Group #15753351 — subgroups

Subgroups — #15753351

Order 3328.

414 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 187 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	#13114582	C₂	1	1	yes	maximal, characteristic
2	C₄×#88043	C₂	1	1	yes	maximal, characteristic
3	#13112663	C₂	1	4	yes	maximal
4	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
6	C₄³×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88043	C₄	1	4	yes	—
8	C₂×C₄×#1055	C₂²	1	2	yes	—
9	C₂×C₄×#1055	C₂²	1	2	yes	—
10	C₁₃×#336	C₄	1	4	yes	—
11	#11718116	C₄	1	4	yes	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
13	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
17	C₂²×#1055	C₂×C₄	1	4	yes	—
18	C₂²×#1055	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₁₃	—	2	4	no	—
20	#88043	—	2	8	no	—
21	C₄×#1055	—	2	4	no	—
22	C₄×#1055	—	2	4	no	—
23	#8134	—	13	1	no	maximal, Sylow
24	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
25	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	—	2	4	no	—
29	C₂×C₈×C₁₃	—	2	8	no	—
30	C₄²×C₁₃	—	2	4	no	—
31	C₄²×C₁₃	—	2	4	no	—
32	C₄²×C₁₃	—	2	4	no	—
33	C₄²×C₁₃	#41	1	4	yes	—
34	C₂×#1055	—	2	4	no	—
35	C₂×#1055	—	2	4	no	—
36	C₂×#1055	—	2	4	no	—
37	C₂×#1055	—	2	8	no	—
38	C₂×#1055	M₁₆	1	8	yes	—
39	#1744	—	13	1	no	—
40	#1744	D₁₃	1	1	yes	characteristic
41	C₄×#97	—	13	1	no	—
42	#1273	—	13	4	no	—
43	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
44	C₂×C₄×C₁₃	—	2	4	no	—
45	C₂×C₄×C₁₃	—	2	4	no	—
46	C₂×C₄×C₁₃	—	2	4	no	—
47	C₂×C₄×C₁₃	#117	1	2	yes	—
48	C₂×C₄×C₁₃	#117	1	2	yes	—
49	C₂×C₄×C₁₃	#117	1	2	yes	—
50	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
51	C₂×C₄×C₁₃	#131	1	4	yes	—
52	C₂×C₄×C₁₃	#131	1	4	yes	—
53	C₈×C₁₃	—	4	4	no	—
54	#1055	—	2	8	no	—
55	#1055	—	4	4	no	—
56	C₂×#97	—	13	4	no	—
57	C₂×C₄×C₈	—	13	2	no	—
58	C₂×C₄×C₈	—	13	2	no	—
59	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
60	C₄³	C₂×D₁₃	1	1	yes	characteristic
61	#336	—	13	4	no	—
62	#336	Dic₁₃	1	4	yes	—
63	C₂²×C₁₃	#376	1	1	yes	characteristic
64	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
65	C₂²×C₁₃	#405	1	2	yes	—
66	C₂²×C₁₃	#405	1	2	yes	—
67	C₄×C₁₃	—	4	4	no	—
68	C₄×C₁₃	#432	1	4	yes	—
69	C₄×C₁₃	#433	1	4	yes	—
70	C₄×C₁₃	#433	1	4	yes	—
71	C₂²×C₈	—	13	4	no	—
72	C₂²×C₈	—	13	4	no	—
73	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
74	C₂×C₄²	C₄×D₁₃	1	2	yes	—
75	C₂×C₄²	C₄×D₁₃	1	2	yes	—
76	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
77	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
78	#97	—	26	8	no	—
79	C₄×C₈	—	2	4	no	—
80	C₄×C₈	—	26	4	no	—
81	C₄×C₈	—	26	4	no	—
82	C₂×C₁₃	#1453	1	4	yes	—
83	C₂×C₁₃	#1745	1	1	yes	characteristic
84	C₂×C₁₃	#1746	1	1	yes	characteristic
85	C₂×C₁₃	#1746	1	1	yes	characteristic
86	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
87	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
88	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
89	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
90	C₂×C₈	—	2	4	no	—
91	C₂×C₈	—	2	8	no	—
92	C₂×C₈	—	13	8	no	—
93	C₂×C₈	—	26	4	no	—
94	C₂×C₈	—	26	4	no	—
95	C₂×C₈	—	26	4	no	—
96	C₂×C₈	—	26	8	no	—
97	C₄²	—	2	4	no	—
98	C₄²	—	2	4	no	—
99	C₄²	—	2	4	no	—
100	C₄²	#6127	1	4	yes	—
101	C₁₃	#8134	1	1	yes	characteristic, complemented, Sylow
102	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	#88126	1	2	yes	—
107	C₂×C₄	#88126	1	2	yes	—
108	C₂×C₄	#88155	1	4	yes	—
109	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
110	C₂×C₄	#88180	1	2	yes	—
111	C₂×C₄	#88202	1	4	yes	—
112	C₈	—	4	4	no	—
113	C₈	—	26	8	no	—
114	C₈	—	52	4	no	—
115	C₂²	#11718593	1	1	yes	characteristic
116	C₂²	#11718658	1	2	yes	—
117	C₂²	#11718762	1	2	yes	—
118	C₂²	M₁₆×Dic₁₃	1	2	yes	—
119	C₄	—	4	4	no	—
120	C₄	#11718351	1	4	yes	—
121	C₄	#11718366	1	4	yes	—
122	C₄	#11718661	1	4	yes	—
123	C₂	#13113131	1	4	yes	—
124	C₂	#13114584	1	1	yes	characteristic
125	C₂	#13114587	1	1	yes	characteristic
126	C₂	#13114588	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13114582

