Group #13130778 — subgroups

Subgroups — #13130778

Order 1664.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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	1	yes	maximal, characteristic
4	#11719052	C₂	1	1	yes	maximal, characteristic
5	D₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×#6118	C₂²	1	2	yes	—
7	C₂×#6118	C₂²	1	1	yes	characteristic
8	C₂×#6118	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₃	C₂²	1	2	yes	—
10	C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#88112	—	2	2	no	—
12	C₄⋊#1057	—	2	2	no	—
13	#88104	—	2	4	no	—
14	#88103	—	2	4	no	—
15	C₁₃×#97	C₄	1	1	yes	characteristic
16	#88055	C₄	1	2	yes	—
17	#88043	C₄	1	1	yes	characteristic
18	C₂×C₄×D₁₃	Q₈	1	2	yes	—
19	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
20	C₂×#1057	—	2	2	no	—
21	C₂×#1057	—	2	1	no	—
22	C₂×#1057	—	2	1	no	—
23	#6118	—	2	2	no	—
24	#6118	—	2	2	no	—
25	#6118	—	2	2	no	—
26	#6118	—	2	2	no	—
27	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₃	D₄	1	2	yes	—
31	C₂×#1055	C₂×C₄	1	2	yes	—
32	C₈×D₁₃	D₄	1	4	yes	—
33	C₈×D₁₃	Q₈	1	4	yes	—
34	#1849	—	13	1	no	maximal, Sylow
35	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
40	C₄×D₁₃	—	4	2	no	—
41	C₄×D₁₃	C₂×D₄	1	2	yes	—
42	C₄×D₁₃	C₂×Q₈	1	2	yes	—
43	#1057	—	4	1	no	—
44	#1057	—	4	2	no	—
45	#1057	—	4	1	no	—
46	C₈×C₁₃	C₄⋊C₄	1	4	yes	—
47	#1055	C₄⋊C₄	1	4	yes	—
48	C₂×#108	—	13	2	no	—
49	C₂×#108	—	13	2	no	—
50	#423	—	13	1	no	—
51	#423	—	13	1	no	—
52	C₂×#97	—	13	1	no	—
53	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×D₁₃	—	2	2	no	—
55	C₂×D₁₃	C₄⋊Q₈	1	2	yes	—
56	C₄×C₁₃	—	2	2	no	—
57	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
58	Dic₁₃	—	2	2	no	—
59	Dic₁₃	#127	1	1	yes	characteristic
60	Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×M₁₆	—	13	2	no	—
62	C₂×M₁₆	—	13	1	no	—
63	C₂×M₁₆	—	13	1	no	—
64	C₂²×C₈	—	13	2	no	—
65	C₂×C₄²	—	13	1	no	—
66	#108	—	26	4	no	—
67	#108	—	26	4	no	—
68	C₄⋊C₈	—	26	2	no	—
69	C₄⋊C₈	—	26	2	no	—
70	#97	—	13	2	no	—
71	#97	—	13	1	no	—
72	#97	#261	1	1	yes	characteristic
73	C₂×C₁₃	#384	1	1	yes	characteristic
74	C₂×C₁₃	#430	1	2	yes	—
75	D₁₃	—	2	2	no	—
76	C₂²×C₄	—	13	1	no	—
77	C₂²×C₄	—	13	2	no	—
78	M₁₆	—	26	2	no	—
79	M₁₆	—	26	2	no	—
80	M₁₆	—	26	2	no	—
81	M₁₆	—	26	2	no	—
82	C₂×C₈	—	13	2	no	—
83	C₂×C₈	—	13	4	no	—
84	C₂×C₈	—	13	4	no	—
85	C₂×C₈	—	26	2	no	—
86	C₂×C₈	—	26	1	no	—
87	C₂×C₈	—	26	1	no	—
88	C₂×C₈	C₂×#261	1	2	yes	—
89	C₄²	—	13	2	no	—
90	C₄²	—	13	1	no	—
91	C₄²	C₂×#261	1	1	yes	characteristic
92	C₁₃	#1849	1	1	yes	characteristic, complemented, Sylow
93	C₂³	—	13	1	no	—
94	C₂×C₄	—	13	1	no	—
95	C₂×C₄	—	13	2	no	—
96	C₂×C₄	—	13	2	no	—
97	C₂×C₄	—	13	2	no	—
98	C₂×C₄	—	52	2	no	—
99	C₂×C₄	C₄⋊#261	1	2	yes	—
100	C₂×C₄	C₂²×#261	1	1	yes	characteristic
101	C₈	—	13	4	no	—
102	C₈	—	52	2	no	—
103	C₈	—	52	1	no	—
104	C₈	—	52	1	no	—
105	C₈	C₄⋊#261	1	4	yes	—
106	C₂²	—	13	2	no	—
107	C₂²	—	26	2	no	—
108	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	13	1	no	—
111	C₄	—	13	1	no	—
112	C₄	—	26	2	no	—
113	C₄	C₂×C₄⋊#261	1	2	yes	—
114	C₂	—	26	2	no	—
115	C₂	#11719059	1	1	yes	characteristic
116	C₂	#11719100	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, characteristic

#11719052

C₂

yes

maximal, characteristic

D₁₃×#97

C₂

yes

maximal, characteristic

C₂×#6118

C₂²

yes

—

C₂×#6118

C₂²

yes

characteristic

C₂×#6118

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

—

—

—

—

C₁₃×#97

C₄

yes

characteristic

#88055

C₄

yes

—

#88043

C₄

yes

characteristic

C₂×C₄×D₁₃

Q₈

yes

—

C₂×C₄×D₁₃

C₂³

yes

—

—

—

—

—

—

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

C₂×#1055

C₂×C₄

yes

—

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

#1849

—

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

—

C₄×D₁₃

C₂×Q₈

yes

—

#1057

—

#1057

—

#1057

—

C₈×C₁₃

C₄⋊C₄

yes

—

#1055

C₄⋊C₄

yes

—

—

—

—

—

C₂×#97

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄⋊Q₈

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

—

Dic₁₃

—

Dic₁₃

#127

yes

characteristic

Dic₁₃

C₄⋊Q₈

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₃

#1849

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#261

yes

—

100

C₂×C₄

C₂²×#261

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

C₄⋊#261

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂×C₄⋊#261

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₂×C₄⋊#261

yes

—

114

C₂

—

115

C₂

#11719059

yes

characteristic

116

C₂

#11719100

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
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	#1849
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

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 ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
92. C₁₃	#1849	semidirect

H ≅ G/N

type

92. C₁₃

#1849

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
#11719052	2
D₁₃×#97	2
#1849	13

subgroup

index

D₁₃×#97

Subgroups — #13130778

Conjugacy classes of subgroups

Complements

Maximal subgroups