Group #13130656 — subgroups

Subgroups — #13130656

Order 1664.

220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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×#88103	C₂	1	1	yes	maximal, characteristic
3	C₄×#6118	C₂	1	2	yes	maximal
4	D₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	#11718268	C₂	1	2	yes	maximal
6	C₂×#6118	C₂²	1	2	yes	—
7	C₂×#6118	C₂²	1	2	yes	—
8	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#88110	—	2	2	no	—
12	C₄×#1057	—	2	2	no	—
13	#88104	C₄	1	4	yes	complemented
14	#88103	C₄	1	4	yes	complemented
15	C₁₃×#97	C₄	1	1	yes	characteristic
16	#88055	C₄	1	1	yes	characteristic
17	#88055	C₄	1	1	yes	characteristic
18	#88043	C₄	1	1	yes	characteristic
19	C₂×C₄×D₁₃	Q₈	1	2	yes	—
20	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
21	C₂×#1057	—	2	2	no	—
22	C₂×#1057	—	2	2	no	—
23	#6118	—	2	2	no	—
24	#6118	—	2	2	no	—
25	#6118	C₂×C₄	1	4	yes	—
26	#6118	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₁₃	D₄	1	2	yes	—
32	C₂×#1055	C₂×C₄	1	1	yes	characteristic
33	C₂×#1055	C₂×C₄	1	1	yes	characteristic
34	C₈×D₁₃	—	2	1	no	—
35	C₈×D₁₃	—	2	1	no	—
36	C₈×D₁₃	C₂×C₄	1	2	yes	—
37	C₈×D₁₃	C₂×C₄	1	2	yes	—
38	#1778	—	13	1	no	maximal, Sylow
39	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
43	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
44	C₄×D₁₃	—	4	2	no	—
45	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₄×D₁₃	#41	1	1	yes	characteristic
48	C₄×D₁₃	#41	1	1	yes	characteristic
49	#1057	—	2	4	no	—
50	#1057	—	2	4	no	—
51	C₈×C₁₃	—	2	1	no	—
52	C₈×C₁₃	C₄²	1	2	yes	—
53	#1055	—	2	1	no	—
54	#1055	C₄²	1	2	yes	—
55	C₂×#108	—	13	1	no	—
56	C₂×#108	—	13	1	no	—
57	C₄×M₁₆	—	13	2	no	—
58	C₂×#97	—	13	1	no	—
59	#341	—	13	2	no	—
60	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×D₁₃	—	2	2	no	—
62	C₂×D₁₃	C₄×Q₈	1	1	yes	characteristic
63	C₂×D₁₃	C₄×Q₈	1	1	yes	characteristic
64	C₄×C₁₃	—	2	2	no	—
65	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
66	C₄×C₁₃	#117	1	1	yes	characteristic
67	Dic₁₃	—	2	2	no	—
68	Dic₁₃	C₄×D₄	1	1	yes	characteristic
69	Dic₁₃	C₄×D₄	1	1	yes	characteristic
70	C₂×M₁₆	—	13	2	no	—
71	C₂×M₁₆	—	13	2	no	—
72	C₂²×C₈	—	13	1	no	—
73	C₂²×C₈	—	13	1	no	—
74	C₂×C₄²	—	13	1	no	—
75	#108	—	13	4	no	—
76	#108	—	13	4	no	—
77	#97	—	13	1	no	—
78	#97	—	13	1	no	—
79	#97	—	13	1	no	—
80	#97	—	26	2	no	—
81	#97	#261	1	1	yes	characteristic
82	C₄×C₈	—	26	2	no	—
83	C₂×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₁₃	#430	1	2	yes	—
85	D₁₃	—	2	1	no	—
86	D₁₃	—	2	1	no	—
87	C₂²×C₄	—	13	1	no	—
88	C₂²×C₄	—	13	2	no	—
89	M₁₆	—	13	4	no	—
90	M₁₆	—	13	4	no	—
91	M₁₆	—	26	2	no	—
92	M₁₆	—	26	2	no	—
93	C₂×C₈	—	13	1	no	—
94	C₂×C₈	—	13	2	no	—
95	C₂×C₈	—	13	2	no	—
96	C₂×C₈	—	13	1	no	—
97	C₂×C₈	—	26	1	no	—
98	C₂×C₈	—	26	1	no	—
99	C₂×C₈	—	26	2	no	—
100	C₂×C₈	—	26	2	no	—
101	C₂×C₈	C₂×#261	1	1	yes	characteristic
102	C₂×C₈	C₂×#261	1	1	yes	characteristic
103	C₄²	—	13	2	no	—
104	C₄²	—	13	1	no	—
105	C₄²	C₂×#261	1	1	yes	characteristic
106	C₁₃	#1778	1	1	yes	characteristic, complemented, Sylow
107	C₂³	—	13	1	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	—	13	2	no	—
114	C₂×C₄	—	52	2	no	—
115	C₂×C₄	C₄⋊#261	1	2	yes	—
116	C₂×C₄	C₂²×#261	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	—	13	2	no	—
119	C₈	—	26	4	no	—
120	C₈	—	26	4	no	—
121	C₈	—	26	1	no	—
122	C₈	C₄×#261	1	2	yes	—
123	C₂²	—	13	1	no	—
124	C₂²	—	13	1	no	—
125	C₂²	—	26	2	no	—
126	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	13	1	no	—
129	C₄	—	13	1	no	—
130	C₄	—	26	2	no	—
131	C₄	C₂×C₄×#261	1	1	yes	characteristic
132	C₄	#88237	1	1	yes	characteristic
133	C₂	—	26	1	no	—
134	C₂	—	26	1	no	—
135	C₂	C₄×C₄⋊#261	1	1	yes	characteristic
136	C₂	#11719100	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88104