C₂

yes

maximal, characteristic

C₄×#88043

C₂

yes

maximal, characteristic

#13112663

C₂

yes

maximal

C₁₃×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×#88043

C₄

yes

—

C₂×C₄×#1055

C₂²

yes

—

C₂×C₄×#1055

C₂²

yes

—

C₁₃×#336

C₄

yes

—

#11718116

C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂²×#1055

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₄×C₈×C₁₃

—

—

—

—

—

C₂²×C₄×C₁₃

C₄²

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

#41

yes

—

—

—

—

—

M₁₆

yes

—

#1744

—

#1744

D₁₃

yes

characteristic

C₄×#97

—

#1273

—

C₂³×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₈×C₁₃

—

#1055

—

#1055

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

C₄³

C₂×D₁₃

yes

characteristic

#336

—

#336

Dic₁₃

yes

—

C₂²×C₁₃

#376

yes

characteristic

C₂²×C₁₃

C₄×M₁₆

yes

—

C₂²×C₁₃

#405

yes

—

C₂²×C₁₃

#405

yes

—

C₄×C₁₃

—

C₄×C₁₃

#432

yes

—

C₄×C₁₃

#433

yes

—

C₄×C₁₃

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂×C₄²

C₄×D₁₃

yes

—

C₂×C₄²

C₄×D₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

#1453

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂²×C₄

C₄×Dic₁₃

yes

—

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

100

C₄²

#6127

yes

—

101

C₁₃

#8134

yes

characteristic, complemented, Sylow

102

C₂³

C₂×C₄×Dic₁₃

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#88126

yes

—

107

C₂×C₄

#88126

yes

—

108

C₂×C₄

#88155

yes

—

109

C₂×C₄

M₁₆×D₁₃

yes

—

110

C₂×C₄

#88180

yes

—

111

C₂×C₄

#88202

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

#11718593

yes

characteristic

116

C₂²

#11718658

yes

—

117

C₂²

#11718762

yes

—

118

C₂²

M₁₆×Dic₁₃

yes

—

119

C₄

—

120

C₄

#11718351

yes

—

121

C₄

#11718366

yes

—

122

C₄

#11718661

yes

—

123

C₂

#13113131

yes

—

124

C₂

#13114584

yes

characteristic

125

C₂

#13114587

yes

characteristic

126

C₂

#13114588

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂×C₄²
Fitting	C₁₃×#1744	C₂
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1744	D₁₃
hypocenter	C₁₃	#8134
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₁₃

commutator, socle, prime radical

C₂³×C₁₃

C₂×C₄²

Fitting

C₁₃×#1744

C₂

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
101. C₁₃	#8134	semidirect

H ≅ G/N

type

101. C₁₃

#8134

semidirect

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

subgroup	index
#13114582	2
C₄×#88043	2
#13112663	2
C₁₃×#1744	2
#8134	13

subgroup

index

C₁₃×#1744

Subgroups — #15753351

Conjugacy classes of subgroups

Complements

Maximal subgroups