Group #13114961 — subgroups

Subgroups — #13114961

Order 1664.

172 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 81 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×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
2	#11718767	C₂	1	1	yes	maximal, characteristic
3	#11718762	C₂	1	1	yes	maximal, characteristic
4	#11718151	C₂	1	2	yes	maximal
5	#11718149	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	#88180	C₂²	1	2	yes	—
9	#88180	C₂²	1	1	yes	characteristic
10	C₂×#6099	C₂²	1	1	yes	characteristic
11	C₁₃×#108	—	2	1	no	—
12	C₁₃×#108	—	2	1	no	—
13	#88058	—	2	1	no	—
14	#88057	—	2	1	no	—
15	#88055	C₄	1	2	yes	complemented
16	C₈×Dic₁₃	C₄	1	2	yes	complemented
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×M₁₆	—	2	2	no	—
19	C₁₃×M₁₆	—	2	2	no	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
26	C₂×C₈×C₁₃	Q₈	1	1	yes	characteristic
27	C₂²⋊Dic₁₃	—	2	1	no	—
28	C₂²⋊Dic₁₃	—	2	2	no	—
29	C₄⋊Dic₁₃	—	2	1	no	—
30	C₄⋊Dic₁₃	—	2	2	no	—
31	C₄×Dic₁₃	—	2	2	no	—
32	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
33	#6099	—	2	1	no	—
34	#6099	—	2	1	no	—
35	C₂×#1055	C₂×C₄	1	2	yes	—
36	#1833	—	13	1	no	maximal, Sylow
37	C₂³×C₁₃	#41	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
42	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
43	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
44	C₂×Dic₁₃	—	2	2	no	—
45	C₂×Dic₁₃	—	4	2	no	—
46	C₈×C₁₃	—	4	2	no	—
47	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
48	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
49	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
50	C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
51	#1055	—	2	2	no	—
52	C₂×#108	D₁₃	1	1	yes	characteristic
53	#427	—	13	1	no	—
54	#405	—	13	1	no	—
55	#344	—	13	2	no	—
56	H(3,ℤ/4)	—	13	2	no	—
57	C₂²×C₁₃	—	4	1	no	—
58	C₂²×C₁₃	#117	1	1	yes	characteristic
59	C₂²×C₁₃	#124	1	1	yes	characteristic
60	C₂²×C₁₃	#125	1	1	yes	characteristic
61	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₄×C₁₃	#117	1	1	yes	characteristic
63	C₄×C₁₃	#124	1	1	yes	characteristic
64	C₄×C₁₃	#125	1	1	yes	characteristic
65	Dic₁₃	—	4	2	no	—
66	Dic₁₃	—	8	2	no	—
67	C₂×M₁₆	—	13	1	no	—
68	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
69	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
70	#117	—	13	1	no	—
71	#117	—	13	2	no	—
72	#108	—	2	1	no	—
73	#108	—	2	1	no	—
74	#107	—	26	1	no	—
75	#106	—	26	1	no	—
76	#97	—	13	2	no	—
77	C₄×C₈	—	13	2	no	—
78	C₂×C₁₃	—	2	1	no	—
79	C₂×C₁₃	—	2	1	no	—
80	C₂×C₁₃	—	2	1	no	—
81	C₂×C₁₃	#382	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
83	M₁₆	—	2	2	no	—
84	M₁₆	—	2	2	no	—
85	M₁₆	—	26	1	no	—
86	M₁₆	—	26	1	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	13	2	no	—
89	C₂×C₈	Dic₂₆	1	1	yes	characteristic
90	C₂×C₈	Dic₂₆	1	1	yes	characteristic
91	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
92	C₂×C₈	C₄×D₁₃	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
94	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
95	C₄⋊C₄	—	26	1	no	—
96	C₄⋊C₄	—	26	2	no	—
97	C₂²⋊C₄	—	26	1	no	—
98	C₂²⋊C₄	—	26	2	no	—
99	C₄²	—	13	2	no	—
100	C₄²	—	26	2	no	—
101	C₁₃	#1833	1	1	yes	characteristic, complemented, Sylow
102	C₂³	#6131	1	1	yes	characteristic
103	C₂×C₄	—	26	2	no	—
104	C₂×C₄	—	52	2	no	—
105	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
106	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
107	C₂×C₄	#6129	1	1	yes	characteristic
108	C₂×C₄	#6129	1	1	yes	characteristic
109	C₂×C₄	#6131	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
111	C₈	—	4	2	no	—
112	C₈	—	26	2	no	—
113	C₈	#6101	1	1	yes	characteristic
114	C₈	#6101	1	1	yes	characteristic
115	C₈	#6101	1	1	yes	characteristic
116	C₈	#6101	1	1	yes	characteristic
117	C₂²	—	4	1	no	—
118	C₂²	#88144	1	1	yes	characteristic
119	C₂²	#88146	1	1	yes	characteristic
120	C₂²	#88201	1	1	yes	characteristic
121	C₄	—	52	2	no	—
122	C₄	—	104	2	no	—
123	C₄	#88144	1	1	yes	characteristic
124	C₄	#88146	1	1	yes	characteristic
125	C₄	C₂×#6101	1	1	yes	characteristic
126	C₄	#88190	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#11718638	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#108

