Group #13130955 — subgroups

Subgroups — #13130955

Order 1664.

184 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 66 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	#11719100	C₂	1	2	yes	maximal
2	C₂×#88103	C₂	1	1	yes	maximal, characteristic
3	#11719089	C₂	1	1	yes	maximal, characteristic
4	D₁₃×#108	C₂	1	1	yes	maximal, characteristic
5	#11718274	C₂	1	2	yes	maximal
6	#88237	C₂²	1	1	yes	characteristic
7	D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
8	C₂×#6118	C₂²	1	2	yes	—
9	M₁₆×D₁₃	C₂²	1	2	yes	—
10	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	#88104	—	2	2	no	—
12	#88103	—	2	2	no	—
13	#88103	—	2	1	no	—
14	#88103	—	2	1	no	—
15	#88100	—	2	1	no	—
16	C₈×#261	—	2	1	no	—
17	C₁₃×#108	C₄	1	1	yes	characteristic, complemented
18	#88062	C₄	1	2	yes	complemented
19	#88059	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
21	C₂²⋊#261	Q₈	1	2	yes	—
22	#6122	—	2	1	no	—
23	C₂×#1057	—	2	2	no	—
24	C₄⋊#261	—	2	1	no	—
25	C₄×#261	—	2	1	no	—
26	#6118	—	2	2	no	—
27	#6118	—	2	2	no	—
28	#6118	D₄	1	2	yes	—
29	D₁₃⋊C₈	—	2	1	no	—
30	C₁₃×M₁₆	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	#6099	C₂×C₄	1	2	yes	—
33	C₂×#1055	C₂×C₄	1	1	yes	characteristic
34	#6094	—	2	2	no	—
35	C₈×D₁₃	—	2	2	no	—
36	C₈×D₁₃	D₄	1	1	yes	characteristic
37	C₈×D₁₃	D₄	1	1	yes	characteristic
38	C₈×D₁₃	Q₈	1	1	yes	characteristic
39	C₈×D₁₃	Q₈	1	1	yes	characteristic
40	#1953	—	13	1	no	maximal, Sylow
41	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×#261	—	2	2	no	—
43	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×Dic₁₃	#41	1	1	yes	characteristic
45	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
46	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
47	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₁₃	#41	1	1	yes	characteristic
49	#1057	—	2	2	no	—
50	#1057	—	4	2	no	—
51	C₈×C₁₃	—	2	2	no	—
52	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
54	#1055	—	2	2	no	—
55	#1055	C₄⋊C₄	1	1	yes	characteristic
56	#1055	C₄⋊C₄	1	1	yes	characteristic
57	#430	—	13	2	no	—
58	C₂×#108	—	13	1	no	—
59	C₂×#108	—	13	1	no	—
60	#405	—	13	1	no	—
61	#344	—	13	2	no	—
62	C₂²×C₁₃	C₄×Q₈	1	1	yes	characteristic
63	C₂×D₁₃	—	4	1	no	—
64	C₂×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
66	#261	—	4	2	no	—
67	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
69	Dic₁₃	#121	1	1	yes	characteristic
70	Dic₁₃	#125	1	1	yes	characteristic
71	C₂×M₁₆	—	13	1	no	—
72	C₂×M₁₆	—	13	2	no	—
73	C₂×M₁₆	—	13	2	no	—
74	C₂²×C₈	—	13	1	no	—
75	#117	—	13	1	no	—
76	#108	—	13	2	no	—
77	#108	—	13	1	no	—
78	#108	—	26	1	no	—
79	#108	—	26	1	no	—
80	#108	—	26	2	no	—
81	#108	—	26	2	no	—
82	#108	#261	1	1	yes	characteristic, complemented
83	#97	—	26	1	no	—
84	C₄×C₈	—	26	1	no	—
85	C₂×C₁₃	—	2	1	no	—
86	C₂×C₁₃	#389	1	1	yes	characteristic
87	D₁₃	—	2	1	no	—
88	D₁₃	—	2	1	no	—
89	C₂²×C₄	—	13	1	no	—
90	M₁₆	—	13	2	no	—
91	M₁₆	—	13	2	no	—
92	M₁₆	—	26	2	no	—
93	M₁₆	—	26	1	no	—
94	M₁₆	—	26	2	no	—
95	M₁₆	—	26	2	no	—
96	M₁₆	C₂×#261	1	2	yes	—
97	C₂×C₈	—	13	1	no	—
98	C₂×C₈	—	13	1	no	—
99	C₂×C₈	—	13	1	no	—
100	C₂×C₈	—	13	1	no	—
101	C₂×C₈	—	13	1	no	—
102	C₂×C₈	—	26	2	no	—
103	C₂×C₈	—	26	1	no	—
104	C₂×C₈	—	26	2	no	—
105	C₂×C₈	C₂×#261	1	1	yes	characteristic
106	C₄⋊C₄	—	26	1	no	—
107	C₂²⋊C₄	—	13	2	no	—
108	C₄²	—	26	1	no	—
109	C₁₃	#1953	1	1	yes	characteristic, complemented, Sylow
110	C₂³	—	13	1	no	—
111	C₂×C₄	—	13	1	no	—
112	C₂×C₄	—	13	1	no	—
113	C₂×C₄	—	13	1	no	—
114	C₂×C₄	—	13	1	no	—
115	C₂×C₄	—	13	1	no	—
116	C₂×C₄	—	26	2	no	—
117	C₂×C₄	C₂²×#261	1	1	yes	characteristic
118	C₈	—	2	2	no	—
119	C₈	—	13	1	no	—
120	C₈	—	13	1	no	—
121	C₈	—	26	2	no	—
122	C₈	—	26	2	no	—
123	C₈	—	52	2	no	—
124	C₈	C₄⋊#261	1	1	yes	characteristic
125	C₈	C₄⋊#261	1	1	yes	characteristic
126	C₂²	—	13	1	no	—
127	C₂²	—	13	1	no	—
128	C₂²	—	52	1	no	—
129	C₂²	Q₈×#261	1	1	yes	characteristic
130	C₄	—	13	1	no	—
131	C₄	—	13	1	no	—
132	C₄	—	52	2	no	—
133	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
134	C₄	D₄×#261	1	1	yes	characteristic
135	C₂	—	2	1	no	—
136	C₂	—	26	1	no	—
137	C₂	—	26	1	no	—
138	C₂	#11719083	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11719100