C₂

yes

maximal, characteristic

C₂×#88103

C₂

yes

maximal, characteristic

C₄×#6118

C₂

yes

maximal

D₁₃×#97

C₂

yes

maximal, characteristic

#11718268

C₂

yes

maximal

C₂×#6118

C₂²

yes

—

C₂×#6118

C₂²

yes

—

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₄²×D₁₃

C₂²

yes

—

—

C₄

yes

complemented

#88103

C₄

yes

complemented

C₁₃×#97

C₄

yes

characteristic

#88055

C₄

yes

characteristic

#88055

C₄

yes

characteristic

#88043

C₄

yes

characteristic

C₂×C₄×D₁₃

Q₈

yes

—

C₂×C₄×D₁₃

C₂³

yes

—

—

—

—

C₂×C₄

yes

—

#6118

C₂×C₄

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

C₂×C₄

yes

—

C₈×D₁₃

C₂×C₄

yes

—

#1778

—

maximal, Sylow

C₂²×D₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₂²×C₄

yes

characteristic

C₄×D₁₃

C₂²×C₄

yes

C₄×D₁₃

yes

C₄×D₁₃

yes

—

—

C₈×C₁₃

—

C₈×C₁₃

C₄²

yes

—

#1055

—

#1055

C₄²

yes

—

C₂×#108

—

C₂×#108

—

C₄×M₁₆

—

C₂×#97

—

#341

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄×Q₈

yes

characteristic

C₂×D₁₃

C₄×Q₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄²

yes

characteristic

C₄×C₁₃

#117

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄×D₄

yes

characteristic

Dic₁₃

C₄×D₄

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

—

—

—

—

—

—

yes

C₄×C₈

—

C₂×C₁₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₃

#430

yes

—

D₁₃

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂×#261

yes

characteristic

102

C₂×C₈

C₂×#261

yes

characteristic

103

C₄²

—

104

C₄²

—

105

C₄²

C₂×#261

yes

characteristic

106

C₁₃

#1778

yes

characteristic, complemented, Sylow

107

C₂³

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

C₄⋊#261

yes

—

116

C₂×C₄

C₂²×#261

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

C₄×#261

yes

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

C₂×C₄⋊#261

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

C₂×C₄×#261

yes

characteristic

132

C₄

#88237

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

C₄×C₄⋊#261

yes

characteristic

136

C₂

#11719100

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#1778
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#261

commutator

C₄×C₁₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#97

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂²×D₁₃

C₂×Q₈

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
13. #88104	C₄	semidirect
14. #88103	C₄	semidirect
106. C₁₃	#1778	semidirect

H ≅ G/N

type

13. #88104

C₄

semidirect

14. #88103

C₄

semidirect

106. C₁₃

#1778

semidirect

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

subgroup	index
C₂×#88104	2
C₂×#88103	2
C₄×#6118	2
D₁₃×#97	2
#11718268	2
#1778	13

subgroup

index

D₁₃×#97

Subgroups — #13130656

Conjugacy classes of subgroups

Complements

Maximal subgroups