Group #15771956 — subgroups

Subgroups — #15771956

Order 3328.

260 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 163 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	#13116635	C₂	1	2	yes	maximal
2	#13112754	C₂	1	2	yes	maximal, complemented
3	#13112753	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#6090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1450	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#431	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#322	C₄	1	2	yes	—
9	C₈²×C₁₃	C₂²	1	1	yes	characteristic
10	C₈²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²⋊#6090	C₄	1	4	yes	—
12	C₄⋊#6090	C₄	1	4	yes	—
13	C₄×#6090	C₂²	1	2	yes	—
14	C₄×#6090	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₁₃×C₄⋊C₈	C₈	1	4	yes	—
18	C₁₃×C₂²⋊C₈	C₈	1	4	yes	—
19	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×#6090	C₂×C₄	1	4	yes	—
25	C₂×#6090	C₂×C₄	1	4	yes	—
26	#11412	—	13	1	no	maximal, Sylow
27	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₁₃	—	2	4	no	—
30	C₂×C₈×C₁₃	C₄²	1	2	yes	—
31	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
32	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
34	C₄²×C₁₃	C₄²	1	1	yes	characteristic
35	C₄²×C₁₃	C₂×C₈	1	2	yes	—
36	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	#6090	—	2	4	no	—
38	#6090	—	2	4	no	—
39	#2162	—	13	2	no	—
40	#1450	D₁₃	1	1	yes	characteristic
41	#1312	—	13	2	no	—
42	#1311	—	13	1	no	—
43	C₈×C₁₆	—	13	1	no	—
44	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃	—	2	2	no	—
46	C₂×C₄×C₁₃	—	2	4	no	—
47	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
48	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
51	C₈×C₁₃	—	2	2	no	—
52	C₈×C₁₃	—	2	4	no	—
53	C₈×C₁₃	—	2	4	no	—
54	C₈×C₁₃	#131	1	4	yes	—
55	#431	Dic₁₃	1	2	yes	—
56	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
57	C₄⋊C₁₆	—	13	4	no	—
58	C₂²⋊C₁₆	—	13	4	no	—
59	C₄×C₁₆	—	13	2	no	—
60	C₄×C₁₆	—	13	2	no	—
61	#322	Dic₁₃	1	2	yes	—
62	C₈²	C₂×D₁₃	1	1	yes	characteristic
63	C₈²	C₂×D₁₃	1	1	yes	characteristic
64	C₂²×C₁₃	—	2	2	no	—
65	C₂²×C₁₃	—	2	1	no	—
66	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
67	C₄×C₁₃	—	2	2	no	—
68	C₄×C₁₃	—	2	1	no	—
69	C₄×C₁₃	#405	1	2	yes	—
70	C₄×C₁₃	#504	1	4	yes	—
71	C₂²×C₈	C₄×D₁₃	1	2	yes	—
72	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
73	C₂×C₁₆	—	13	4	no	—
74	C₂×C₁₆	—	13	4	no	—
75	C₄⋊C₈	#1055	1	4	yes	—
76	C₂²⋊C₈	#1055	1	4	yes	—
77	C₄×C₈	C₄×D₁₃	1	2	yes	—
78	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
79	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
80	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
81	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
82	C₂×C₁₃	—	4	1	no	—
83	C₂×C₁₃	#1450	1	1	yes	characteristic
84	C₂×C₁₃	#2108	1	2	yes	—
85	C₂²×C₄	C₂×#1055	1	2	yes	—
86	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
87	C₂×C₈	—	2	4	no	—
88	C₂×C₈	C₂×#1055	1	4	yes	—
89	C₂×C₈	C₂×#1055	1	4	yes	—
90	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
91	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
92	C₄²	C₂×#1055	1	2	yes	—
93	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
94	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
95	C₁₆	—	26	4	no	—
96	C₁₆	—	26	4	no	—
97	C₁₃	#11412	1	1	yes	characteristic, complemented, Sylow
98	C₂³	C₄×#1055	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	C₄×#1055	1	1	yes	characteristic
102	C₂×C₄	C₄×#1055	1	2	yes	—
103	C₂×C₄	C₂²×#1055	1	2	yes	—
104	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	2	4	no	—
107	C₈	—	2	4	no	—
108	C₈	#88155	1	4	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	—	2	1	no	—
111	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	2	1	no	—
114	C₄	#11718762	1	2	yes	—
115	C₄	#11718801	1	4	yes	—
116	C₂	—	4	1	no	—
117	C₂	#13113119	1	1	yes	characteristic
118	C₂	#13116433	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13116635

