Group #13130946 — subgroups

Subgroups — #13130946

Order 1664.

200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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	C₂×#88104	C₂	1	1	yes	maximal, characteristic
2	C₂×#88100	C₂	1	1	yes	maximal, characteristic
3	#11719079	C₂	1	2	yes	maximal
4	#11718521	C₂	1	1	yes	maximal, characteristic
5	#11718247	C₂	1	2	yes	maximal
6	C₂×C₄×#261	C₂²	1	1	yes	characteristic
7	C₂×#6118	C₂²	1	2	yes	—
8	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	#88146	C₂²	1	2	yes	—
11	#88112	—	2	2	no	—
12	C₄⋊#1057	—	2	2	no	—
13	#88104	—	2	2	no	—
14	#88100	—	2	2	no	—
15	C₁₃×#106	C₄	1	1	yes	characteristic, complemented
16	#88057	C₄	1	1	yes	characteristic, complemented
17	#88047	C₄	1	2	yes	complemented
18	C₂²×#261	—	2	1	no	—
19	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
20	C₂×#1057	—	2	2	no	—
21	C₂×#1057	D₄	1	1	yes	characteristic
22	C₂×#1057	D₄	1	1	yes	characteristic
23	C₄×#261	—	2	1	no	—
24	C₄×#261	Q₈	1	2	yes	—
25	#6118	—	2	2	no	—
26	#6118	—	2	2	no	—
27	D₁₃⋊C₈	—	2	1	no	—
28	D₁₃⋊C₈	—	2	1	no	—
29	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
31	#6103	—	2	2	no	—
32	C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
33	C₄×Dic₁₃	—	2	2	no	—
34	C₂×#1055	C₂×C₄	1	1	yes	characteristic
35	C₈×D₁₃	D₄	1	2	yes	—
36	C₈×D₁₃	Q₈	1	2	yes	—
37	#1946	—	13	1	no	maximal, Sylow
38	C₂²×D₁₃	#41	1	1	yes	characteristic
39	C₂×#261	—	2	2	no	—
40	C₂×#261	—	4	2	no	—
41	C₂×C₄×C₁₃	—	2	2	no	—
42	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₁₃	—	2	2	no	—
44	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
45	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
46	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₁₃	#41	1	1	yes	characteristic
49	#1057	—	2	1	no	—
50	#1057	—	2	1	no	—
51	#1057	—	4	2	no	—
52	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
53	#1055	C₄⋊C₄	1	2	yes	—
54	C₂×#108	—	13	1	no	—
55	#427	—	13	1	no	—
56	#424	—	13	2	no	—
57	C₂×#97	—	13	1	no	—
58	#339	—	13	2	no	—
59	C₂²×C₁₃	C₄×D₄	1	1	yes	characteristic
60	C₂×D₁₃	—	2	2	no	—
61	C₂×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
62	C₂×D₁₃	#125	1	1	yes	characteristic
63	#261	—	4	2	no	—
64	C₄×C₁₃	—	4	2	no	—
65	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
67	Dic₁₃	—	4	2	no	—
68	Dic₁₃	#121	1	1	yes	characteristic
69	Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×M₁₆	—	13	2	no	—
71	C₂²×C₈	—	13	1	no	—
72	C₂²×C₈	—	13	1	no	—
73	#117	—	13	2	no	—
74	C₂×C₄²	—	13	1	no	—
75	#108	—	26	2	no	—
76	#107	—	13	2	no	—
77	#106	—	13	1	no	—
78	#106	#261	1	1	yes	characteristic, complemented
79	C₄⋊C₈	—	26	2	no	—
80	C₄⋊C₈	—	26	2	no	—
81	#97	—	26	2	no	—
82	C₂×C₁₃	#389	1	1	yes	characteristic
83	C₂×C₁₃	#444	1	2	yes	—
84	D₁₃	—	2	1	no	—
85	D₁₃	—	2	1	no	—
86	C₂²×C₄	—	13	1	no	—
87	C₂²×C₄	—	26	1	no	—
88	M₁₆	—	26	2	no	—
89	M₁₆	—	26	2	no	—
90	C₂×C₈	—	13	1	no	—
91	C₂×C₈	—	13	2	no	—
92	C₂×C₈	—	13	2	no	—
93	C₂×C₈	—	13	1	no	—
94	C₂×C₈	—	13	1	no	—
95	C₂×C₈	—	26	1	no	—
96	C₂×C₈	—	26	1	no	—
97	C₂×C₈	—	26	2	no	—
98	C₂×C₈	C₂×#261	1	1	yes	characteristic
99	C₄⋊C₄	—	13	2	no	—
100	C₄⋊C₄	C₂×#261	1	2	yes	—
101	C₂²⋊C₄	—	26	2	no	—
102	C₄²	—	13	2	no	—
103	C₄²	—	26	2	no	—
104	C₄²	—	26	1	no	—
105	C₁₃	#1946	1	1	yes	characteristic, complemented, Sylow
106	C₂³	—	13	1	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	13	1	no	—
109	C₂×C₄	—	13	1	no	—
110	C₂×C₄	—	13	1	no	—
111	C₂×C₄	—	13	1	no	—
112	C₂×C₄	—	13	1	no	—
113	C₂×C₄	—	26	2	no	—
114	C₂×C₄	—	26	2	no	—
115	C₂×C₄	—	52	2	no	—
116	C₂×C₄	C₂²×#261	1	1	yes	characteristic
117	C₈	—	13	2	no	—
118	C₈	—	26	1	no	—
119	C₈	—	26	1	no	—
120	C₈	—	52	2	no	—
121	C₈	C₄⋊#261	1	2	yes	—
122	C₂²	—	13	1	no	—
123	C₂²	—	13	1	no	—
124	C₂²	—	26	2	no	—
125	C₂²	D₄×#261	1	1	yes	characteristic
126	C₄	—	4	2	no	—
127	C₄	—	13	1	no	—
128	C₄	—	13	1	no	—
129	C₄	—	52	2	no	—
130	C₄	—	52	2	no	—
131	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
132	C₄	Q₈×#261	1	1	yes	characteristic
133	C₂	—	26	1	no	—
134	C₂	—	26	1	no	—
135	C₂	#11719083	1	1	yes	characteristic
136	C₂	#11719108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88104

