Group #13115667 — subgroups

Subgroups — #13115667

Order 1664.

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

normal subgroups only

This group has 320 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	#11719182	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88065	C₂	1	4	yes	maximal, complemented
4	#11718593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6127	C₂²	1	2	yes	—
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	#88184	—	2	2	no	—
9	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
10	#88129	C₄	1	2	yes	complemented
11	#88128	C₄	1	1	yes	characteristic, complemented
12	C₄×D₅₂	—	2	2	no	—
13	#88123	C₄	1	1	yes	characteristic, complemented
14	C₁₃×C₄⋊C₈	—	2	2	no	—
15	#88071	—	2	2	no	—
16	#88065	—	2	8	no	—
17	C₂²×C₄×C₁₃	D₄	1	2	yes	—
18	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₂²⋊D₁₃	—	2	2	no	—
20	C₂²×Dic₁₃	—	2	2	no	—
21	#6127	—	2	4	no	—
22	#6127	—	2	4	no	—
23	C₂×D₅₂	—	2	2	no	—
24	C₂×D₅₂	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₁₃	—	2	2	no	—
26	C₂×Dic₂₆	C₂×C₄	1	2	yes	—
27	C₁₃×M₁₆	—	2	4	no	—
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₁₃	D₄	1	2	yes	—
32	#6103	—	2	4	no	—
33	C₄⋊Dic₁₃	—	2	2	no	—
34	C₄×Dic₁₃	—	2	2	no	—
35	C₄×Dic₁₃	D₄	1	4	yes	complemented
36	#1963	—	13	1	no	maximal, Sylow
37	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×D₁₃	—	2	2	no	—
39	C₂×C₄×C₁₃	—	4	2	no	—
40	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₃	#41	1	2	yes	—
46	C₂²⋊D₁₃	—	4	4	no	—
47	C₂×Dic₁₃	—	2	2	no	—
48	C₂×Dic₁₃	—	2	4	no	—
49	C₂×Dic₁₃	—	4	4	no	—
50	D₅₂	—	2	4	no	—
51	D₅₂	—	4	4	no	—
52	C₄×D₁₃	—	4	2	no	—
53	C₄×D₁₃	—	4	2	no	—
54	Dic₂₆	—	2	4	no	—
55	C₈×C₁₃	—	4	2	no	—
56	#532	—	13	1	no	—
57	#423	D₁₃	1	1	yes	characteristic, complemented
58	C₂×#104	—	13	4	no	—
59	#376	—	13	1	no	—
60	C₂²×C₁₃	—	2	2	no	—
61	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₁₃	#121	1	2	yes	—
63	C₂×D₁₃	—	4	2	no	—
64	C₂×D₁₃	—	4	4	no	—
65	C₄×C₁₃	—	2	2	no	—
66	C₄×C₁₃	—	2	2	no	—
67	C₄×C₁₃	C₄×D₄	1	2	yes	—
68	C₄×C₁₃	#124	1	1	yes	characteristic
69	C₄×C₁₃	#127	1	1	yes	characteristic
70	Dic₁₃	—	4	4	no	—
71	Dic₁₃	—	4	2	no	—
72	C₂×#41	—	13	2	no	—
73	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
74	C₄⋊Q₈	—	13	1	no	—
75	#127	—	13	1	no	—
76	#124	—	13	2	no	—
77	#121	—	26	2	no	—
78	C₄×D₄	—	26	2	no	—
79	C₂×C₄²	—	13	2	no	—
80	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
81	C₄⋊C₈	—	2	2	no	—
82	#104	—	26	8	no	—
83	#95	—	26	2	no	—
84	C₂×C₁₃	—	2	2	no	—
85	C₂×C₁₃	#390	1	1	yes	characteristic
86	C₂×C₁₃	#421	1	2	yes	—
87	D₁₃	—	8	2	no	—
88	#41	—	26	4	no	—
89	#41	—	26	4	no	—
90	C₂×Q₈	—	13	2	no	—
91	C₂×D₄	—	13	2	no	—
92	C₂×D₄	—	26	2	no	—
93	C₂×D₄	—	26	2	no	—
94	C₂²×C₄	—	26	2	no	—
95	C₂²×C₄	—	26	2	no	—
96	C₂²×C₄	D₅₂	1	2	yes	—
97	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
98	M₁₆	—	2	4	no	—
99	C₂×C₈	—	2	2	no	—
100	C₄⋊C₄	—	26	2	no	—
101	C₂²⋊C₄	—	26	4	no	—
102	C₄²	—	13	4	no	—
103	C₄²	—	26	2	no	—
104	C₄²	C₄×D₁₃	1	1	yes	characteristic
105	C₄²	C₄×D₁₃	1	1	yes	characteristic
106	C₄²	C₂²⋊D₁₃	1	2	yes	—
107	C₁₃	#1963	1	1	yes	characteristic, complemented, Sylow
108	C₂³	—	26	2	no	—
109	C₂³	C₂×D₅₂	1	1	yes	characteristic
110	Q₈	—	26	4	no	—
111	D₄	—	26	4	no	—
112	D₄	—	52	4	no	—
113	D₄	—	52	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	26	4	no	—
116	C₂×C₄	—	26	2	no	—
117	C₂×C₄	—	52	4	no	—
118	C₂×C₄	—	52	2	no	—
119	C₂×C₄	—	52	2	no	—
120	C₂×C₄	#6103	1	2	yes	—
121	C₂×C₄	#6103	1	2	yes	—
122	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
123	C₂×C₄	D₄×D₁₃	1	2	yes	—
124	C₂×C₄	#6131	1	2	yes	—
125	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
126	C₈	—	4	2	no	—
127	C₂²	—	2	2	no	—
128	C₂²	—	52	4	no	—
129	C₂²	—	52	2	no	—
130	C₂²	#88149	1	2	yes	—
131	C₂²	C₂×#6103	1	1	yes	characteristic
132	C₄	—	2	2	no	—
133	C₄	—	2	2	no	—
134	C₄	—	52	4	no	—
135	C₄	—	52	2	no	—
136	C₄	#88147	1	2	yes	—
137	C₄	#88194	1	1	yes	characteristic
138	C₄	#88201	1	1	yes	characteristic
139	C₂	—	2	2	no	—
140	C₂	—	104	2	no	—
141	C₂	#11718649	1	1	yes	characteristic
142	C₂	#11718800	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719182

