Group #13131628 — subgroups

Subgroups — #13131628

Order 1664.

348 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 162 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	#11719393	C₂	1	1	yes	maximal, characteristic
2	#11719080	C₂	1	4	yes	maximal, complemented
3	#11719079	C₂	1	2	yes	maximal
4	#11719078	C₂	1	4	yes	maximal, complemented
5	#11719072	C₂	1	2	yes	maximal
6	#11719052	C₂	1	1	yes	maximal, characteristic
7	#11719047	C₂	1	1	yes	maximal, characteristic
8	C₂×#6118	C₂²	1	2	yes	—
9	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₃×#125	C₄	1	1	yes	characteristic
12	#88150	C₄	1	4	yes	—
13	#88146	C₂²	1	2	yes	—
14	#88142	C₄	1	2	yes	—
15	#88141	C₂²	1	4	yes	—
16	C₄²×D₁₃	C₂²	1	1	yes	characteristic
17	#88124	C₄	1	1	yes	characteristic
18	#88112	C₂²	1	4	yes	—
19	#88110	C₂²	1	2	yes	—
20	#88110	C₂²	1	2	yes	—
21	#88110	C₂²	1	4	yes	—
22	C₄⋊#1057	C₂²	1	4	yes	—
23	C₄⋊#1057	C₂²	1	4	yes	—
24	C₄×#1057	C₂²	1	4	yes	—
25	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
27	C₂×Dic₂₆	C₂×C₄	1	4	yes	—
28	C₂×#1057	C₂³	1	4	yes	—
29	C₂×#1057	C₂³	1	1	yes	characteristic
30	C₂×#1057	C₂³	1	1	yes	characteristic
31	C₂×#1057	C₂³	1	2	yes	—
32	#6118	—	2	4	no	—
33	D₁₃⋊C₈	—	2	2	no	—
34	D₁₃⋊C₈	Q₈	1	4	yes	complemented
35	C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
36	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
37	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	#6103	C₂×C₄	1	4	yes	—
39	C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
40	#6101	C₂×C₄	1	4	yes	—
41	#6101	C₂×C₄	1	4	yes	—
42	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₄×Dic₁₃	C₂³	1	4	yes	—
44	C₄×Dic₁₃	C₂³	1	2	yes	—
45	#2961	—	13	1	no	maximal, Sylow
46	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
51	C₂×Dic₁₃	C₂²×C₄	1	4	yes	—
52	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
53	C₄×D₁₃	—	4	2	no	—
54	C₄×D₁₃	C₂×Q₈	1	2	yes	—
55	C₄×D₁₃	#41	1	2	yes	—
56	Dic₂₆	—	4	4	no	—
57	#1057	—	2	1	no	—
58	#1057	—	2	1	no	—
59	#1057	—	2	4	no	—
60	#1057	C₂×Q₈	1	4	yes	—
61	#533	—	13	1	no	—
62	#446	—	13	4	no	—
63	#446	—	13	4	no	—
64	#424	—	13	2	no	—
65	#423	—	13	1	no	—
66	#405	—	13	2	no	—
67	C₂×#97	—	13	1	no	—
68	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
69	C₂×D₁₃	—	2	2	no	—
70	C₂×D₁₃	C₄×Q₈	1	2	yes	—
71	C₄×C₁₃	—	2	4	no	—
72	C₄×C₁₃	—	2	2	no	—
73	C₄×C₁₃	C₄×Q₈	1	2	yes	—
74	Dic₁₃	—	2	2	no	—
75	Dic₁₃	—	2	4	no	—
76	Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
77	Dic₁₃	C₂×#41	1	1	yes	characteristic
78	C₂×M₁₆	—	13	2	no	—
79	C₂²×C₈	—	13	1	no	—
80	C₂²×C₈	—	13	1	no	—
81	C₄⋊Q₈	—	13	2	no	—
82	#125	—	13	1	no	—
83	#125	#261	1	1	yes	characteristic
84	C₂²⋊Q₈	—	13	4	no	—
85	C₄×Q₈	—	13	4	no	—
86	#117	—	13	2	no	—
87	C₂×C₄²	—	13	1	no	—
88	C₄⋊C₈	—	13	4	no	—
89	C₄⋊C₈	—	13	4	no	—
90	C₄⋊C₈	—	13	4	no	—
91	#97	—	13	2	no	—
92	#97	—	13	2	no	—
93	#97	—	13	4	no	—
94	C₄×C₈	—	13	4	no	—
95	C₂×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
96	C₂×C₁₃	#568	1	2	yes	—
97	D₁₃	—	2	2	no	—
98	C₂×Q₈	—	13	4	no	—
99	C₂²×C₄	—	13	1	no	—
100	C₂²×C₄	—	13	2	no	—
101	M₁₆	—	26	4	no	—
102	C₂×C₈	—	13	2	no	—
103	C₂×C₈	—	13	4	no	—
104	C₂×C₈	—	13	4	no	—
105	C₂×C₈	—	13	1	no	—
106	C₂×C₈	—	13	1	no	—
107	C₂×C₈	—	26	2	no	—
108	C₄⋊C₄	—	13	2	no	—
109	C₄⋊C₄	—	13	4	no	—
110	C₄⋊C₄	—	13	4	no	—
111	C₄⋊C₄	C₂×#261	1	2	yes	—
112	C₄⋊C₄	C₂×#261	1	4	yes	—
113	C₂²⋊C₄	—	13	4	no	—
114	C₄²	—	13	4	no	—
115	C₄²	—	13	2	no	—
116	C₄²	—	13	1	no	—
117	C₄²	C₂×#261	1	1	yes	characteristic
118	C₁₃	#2961	1	1	yes	characteristic, complemented, Sylow
119	C₂³	—	13	1	no	—
120	Q₈	—	52	4	no	—
121	C₂×C₄	—	13	1	no	—
122	C₂×C₄	—	13	2	no	—
123	C₂×C₄	—	13	2	no	—
124	C₂×C₄	—	13	2	no	—
125	C₂×C₄	—	13	4	no	—
126	C₂×C₄	—	52	2	no	—
127	C₂×C₄	C₂²×#261	1	2	yes	—
128	C₂×C₄	C₂²×#261	1	4	yes	—
129	C₂×C₄	C₂²×#261	1	1	yes	characteristic
130	C₈	—	13	4	no	—
131	C₈	—	26	1	no	—
132	C₈	—	26	1	no	—
133	C₈	—	26	4	no	—
134	C₂²	—	13	2	no	—
135	C₂²	—	26	2	no	—
136	C₂²	C₂³×#261	1	1	yes	characteristic
137	C₄	—	2	2	no	—
138	C₄	—	2	4	no	—
139	C₄	—	13	1	no	—
140	C₄	—	13	1	no	—
141	C₄	—	26	2	no	—
142	C₄	—	26	4	no	—
143	C₄	Q₈×#261	1	2	yes	—
144	C₂	—	26	2	no	—
145	C₂	C₂×Q₈×#261	1	1	yes	characteristic
146	C₂	#11719629	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719393

