Group #13130759 — subgroups

Subgroups — #13130759

Order 1664.

224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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	#11719060	C₂	1	1	yes	maximal, characteristic
2	#11719059	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#97	C₂	1	1	yes	maximal, characteristic
4	#11718265	C₂	1	4	yes	maximal
5	C₂×C₄⋊#261	—	2	2	no	—
6	C₂×C₄⋊#261	C₂²	1	2	yes	—
7	C₂×C₄⋊#261	C₂²	1	2	yes	—
8	C₂×C₈×D₁₃	C₂²	1	2	yes	—
9	C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	(C₂×#261)⋊C₄	—	2	2	no	—
11	C₁₃×#97	C₄	1	1	yes	characteristic, complemented
12	#88055	C₄	1	2	yes	complemented
13	#88043	C₄	1	1	yes	characteristic, complemented
14	C₂²×#261	—	2	2	no	—
15	C₂²×#261	—	2	2	no	—
16	C₂×C₄×D₁₃	D₄	1	2	yes	—
17	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
18	C₄⋊#261	—	2	4	no	—
19	C₄⋊#261	—	2	4	no	—
20	C₄⋊#261	—	4	4	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₃	Q₈	1	2	yes	—
25	C₂×#1055	C₂×C₄	1	2	yes	—
26	C₈×D₁₃	—	2	2	no	—
27	C₈×D₁₃	—	2	2	no	—
28	#1836	—	13	1	no	maximal, Sylow
29	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×#261	—	4	2	no	—
31	C₂×#261	—	4	2	no	—
32	C₂×#261	—	4	4	no	—
33	C₂×#261	—	4	2	no	—
34	C₂×#261	—	4	2	no	—
35	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
38	C₂×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₄×D₁₃	—	2	2	no	—
40	C₄×D₁₃	—	2	2	no	—
41	C₄×D₁₃	#41	1	2	yes	—
42	C₄×D₁₃	#41	1	2	yes	—
43	C₈×C₁₃	—	2	2	no	—
44	#1055	—	2	2	no	—
45	C₂×#97	—	13	1	no	—
46	#384	—	13	1	no	—
47	#382	—	13	1	no	—
48	#340	—	13	4	no	—
49	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×D₁₃	#124	1	1	yes	characteristic
51	C₂×D₁₃	#124	1	1	yes	characteristic
52	C₂×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
53	C₂×D₁₃	#137	1	2	yes	—
54	#261	—	8	2	no	—
55	#261	—	8	2	no	—
56	C₄×C₁₃	—	2	2	no	—
57	C₄×C₁₃	#117	1	2	yes	—
58	Dic₁₃	—	2	2	no	—
59	Dic₁₃	#125	1	2	yes	—
60	C₂²×C₈	—	13	2	no	—
61	C₂×C₄⋊C₄	—	13	2	no	—
62	C₂×C₄⋊C₄	—	13	2	no	—
63	C₂×C₄⋊C₄	—	26	2	no	—
64	C₂×C₄²	—	13	1	no	—
65	#97	—	13	2	no	—
66	#97	—	13	1	no	—
67	#97	#261	1	1	yes	characteristic, complemented
68	#95	—	26	2	no	—
69	C₂×C₁₃	#382	1	1	yes	characteristic
70	C₂×C₁₃	#428	1	2	yes	—
71	D₁₃	#489	1	2	yes	—
72	D₁₃	#490	1	1	yes	characteristic
73	D₁₃	#491	1	1	yes	characteristic
74	C₂²×C₄	—	13	1	no	—
75	C₂²×C₄	—	13	2	no	—
76	C₂²×C₄	—	26	2	no	—
77	C₂²×C₄	—	26	2	no	—
78	C₂×C₈	—	13	2	no	—
79	C₂×C₈	—	26	2	no	—
80	C₂×C₈	—	26	2	no	—
81	C₂×C₈	C₂×#261	1	2	yes	—
82	C₄⋊C₄	—	26	4	no	—
83	C₄⋊C₄	—	26	4	no	—
84	C₄⋊C₄	—	52	4	no	—
85	C₄²	—	13	2	no	—
86	C₄²	—	13	1	no	—
87	C₄²	C₂×#261	1	1	yes	characteristic
88	C₁₃	#1836	1	1	yes	characteristic, complemented, Sylow
89	C₂³	—	13	1	no	—
90	C₂×C₄	—	13	1	no	—
91	C₂×C₄	—	13	2	no	—
92	C₂×C₄	—	13	2	no	—
93	C₂×C₄	—	13	2	no	—
94	C₂×C₄	—	26	2	no	—
95	C₂×C₄	—	26	2	no	—
96	C₂×C₄	—	52	2	no	—
97	C₂×C₄	—	52	2	no	—
98	C₂×C₄	—	52	4	no	—
99	C₂×C₄	—	52	2	no	—
100	C₂×C₄	—	52	2	no	—
101	C₂×C₄	C₄⋊#261	1	2	yes	—
102	C₂×C₄	C₂²×#261	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	26	2	no	—
105	C₂²	—	13	1	no	—
106	C₂²	—	13	1	no	—
107	C₂²	—	13	2	no	—
108	C₂²	—	13	2	no	—
109	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	13	2	no	—
112	C₄	—	26	2	no	—
113	C₄	—	104	2	no	—
114	C₄	—	104	2	no	—
115	C₄	#88237	1	2	yes	—
116	C₂	—	13	1	no	—
117	C₂	—	13	2	no	—
118	C₂	—	13	1	no	—
119	C₂	#11719060	1	1	yes	characteristic
120	C₂	#11719098	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719060