C₂

yes

maximal, characteristic

C₁₃×#423

C₂

yes

maximal, characteristic, complemented

C₂×#88065

C₂

yes

maximal, complemented

#11718593

C₂

yes

maximal, characteristic, complemented

C₂×#6127

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

#88184

—

C₂×C₄×Dic₁₃

C₂²

yes

—

#88129

C₄

yes

complemented

#88128

C₄

yes

characteristic, complemented

C₄×D₅₂

—

#88123

C₄

yes

characteristic, complemented

C₁₃×C₄⋊C₈

—

#88071

—

#88065

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₂²⋊D₁₃

—

C₂²×Dic₁₃

—

#6127

—

#6127

—

C₂×D₅₂

—

C₂×D₅₂

C₂×C₄

yes

—

C₂×C₄×D₁₃

—

C₂×Dic₂₆

C₂×C₄

yes

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

D₄

yes

—

#6103

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

D₄

yes

complemented

#1963

—

maximal, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂²⋊D₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

C₈×C₁₃

—

#532

—

#423

D₁₃

yes

characteristic, complemented

C₂×#104

—

#376

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃

#121

yes

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₄×D₄

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

C₂×#41

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

#104

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#390

yes

characteristic

C₂×C₁₃

#421

yes

—

D₁₃

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₅₂

yes

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

C₄×D₁₃

yes

characteristic

105

C₄²

C₄×D₁₃

yes

characteristic

106

C₄²

C₂²⋊D₁₃

yes

—

107

C₁₃

#1963

yes

characteristic, complemented, Sylow

108

C₂³

—

109

C₂³

C₂×D₅₂

yes

characteristic

110

Q₈

—

111

D₄

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

#6103

yes

—

121

C₂×C₄

#6103

yes

—

122

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

123

C₂×C₄

D₄×D₁₃

yes

—

124

C₂×C₄

#6131

yes

—

125

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

#88149

yes

—

131

C₂²

C₂×#6103

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#88147

yes

—

137

C₄

#88194

yes

characteristic

138

C₄

#88201

yes

characteristic

139

C₂

—

140

C₂

—

104

—

141

C₂

#11718649

yes

characteristic

142

C₂

#11718800

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#423	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	#11719182	C₂
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	#423	D₁₃
hypocenter	C₁₃	#1963
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#423

C₂

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

prime radical

#11719182

C₂

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
2. C₁₃×#423	C₂	semidirect
3. C₂×#88065	C₂	semidirect
4. #11718593	C₂	semidirect
10. #88129	C₄	semidirect
11. #88128	C₄	semidirect
13. #88123	C₄	semidirect
35. C₄×Dic₁₃	D₄	semidirect
57. #423	D₁₃	semidirect
107. C₁₃	#1963	semidirect

H ≅ G/N

type

2. C₁₃×#423

C₂

semidirect

3. C₂×#88065

C₂

semidirect

4. #11718593

C₂

semidirect

10. #88129

C₄

semidirect

11. #88128

C₄

semidirect

13. #88123

C₄

semidirect

35. C₄×Dic₁₃

D₄

semidirect

57. #423

D₁₃

semidirect

107. C₁₃

#1963

semidirect

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

subgroup	index
#11719182	2
C₁₃×#423	2
C₂×#88065	2
#11718593	2
#1963	13

subgroup

index

C₁₃×#423

Subgroups — #13115667

Conjugacy classes of subgroups

Complements

Maximal subgroups