C₂

yes

maximal, characteristic

C₂×#88100

C₂

yes

maximal, characteristic

#11719079

C₂

yes

maximal

#11718521

C₂

yes

maximal, characteristic

#11718247

C₂

yes

maximal

C₂×C₄×#261

C₂²

yes

characteristic

C₂×#6118

C₂²

yes

—

C₂×D₁₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

#88146

C₂²

yes

—

—

—

—

—

C₁₃×#106

C₄

yes

characteristic, complemented

#88057

C₄

yes

characteristic, complemented

#88047

C₄

yes

complemented

C₂²×#261

—

C₂×C₄×D₁₃

C₂³

yes

characteristic

C₂×#1057

—

C₂×#1057

D₄

yes

characteristic

C₂×#1057

D₄

yes

characteristic

C₄×#261

—

C₄×#261

Q₈

yes

—

#6118

—

#6118

—

D₁₃⋊C₈

—

D₁₃⋊C₈

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

#6103

—

C₄⋊Dic₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

—

C₂×#1055

C₂×C₄

yes

characteristic

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

—

C₂²×D₁₃

yes

—

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

C₄×D₁₃

yes

—

—

—

C₈×C₁₃

C₄⋊C₄

yes

—

#1055

C₄⋊C₄

yes

—

C₂×#108

—

#427

—

#424

—

C₂×#97

—

#339

—

C₂²×C₁₃

C₄×D₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₂²⋊Q₈

yes

C₂×D₁₃

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₄×Q₈

yes

characteristic

Dic₁₃

—

Dic₁₃

#121

yes

characteristic

Dic₁₃

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₂×C₁₃

#389

yes

characteristic

C₂×C₁₃

#444

yes

—

D₁₃

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

C₂×#261

yes

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₁₃

#1946

yes

characteristic, complemented, Sylow

106

C₂³

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₂²×#261

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

C₄⋊#261

yes

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

D₄×#261

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

C₂×C₄⋊#261

yes

characteristic

132

C₄

Q₈×#261

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

#11719083

yes

characteristic

136

C₂

#11719108

yes

—

	subgroup	G/H
center	C₂²	D₄×#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#106	C₄
socle	C₂²×C₁₃	C₄×D₄
prime radical	C₂²×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#106	#261
hypocenter	C₁₃	#1946
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#106

C₄

socle

C₂²×C₁₃

C₄×D₄

prime radical

C₂²×D₁₃

#41

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
15. C₁₃×#106	C₄	semidirect
16. #88057	C₄	semidirect
17. #88047	C₄	semidirect
78. #106	#261	semidirect
105. C₁₃	#1946	semidirect

H ≅ G/N

type

15. C₁₃×#106

C₄

semidirect

16. #88057

C₄

semidirect

17. #88047

C₄

semidirect

78. #106

#261

semidirect

105. C₁₃

#1946

semidirect

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

subgroup	index
C₂×#88104	2
C₂×#88100	2
#11719079	2
#11718521	2
#11718247	2
#1946	13

subgroup

index

Subgroups — #13130946

Conjugacy classes of subgroups

Complements

Maximal subgroups