C₂

yes

maximal, characteristic

#11719059

C₂

yes

maximal, characteristic

D₁₃×#97

C₂

yes

maximal, characteristic

#11718265

C₂

yes

maximal

C₂×C₄⋊#261

—

C₂×C₄⋊#261

C₂²

yes

—

C₂×C₄⋊#261

C₂²

yes

—

C₂×C₈×D₁₃

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

characteristic

(C₂×#261)⋊C₄

—

C₁₃×#97

C₄

yes

characteristic, complemented

#88055

C₄

yes

complemented

#88043

C₄

yes

characteristic, complemented

C₂²×#261

—

C₂²×#261

—

C₂×C₄×D₁₃

D₄

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

Q₈

yes

—

C₂×#1055

C₂×C₄

yes

—

C₈×D₁₃

—

C₈×D₁₃

—

#1836

—

maximal, Sylow

C₂²×D₁₃

C₂×D₄

yes

—

—

—

—

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×Q₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

#41

yes

—

C₄×D₁₃

#41

yes

—

C₈×C₁₃

—

#1055

—

C₂×#97

—

#384

—

#382

—

#340

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

C₂×D₁₃

yes

C₂×D₁₃

yes

C₂×D₁₃

yes

—

C₂×D₁₃

#137

yes

—

#261

—

#261

—

C₄×C₁₃

—

C₄×C₁₃

#117

yes

—

Dic₁₃

—

Dic₁₃

#125

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#95

—

C₂×C₁₃

#382

yes

characteristic

C₂×C₁₃

#428

yes

—

D₁₃

#489

yes

—

D₁₃

yes

D₁₃

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₃

#1836

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₄⋊#261

yes

—

102

C₂×C₄

C₂²×#261

yes

characteristic

103

C₈

—

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₄⋊#261

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

104

—

114

C₄

—

104

—

115

C₄

#88237

yes

—

116

C₂

—

117

C₂

—

118

C₂

—

119

C₂

#11719060

yes

characteristic

120

C₂

#11719098

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×D₄
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#1836
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×D₄

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
11. C₁₃×#97	C₄	semidirect
12. #88055	C₄	semidirect
13. #88043	C₄	semidirect
67. #97	#261	semidirect
88. C₁₃	#1836	semidirect

H ≅ G/N

type

11. C₁₃×#97

C₄

semidirect

12. #88055

C₄

semidirect

13. #88043

C₄

semidirect

67. #97

#261

semidirect

88. C₁₃

#1836

semidirect

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

subgroup	index
#11719060	2
#11719059	2
D₁₃×#97	2
#11718265	2
#1836	13

subgroup

index

D₁₃×#97

Subgroups — #13130759

Conjugacy classes of subgroups

Complements

Maximal subgroups