Group #13130776 — subgroups

Subgroups — #13130776

Order 1664.

220 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 90 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	2	yes	maximal
2	C₂×#88103	C₂	1	2	yes	maximal
3	#11719053	C₂	1	2	yes	maximal
4	C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#6118	C₂²	1	4	yes	—
6	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	#88112	—	2	4	no	—
10	#88104	—	2	4	no	—
11	#88103	—	2	4	no	—
12	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₈×Dic₁₃	C₄	1	1	yes	characteristic
14	C₈×Dic₁₃	C₄	1	1	yes	characteristic
15	C₄×#1055	C₄	1	1	yes	characteristic
16	C₂×C₄×D₁₃	Q₈	1	2	yes	—
17	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
18	C₂×#1057	—	2	4	no	—
19	#6118	—	2	4	no	—
20	#6118	—	2	4	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₁₃	D₄	1	2	yes	—
26	C₂×#1055	C₂×C₄	1	1	yes	characteristic
27	C₂×#1055	C₂×C₄	1	1	yes	characteristic
28	C₈×D₁₃	D₄	1	2	yes	—
29	C₈×D₁₃	D₄	1	2	yes	—
30	C₈×D₁₃	Q₈	1	2	yes	—
31	C₈×D₁₃	Q₈	1	2	yes	—
32	#1848	—	13	1	no	maximal, Sylow
33	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
37	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
38	C₄×D₁₃	—	2	4	no	—
39	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
40	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
41	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
43	#1057	—	4	4	no	—
44	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
46	#1055	C₄⋊C₄	1	2	yes	—
47	#1055	C₄⋊C₄	1	2	yes	—
48	C₂×#108	—	13	2	no	—
49	C₂×#108	—	13	2	no	—
50	#423	—	13	2	no	—
51	C₂×C₄×C₈	—	13	1	no	—
52	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×D₁₃	—	2	2	no	—
54	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
55	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
56	C₄×C₁₃	—	2	2	no	—
57	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	Dic₁₃	#108	1	4	yes	complemented
60	Dic₁₃	#127	1	1	yes	characteristic
61	Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
62	C₂×M₁₆	—	13	4	no	—
63	C₂²×C₈	—	13	1	no	—
64	C₂²×C₈	—	13	1	no	—
65	C₂×C₄²	—	13	1	no	—
66	#108	—	26	4	no	—
67	#108	—	26	4	no	—
68	C₄⋊C₈	—	26	4	no	—
69	C₄×C₈	—	13	1	no	—
70	C₄×C₈	—	13	1	no	—
71	C₄×C₈	—	13	1	no	—
72	C₄×C₈	#261	1	1	yes	characteristic
73	C₂×C₁₃	#384	1	1	yes	characteristic
74	C₂×C₁₃	C₂×#108	1	2	yes	—
75	D₁₃	—	2	1	no	—
76	D₁₃	—	2	1	no	—
77	C₂²×C₄	—	13	1	no	—
78	C₂²×C₄	—	13	2	no	—
79	M₁₆	—	26	4	no	—
80	M₁₆	—	26	4	no	—
81	C₂×C₈	—	13	1	no	—
82	C₂×C₈	—	13	1	no	—
83	C₂×C₈	—	13	2	no	—
84	C₂×C₈	—	13	2	no	—
85	C₂×C₈	—	13	2	no	—
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	—	26	4	no	—
88	C₂×C₈	C₂×#261	1	1	yes	characteristic
89	C₂×C₈	C₂×#261	1	1	yes	characteristic
90	C₄²	—	13	2	no	—
91	C₄²	—	13	1	no	—
92	C₄²	C₂×#261	1	1	yes	characteristic
93	C₁₃	#1848	1	1	yes	characteristic, complemented, Sylow
94	C₂³	—	13	1	no	—
95	C₂×C₄	—	13	1	no	—
96	C₂×C₄	—	13	2	no	—
97	C₂×C₄	—	13	1	no	—
98	C₂×C₄	—	13	1	no	—
99	C₂×C₄	—	13	1	no	—
100	C₂×C₄	—	13	1	no	—
101	C₂×C₄	—	26	4	no	—
102	C₂×C₄	C₄⋊#261	1	2	yes	—
103	C₂×C₄	C₂²×#261	1	1	yes	characteristic
104	C₈	—	13	2	no	—
105	C₈	—	13	2	no	—
106	C₈	—	52	4	no	—
107	C₈	C₄⋊#261	1	2	yes	—
108	C₈	C₄⋊#261	1	2	yes	—
109	C₂²	—	13	1	no	—
110	C₂²	—	13	1	no	—
111	C₂²	—	26	2	no	—
112	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	13	1	no	—
115	C₄	—	13	1	no	—
116	C₄	—	13	4	no	—
117	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
118	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
119	C₂	—	26	1	no	—
120	C₂	—	26	1	no	—
121	C₂	#11719059	1	1	yes	characteristic
122	C₂	D₁₃⋊#108	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88104

C₂

yes

maximal

C₂×#88103

C₂

yes

maximal

#11719053

C₂

yes

maximal

C₄×C₈×D₁₃

C₂

yes

maximal, characteristic

C₂×#6118

C₂²

yes

—

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₄²×D₁₃

C₂²

yes

—

—

—

C₄×C₈×C₁₃

C₄

yes

characteristic

C₈×Dic₁₃

C₄

yes

characteristic

C₈×Dic₁₃

C₄

yes

characteristic

C₄×#1055

C₄

yes

characteristic

C₂×C₄×D₁₃

Q₈

yes

—

C₂×C₄×D₁₃

C₂³

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

D₄

yes

—

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

C₈×D₁₃

Q₈

yes

—

#1848

—

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

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

characteristic

#1057

—

C₈×C₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

C₄⋊C₄

yes

—

#1055

C₄⋊C₄

yes

—

#1055

C₄⋊C₄

yes

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

—

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×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₂×C₄⋊C₄

yes

Dic₁₃

yes

Dic₁₃

yes

Dic₁₃

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

yes

C₂×C₁₃

yes

C₂×C₁₃

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

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₃

#1848

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄⋊#261

yes

—

103

C₂×C₄

C₂²×#261

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

C₄⋊#261

yes

—

108

C₈

C₄⋊#261

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×C₄⋊#261

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×C₄⋊#261

yes

characteristic

118

C₄

C₂×C₄⋊#261

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#11719059

yes

characteristic

122

C₂

D₁₃⋊#108

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	C₄×C₈	#261
hypocenter	C₁₃	#1848
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₄×C₈×C₁₃

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂²×D₁₃

C₂×Q₈

cosocle

C₂×C₄×D₁₃

C₂³

C₄×C₈

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
59. Dic₁₃	#108	semidirect
93. C₁₃	#1848	semidirect

H ≅ G/N

type

59. Dic₁₃

#108

semidirect

93. C₁₃

#1848

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
#11719053	2
C₄×C₈×D₁₃	2
#1848	13

subgroup

index

C₄×C₈×D₁₃

Subgroups — #13130776

Conjugacy classes of subgroups

Complements

Maximal subgroups