C₂

yes

maximal, characteristic

#11718767

C₂

yes

maximal, characteristic

#11718762

C₂

yes

maximal, characteristic

#11718151

C₂

yes

maximal

#11718149

C₂

yes

maximal

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

#88180

C₂²

yes

—

#88180

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

characteristic

C₁₃×#108

—

C₁₃×#108

—

#88058

—

#88057

—

#88055

C₄

yes

complemented

C₈×Dic₁₃

C₄

yes

complemented

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

D₄

yes

characteristic

C₂×C₈×C₁₃

D₄

yes

characteristic

C₂×C₈×C₁₃

Q₈

yes

characteristic

C₂×C₈×C₁₃

Q₈

yes

characteristic

C₂²⋊Dic₁₃

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₂×C₄

yes

—

#6099

—

#6099

—

C₂×#1055

C₂×C₄

yes

—

—

C₂³×C₁₃

yes

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

characteristic

#1055

—

C₂×#108

D₁₃

yes

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₄×C₁₃

C₂×C₄⋊C₄

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

—

—

—

—

—

—

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#382

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₂₆

yes

characteristic

C₂×C₈

Dic₂₆

yes

characteristic

C₂×C₈

C₄×D₁₃

yes

characteristic

C₂×C₈

C₄×D₁₃

yes

characteristic

C₂×C₈

C₂²⋊D₁₃

yes

characteristic

C₂×C₈

C₂²⋊D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

100

C₄²

—

101

C₁₃

#1833

yes

characteristic, complemented, Sylow

102

C₂³

#6131

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×Dic₂₆

yes

characteristic

106

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

107

C₂×C₄

#6129

yes

characteristic

108

C₂×C₄

#6129

yes

characteristic

109

C₂×C₄

#6131

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

#6101

yes

characteristic

114

C₈

#6101

yes

characteristic

115

C₈

#6101

yes

characteristic

116

C₈

#6101

yes

characteristic

117

C₂²

—

118

C₂²

#88144

yes

characteristic

119

C₂²

#88146

yes

characteristic

120

C₂²

#88201

yes

characteristic

121

C₄

—

122

C₄

—

104

—

123

C₄

#88144

yes

characteristic

124

C₄

#88146

yes

characteristic

125

C₄

C₂×#6101

yes

characteristic

126

C₄

#88190

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#11718638

yes

characteristic

	subgroup	G/H
center	C₄	#88146
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#108	C₂
socle	C₂×C₁₃	#382
prime radical	C₂³×C₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×#108	D₁₃
hypocenter	C₁₃	#1833
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#88146

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#108

C₂

C₂×C₁₃

C₂³×C₁₃

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
15. #88055	C₄	semidirect
16. C₈×Dic₁₃	C₄	semidirect
101. C₁₃	#1833	semidirect

H ≅ G/N

type

15. #88055

C₄

semidirect

16. C₈×Dic₁₃

C₄

semidirect

101. C₁₃

#1833

semidirect

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

subgroup	index
C₂×C₁₃×#108	2
#11718767	2
#11718762	2
#11718151	2
#11718149	2
#1833	13

subgroup

index

C₂×C₁₃×#108

Subgroups — #13114961

Conjugacy classes of subgroups

Complements

Maximal subgroups