C₂

yes

maximal

#13112754

C₂

yes

maximal, complemented

#13112753

C₂

yes

maximal, characteristic, complemented

C₈×#6090

C₂

yes

maximal, characteristic, complemented

C₁₃×#1450

C₂

yes

maximal, characteristic

C₁₃×#431

C₄

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#322

C₄

yes

—

C₈²×C₁₃

C₂²

yes

characteristic

C₈²×C₁₃

C₂²

yes

characteristic

C₂²⋊#6090

C₄

yes

—

C₄⋊#6090

C₄

yes

—

C₄×#6090

C₂²

yes

—

C₄×#6090

C₂²

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₁₃×C₄⋊C₈

C₈

yes

—

C₁₃×C₂²⋊C₈

C₈

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂³

yes

characteristic

C₂×#6090

C₂×C₄

yes

—

C₂×#6090

C₂×C₄

yes

—

#11412

—

maximal, Sylow

C₂²×C₄×C₁₃

C₄²

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₄²

yes

characteristic

C₄²×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

C₂²×C₄

yes

—

—

—

D₁₃

yes

characteristic

#1312

—

#1311

—

C₈×C₁₆

—

C₂³×C₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄×C₈

yes

—

C₂×C₄×C₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#131

yes

—

#431

Dic₁₃

yes

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

#322

Dic₁₃

yes

—

C₈²

C₂×D₁₃

yes

characteristic

C₈²

C₂×D₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#405

yes

—

C₄×C₁₃

#504

yes

—

C₂²×C₈

C₄×D₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

#1055

yes

—

C₂²⋊C₈

#1055

yes

—

C₄×C₈

C₄×D₁₃

yes

—

C₄×C₈

C₂×Dic₁₃

yes

—

C₄×C₈

C₂×Dic₁₃

yes

—

C₄×C₈

C₂×Dic₁₃

yes

characteristic

C₄×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₁₃

—

C₂×C₁₃

#1450

yes

characteristic

C₂×C₁₃

#2108

yes

—

C₂²×C₄

C₂×#1055

yes

—

C₂²×C₄

C₄×Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×#1055

yes

—

C₂×C₈

C₂×#1055

yes

—

C₂×C₈

C₄×Dic₁₃

yes

—

C₂×C₈

C₂×C₄×D₁₃

yes

—

C₄²

C₂×#1055

yes

—

C₄²

C₄×Dic₁₃

yes

characteristic

C₄²

C₂²×Dic₁₃

yes

characteristic

C₁₆

—

C₁₆

—

C₁₃

#11412

yes

characteristic, complemented, Sylow

C₂³

C₄×#1055

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₄×#1055

yes

characteristic

102

C₂×C₄

C₄×#1055

yes

—

103

C₂×C₄

C₂²×#1055

yes

—

104

C₂×C₄

C₂×C₄×Dic₁₃

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#88155

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂×C₄×#1055

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#11718762

yes

—

115

C₄

#11718801

yes

—

116

C₂

—

117

C₂

#13113119

yes

characteristic

118

C₂

#13116433

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₁₃×#1450	C₂
prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1450	D₁₃
hypocenter	C₁₃	#11412
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ #1450

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂×C₄×C₈

Fitting

C₁₃×#1450

C₂

prime radical

C₂³×C₁₃

C₄×C₈

cosocle

C₄×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₄×C₈ ◁ #1450

N	H ≅ G/N	type
2. #13112754	C₂	semidirect
3. #13112753	C₂	semidirect
4. C₈×#6090	C₂	semidirect
97. C₁₃	#11412	semidirect

H ≅ G/N

type

2. #13112754

C₂

semidirect

3. #13112753

C₂

semidirect

4. C₈×#6090

C₂

semidirect

97. C₁₃

#11412

semidirect

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

subgroup	index
#13116635	2
#13112754	2
#13112753	2
C₈×#6090	2
C₁₃×#1450	2
#11412	13

subgroup

index

C₁₃×#1450

Subgroups — #15771956

Conjugacy classes of subgroups

Complements

Maximal subgroups