C₂

yes

maximal, characteristic

#11719080

C₂

yes

maximal, complemented

#11719079

C₂

yes

maximal

#11719078

C₂

yes

maximal, complemented

#11719072

C₂

yes

maximal

#11719052

C₂

yes

maximal, characteristic

#11719047

C₂

yes

maximal, characteristic

C₂×#6118

C₂²

yes

—

C₂×D₁₃⋊C₈

C₂²

yes

characteristic

C₂×D₁₃⋊C₈

C₂²

yes

characteristic

C₁₃×#125

C₄

yes

characteristic

#88150

C₄

yes

—

#88146

C₂²

yes

—

#88142

C₄

yes

—

#88141

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

characteristic

#88124

C₄

yes

characteristic

#88112

C₂²

yes

—

#88110

C₂²

yes

—

#88110

C₂²

yes

—

#88110

C₂²

yes

—

C₄⋊#1057

C₂²

yes

—

C₄⋊#1057

C₂²

yes

—

C₄×#1057

C₂²

yes

—

C₂×C₄×D₁₃

C₂×C₄

yes

—

C₂×C₄×D₁₃

C₂³

yes

characteristic

C₂×Dic₂₆

C₂×C₄

yes

—

C₂×#1057

C₂³

yes

—

C₂×#1057

C₂³

yes

characteristic

C₂×#1057

C₂³

yes

characteristic

C₂×#1057

C₂³

yes

—

#6118

—

D₁₃⋊C₈

—

D₁₃⋊C₈

Q₈

yes

complemented

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

#6103

C₂×C₄

yes

—

C₄⋊Dic₁₃

C₂×C₄

yes

—

#6101

C₂×C₄

yes

—

#6101

C₂×C₄

yes

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂³

yes

—

C₄×Dic₁₃

C₂³

yes

—

#2961

—

maximal, Sylow

C₂²×D₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₂²×C₄

yes

—

C₂×Dic₁₃

C₂²×C₄

yes

—

C₂×Dic₁₃

C₂⁴

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₂×Q₈

yes

—

C₄×D₁₃

#41

yes

—

Dic₂₆

—

—

—

—

C₂×Q₈

yes

—

—

—

—

—

—

—

C₂×#97

—

C₂²×C₁₃

C₂³×C₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄×Q₈

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₄×Q₈

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

C₂²×Q₈

yes

characteristic

Dic₁₃

C₂×#41

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

#97

—

#97

—

C₄×C₈

—

C₂×C₁₃

C₂×C₄×Q₈

yes

characteristic

C₂×C₁₃

#568

yes

—

D₁₃

—

C₂×Q₈

—

C₂²×C₄

—

100

C₂²×C₄

—

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

C₂×#261

yes

—

112

C₄⋊C₄

C₂×#261

yes

—

113

C₂²⋊C₄

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₄²

C₂×#261

yes

characteristic

118

C₁₃

#2961

yes

characteristic, complemented, Sylow

119

C₂³

—

120

Q₈

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

C₂²×#261

yes

—

128

C₂×C₄

C₂²×#261

yes

—

129

C₂×C₄

C₂²×#261

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

C₂³×#261

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

Q₈×#261

yes

—

144

C₂

—

145

C₂

C₂×Q₈×#261

yes

characteristic

146

C₂

#11719629

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₄
Fitting	C₁₃×#125	C₄
prime radical	C₂²×D₁₃	C₂²×C₄
cosocle	C₂×Dic₁₃	C₂⁴
hypercenter	#125	#261
hypocenter	C₁₃	#2961
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#261

commutator, socle

C₂²×C₁₃

C₂³×C₄

Fitting

C₁₃×#125

C₄

prime radical

C₂²×D₁₃

C₂²×C₄

cosocle

C₂×Dic₁₃

C₂⁴

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
2. #11719080	C₂	semidirect
4. #11719078	C₂	semidirect
34. D₁₃⋊C₈	Q₈	semidirect
118. C₁₃	#2961	semidirect

H ≅ G/N

type

2. #11719080

C₂

semidirect

4. #11719078

C₂

semidirect

34. D₁₃⋊C₈

Q₈

semidirect

118. C₁₃

#2961

semidirect

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

subgroup	index
#11719393	2
#11719080	2
#11719079	2
#11719078	2
#11719072	2
#11719052	2
#11719047	2
#2961	13

subgroup

index

Subgroups — #13131628

Conjugacy classes of subgroups

Complements

Maximal subgroups