Group #13130754 — subgroups

Subgroups — #13130754

Order 1664.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×#88112	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#1057	C₂	1	1	yes	maximal, characteristic
3	#11718309	C₂	1	1	yes	maximal, characteristic
4	#11718290	C₂	1	4	yes	maximal
5	C₂²×#1057	C₂²	1	2	yes	—
6	C₂²×#1057	C₂²	1	2	yes	—
7	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	#88112	—	2	2	no	—
10	C₄⋊#1057	—	2	2	no	—
11	C₁₃×#95	C₄	1	1	yes	characteristic
12	#88071	C₄	1	1	yes	characteristic
13	#88071	C₄	1	2	yes	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
17	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
19	C₂×#1057	—	2	2	no	—
20	C₂×#1057	—	2	2	no	—
21	C₂×#1057	—	2	4	no	—
22	C₂×#1057	—	2	4	no	—
23	C₄×Dic₁₃	—	2	2	no	—
24	C₄×Dic₁₃	—	2	2	no	—
25	C₄×Dic₁₃	D₄	1	2	yes	—
26	C₄×Dic₁₃	Q₈	1	2	yes	—
27	#1832	—	13	1	no	maximal, Sylow
28	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₃	—	2	2	no	—
30	C₂×C₄×C₁₃	—	2	2	no	—
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
34	C₂×Dic₁₃	—	2	1	no	—
35	C₂×Dic₁₃	—	2	1	no	—
36	C₂×Dic₁₃	—	2	2	no	—
37	C₂×Dic₁₃	—	2	2	no	—
38	C₂×Dic₁₃	—	2	2	no	—
39	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
40	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×Dic₁₃	#41	1	2	yes	—
43	C₂×Dic₁₃	#41	1	2	yes	—
44	#1057	—	4	2	no	—
45	#1057	—	4	2	no	—
46	C₂×C₄⋊C₈	—	13	1	no	—
47	C₂×C₄⋊C₈	—	13	1	no	—
48	#376	—	13	1	no	—
49	#336	—	13	4	no	—
50	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₁₃	#117	1	2	yes	—
52	C₂²×C₁₃	#131	1	2	yes	—
53	C₂²×C₁₃	#131	1	1	yes	characteristic
54	C₂²×C₁₃	#131	1	1	yes	characteristic
55	C₄×C₁₃	—	2	2	no	—
56	C₄×C₁₃	—	4	2	no	—
57	Dic₁₃	—	2	2	no	—
58	Dic₁₃	—	4	2	no	—
59	Dic₁₃	#124	1	1	yes	characteristic
60	Dic₁₃	#124	1	1	yes	characteristic
61	Dic₁₃	#125	1	2	yes	—
62	C₂²×C₈	—	13	2	no	—
63	C₂²×C₈	—	13	2	no	—
64	C₂×C₄²	—	13	1	no	—
65	C₂×C₄²	—	13	2	no	—
66	C₄⋊C₈	—	26	2	no	—
67	C₄⋊C₈	—	26	2	no	—
68	#95	—	13	2	no	—
69	#95	—	13	1	no	—
70	#95	#261	1	1	yes	characteristic
71	C₂×C₁₃	#382	1	1	yes	characteristic
72	C₂×C₁₃	#424	1	1	yes	characteristic
73	C₂×C₁₃	#424	1	1	yes	characteristic
74	C₂×C₁₃	#433	1	2	yes	—
75	C₂×C₁₃	#433	1	2	yes	—
76	C₂²×C₄	—	13	1	no	—
77	C₂²×C₄	—	13	1	no	—
78	C₂²×C₄	—	13	2	no	—
79	C₂²×C₄	C₂×#261	1	2	yes	—
80	C₂²×C₄	C₂×#261	1	1	yes	characteristic
81	C₂×C₈	—	26	2	no	—
82	C₂×C₈	—	26	2	no	—
83	C₂×C₈	—	26	4	no	—
84	C₂×C₈	—	26	4	no	—
85	C₄²	—	13	2	no	—
86	C₄²	—	13	2	no	—
87	C₄²	—	26	2	no	—
88	C₄²	—	26	2	no	—
89	C₁₃	#1832	1	1	yes	characteristic, complemented, Sylow
90	C₂³	C₂²×#261	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	13	1	no	—
96	C₂×C₄	—	13	1	no	—
97	C₂×C₄	—	13	2	no	—
98	C₂×C₄	—	13	2	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	26	1	no	—
101	C₂×C₄	—	26	1	no	—
102	C₂×C₄	—	26	2	no	—
103	C₂×C₄	—	26	2	no	—
104	C₂×C₄	—	26	2	no	—
105	C₂×C₄	C₄⋊#261	1	2	yes	—
106	C₈	—	52	2	no	—
107	C₈	—	52	2	no	—
108	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
109	C₂²	#88237	1	2	yes	—
110	C₂²	#88238	1	2	yes	—
111	C₂²	#88238	1	1	yes	characteristic
112	C₂²	#88240	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	13	1	no	—
116	C₄	—	13	1	no	—
117	C₄	—	13	2	no	—
118	C₄	—	26	2	no	—
119	C₄	—	52	2	no	—
120	C₂	#11719060	1	1	yes	characteristic
121	C₂	#11719067	1	1	yes	characteristic
122	C₂	#11719068	1	2	yes	—
123	C₂	#11719077	1	2	yes	—
124	C₂	#11719079	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88112

C₂

yes

maximal, characteristic

C₂×C₄⋊#1057

C₂

yes

maximal, characteristic

#11718309

C₂

yes

maximal, characteristic

#11718290

C₂

yes

maximal

C₂²×#1057

C₂²

yes

—

C₂²×#1057

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

#88112

—

C₄⋊#1057

—

C₁₃×#95

C₄

yes

characteristic

#88071

C₄

yes

characteristic

#88071

C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

—

—

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

Q₈

yes

—

#1832

—

maximal, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₂×Dic₁₃

C₂×Q₈

yes

characteristic

C₂×Dic₁₃

#41

yes

—

C₂×Dic₁₃

#41

yes

—

#1057

—

#1057

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

—

#336

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

—

C₂²×C₁₃

#131

yes

—

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

yes

Dic₁₃

yes

Dic₁₃

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#433

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

—

C₂²×C₄

C₂×#261

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1832

yes

characteristic, complemented, Sylow

C₂³

C₂²×#261

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₄⋊#261

yes

—

106

C₈

—

107

C₈

—

108

C₂²

C₂×C₄⋊#261

yes

characteristic

109

C₂²

#88237

yes

—

110

C₂²

#88238

yes

—

111

C₂²

#88238

yes

characteristic

112

C₂²

#88240

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

#11719060

yes

characteristic

121

C₂

#11719067

yes

characteristic

122

C₂

#11719068

yes

—

123

C₂

#11719077

yes

—

124

C₂

#11719079

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×#261
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₁₃×#95	C₄
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	#95	#261
hypocenter	C₁₃	#1832
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#261

commutator, socle, prime radical

C₂³×C₁₃

C₂²×C₄

Fitting

C₁₃×#95

C₄

cosocle

C₂²×Dic₁₃

C₂³

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
89. C₁₃	#1832	semidirect

H ≅ G/N

type

89. C₁₃

#1832

semidirect

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

subgroup	index
C₂×#88112	2
C₂×C₄⋊#1057	2
#11718309	2
#11718290	2
#1832	13

subgroup

index

C₂×C₄⋊#1057

Subgroups — #13130754

Conjugacy classes of subgroups

Complements

Maximal subgroups