄³

—

C₂²×C₁₃

—

C₂²×C₁₃

#392

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#453

yes

—

C₄×C₁₃

#454

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

D₅₂

yes

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

#106

—

C₄⋊C₈

—

#104

—

#102

—

C₂×C₁₃

—

C₂×C₁₃

#2006

yes

—

D₁₃

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂×D₅₂

yes

—

105

D₈

—

104

—

106

M₁₆

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

D₄×D₁₃

yes

—

113

C₄²

#6131

yes

characteristic

114

C₁₃

#10300

yes

characteristic, complemented, Sylow

115

C₂³

—

116

C₂³

#88128

yes

characteristic

117

Q₈

—

118

D₄

—

119

D₄

—

120

D₄

—

121

D₄

—

104

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

104

—

127

C₂×C₄

—

104

—

128

C₂×C₄

#88136

yes

—

129

C₂×C₄

#88149

yes

—

130

C₈

—

131

C₂²

—

132

C₂²

—

104

—

133

C₂²

—

104

—

134

C₂²

#11718332

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

104

—

138

C₄

#11718408

yes

—

139

C₄

#11718414

yes

—

140

C₂

—

141

C₂

—

208

—

142

C₂

#13115880

yes

—

	subgroup	G/H
center	C₂²	#11718332
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1309	C₂
socle	C₂²×C₁₃	#392
hypercenter	#1309	D₁₃
hypocenter	C₁₃	#10300
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#11718332

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1309

C₂

C₂²×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
1. #13126217	C₂	semidirect
2. #13115663	C₂	semidirect
3. C₁₃×#1309	C₂	semidirect
46. #1309	D₁₃	semidirect
114. C₁₃	#10300	semidirect

H ≅ G/N

type

1. #13126217

C₂

semidirect

2. #13115663

C₂

semidirect

3. C₁₃×#1309

C₂

semidirect

46. #1309

D₁₃

semidirect

114. C₁₃

#10300

semidirect

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

subgroup	index
#13126217	2
#13115663	2
C₁₃×#1309	2
#10300	13

subgroup

index

#13126217

#13115663

C₁₃×#1309

#10300

Subgroups — #15765672

Conjugacy classes of subgroups

Complements

Maximal subgroups