C₂

yes

maximal

C₂×#88103

C₂

yes

maximal, characteristic

#11719089

C₂

yes

maximal, characteristic

D₁₃×#108

C₂

yes

maximal, characteristic

#11718274

C₂

yes

maximal

#88237

C₂²

yes

characteristic

D₁₃⋊M₁₆

C₂²

yes

characteristic

C₂×#6118

C₂²

yes

—

M₁₆×D₁₃

C₂²

yes

—

C₂×C₈×D₁₃

C₂²

yes

—

—

—

—

—

—

C₁₃×#108

C₄

yes

characteristic, complemented

#88062

C₄

yes

complemented

#88059

C₄

yes

characteristic, complemented

C₂×C₄×D₁₃

C₂³

yes

characteristic

C₂²⋊#261

Q₈

yes

—

—

—

—

—

—

—

D₄

yes

—

D₁₃⋊C₈

—

C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

#6099

C₂×C₄

yes

—

C₂×#1055

C₂×C₄

yes

characteristic

#6094

—

C₈×D₁₃

—

C₈×D₁₃

D₄

yes

characteristic

C₈×D₁₃

D₄

yes

characteristic

C₈×D₁₃

Q₈

yes

characteristic

C₈×D₁₃

Q₈

yes

characteristic

#1953

—

maximal, Sylow

C₂²×D₁₃

C₂×Q₈

yes

characteristic

C₂×#261

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

#41

yes

characteristic

C₄×D₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

C₄×D₁₃

yes

—

—

C₈×C₁₃

—

C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

characteristic

#1055

—

#1055

C₄⋊C₄

yes

characteristic

#1055

C₄⋊C₄

yes

—

—

—

—

—

C₂²×C₁₃

C₄×Q₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₂²⋊Q₈

yes

characteristic

C₂×D₁₃

C₄⋊Q₈

yes

characteristic

#261

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₄×D₄

yes

Dic₁₃

yes

Dic₁₃

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

—

—

—

yes

characteristic, complemented

#97

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#389

yes

characteristic

D₁₃

—

D₁₃

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×#261

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂×#261

yes

characteristic

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₁₃

#1953

yes

characteristic, complemented, Sylow

110

C₂³

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂²×#261

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

C₄⋊#261

yes

characteristic

125

C₈

C₄⋊#261

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

Q₈×#261

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

C₂×C₄⋊#261

yes

characteristic

134

C₄

D₄×#261

yes

characteristic

135

C₂

—

136

C₂

—

137

C₂

—

138

C₂

#11719083

yes

characteristic

	subgroup	G/H
center	C₂	#11719083
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#108	C₄
socle	C₂×C₁₃	#389
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#108	#261
hypocenter	C₁₃	#1953
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

subgroup

G/H

center

C₂

#11719083

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#108

C₄

socle

C₂×C₁₃

#389

prime radical

C₂²×D₁₃

C₂×Q₈

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

N	H ≅ G/N	type
17. C₁₃×#108	C₄	semidirect
18. #88062	C₄	semidirect
19. #88059	C₄	semidirect
82. #108	#261	semidirect
109. C₁₃	#1953	semidirect

H ≅ G/N

type

17. C₁₃×#108

C₄

semidirect

18. #88062

C₄

semidirect

19. #88059

C₄

semidirect

82. #108

#261

semidirect

109. C₁₃

#1953

semidirect

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

subgroup	index
#11719100	2
C₂×#88103	2
#11719089	2
D₁₃×#108	2
#11718274	2
#1953	13

subgroup

index

D₁₃×#108

Subgroups — #13130955

Conjugacy classes of subgroups

Complements

Maximal subgroups