Group #15771957 — subgroups

Subgroups — #15771957

Order 3328.

260 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 131 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	#13116633	C₂	1	2	yes	maximal
2	#13113118	C₂	1	1	yes	maximal, characteristic
3	#13112755	C₂	1	2	yes	maximal, complemented
4	C₈×#6090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1311	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718346	C₄	1	2	yes	—
7	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₈²×C₁₃	C₂²	1	1	yes	characteristic
10	#11718099	C₄	1	4	yes	—
11	#11718093	C₄	1	4	yes	—
12	C₄×#6090	C₂²	1	2	yes	—
13	#11718046	C₄	1	2	yes	—
14	C₈×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
16	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
18	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	#88060	C₈	1	4	yes	—
21	#88054	C₈	1	4	yes	—
22	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×#6090	C₂×C₄	1	4	yes	—
24	C₄×#1055	C₂×C₄	1	1	yes	characteristic
25	C₄×#1055	C₂×C₄	1	2	yes	—
26	#11412	—	13	1	no	maximal, Sylow
27	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
28	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
30	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
31	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
33	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
34	C₂×#1055	C₄²	1	2	yes	—
35	C₂×#1055	C₂×C₈	1	4	yes	—
36	C₈×D₁₃	—	2	4	no	—
37	C₁₃×C₁₆	—	2	4	no	—
38	#6090	—	2	4	no	—
39	#2162	—	13	2	no	—
40	#1450	—	13	1	no	—
41	#1312	—	13	2	no	—
42	#1311	D₁₃	1	1	yes	characteristic, complemented
43	C₈×C₁₆	—	13	1	no	—
44	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
46	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
47	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
48	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
49	C₄×D₁₃	—	2	2	no	—
50	C₄×D₁₃	—	2	4	no	—
51	C₈×C₁₃	—	2	4	no	—
52	C₈×C₁₃	#131	1	4	yes	—
53	#1055	—	2	2	no	—
54	#1055	—	2	4	no	—
55	#431	—	13	2	no	—
56	C₂×C₄×C₈	—	13	1	no	—
57	C₄⋊C₁₆	—	13	4	no	—
58	C₂²⋊C₁₆	—	13	4	no	—
59	C₄×C₁₆	—	13	2	no	—
60	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
61	#322	—	13	2	no	—
62	C₈²	—	13	1	no	—
63	C₈²	C₂×D₁₃	1	1	yes	characteristic
64	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
65	C₂×D₁₃	—	2	2	no	—
66	C₂×D₁₃	—	2	1	no	—
67	C₄×C₁₃	#405	1	2	yes	—
68	C₄×C₁₃	#504	1	4	yes	—
69	Dic₁₃	—	2	2	no	—
70	Dic₁₃	—	2	1	no	—
71	C₂²×C₈	—	13	2	no	—
72	C₂×C₄²	—	13	1	no	—
73	C₂×C₁₆	—	13	4	no	—
74	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
75	C₄⋊C₈	—	13	4	no	—
76	C₂²⋊C₈	—	13	4	no	—
77	C₄×C₈	—	13	2	no	—
78	C₄×C₈	—	13	2	no	—
79	C₄×C₈	—	13	1	no	—
80	C₄×C₈	C₄×D₁₃	1	2	yes	—
81	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
82	C₂×C₁₃	#1450	1	1	yes	characteristic
83	C₂×C₁₃	#2108	1	2	yes	—
84	D₁₃	—	4	1	no	—
85	C₂²×C₄	—	13	1	no	—
86	C₂²×C₄	—	13	2	no	—
87	C₂×C₈	—	13	2	no	—
88	C₂×C₈	—	13	4	no	—
89	C₂×C₈	—	26	4	no	—
90	C₂×C₈	C₈×D₁₃	1	4	yes	—
91	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
92	C₄²	—	13	1	no	—
93	C₄²	—	13	2	no	—
94	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
95	C₁₆	—	2	4	no	—
96	C₁₆	—	26	4	no	—
97	C₁₃	#11412	1	1	yes	characteristic, complemented, Sylow
98	C₂³	—	13	1	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	13	1	no	—
101	C₂×C₄	—	26	4	no	—
102	C₂×C₄	—	26	2	no	—
103	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
104	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
105	C₈	—	2	4	no	—
106	C₈	—	26	4	no	—
107	C₈	—	26	2	no	—
108	C₈	#88155	1	4	yes	—
109	C₂²	—	26	2	no	—
110	C₂²	—	26	1	no	—
111	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
112	C₄	—	26	2	no	—
113	C₄	—	26	1	no	—
114	C₄	#11718350	1	2	yes	—
115	C₄	#11718568	1	4	yes	—
116	C₂	—	52	1	no	—
117	C₂	#13113118	1	1	yes	characteristic
118	C₂	#13116434	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13116633

C₂

yes

maximal

#13113118

C₂

yes

maximal, characteristic

#13112755

C₂

yes

maximal, complemented

C₈×#6090

C₂

yes

maximal, characteristic, complemented

C₁₃×#1311

C₂

yes

maximal, characteristic, complemented

#11718346

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₄×C₁₃×C₁₆

C₂²

yes

—

C₈²×C₁₃

C₂²

yes

characteristic

#11718099

C₄

yes

—

#11718093

C₄

yes

—

C₄×#6090

C₂²

yes

—

#11718046

C₄

yes

—

C₈×#1055

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂³

yes

characteristic

#88060

C₈

yes

—

#88054

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₂×#6090

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

—

#11412

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

C₄²

yes

—

C₂×#1055

C₂×C₈

yes

—

C₈×D₁₃

—

C₁₃×C₁₆

—

—

—

—

—

D₁₃

yes

characteristic, complemented

C₈×C₁₆

—

C₂²×D₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#131

yes

—

#1055

—

#1055

—

#431

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₃

yes

—

#322

—

C₈²

—

C₈²

C₂×D₁₃

yes

characteristic

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

#405

yes

—

C₄×C₁₃

#504

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₃

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₃

yes

—

C₄×C₈

C₂²×D₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₃

yes

—

C₂×C₈

C₂×C₄×D₁₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×C₄×D₁₃

yes

characteristic

C₁₆

—

C₁₆

—

C₁₃

#11412

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₄²×D₁₃

yes

characteristic

104

C₂×C₄

C₂×C₈×D₁₃

yes

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#88155

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₄×C₈×D₁₃

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

#11718350

yes

—

115

C₄

#11718568

yes

—

116

C₂

—

117

C₂

#13113118

yes

characteristic

118

C₂

#13116434

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₁₃×#1311	C₂
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1311	D₁₃
hypocenter	C₁₃	#11412
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ #1311

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂×C₄×C₈

Fitting

C₁₃×#1311

C₂

prime radical

C₂²×D₁₃

C₄×C₈

cosocle

C₄×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₄×C₈ ◁ #1311

N	H ≅ G/N	type
3. #13112755	C₂	semidirect
4. C₈×#6090	C₂	semidirect
5. C₁₃×#1311	C₂	semidirect
42. #1311	D₁₃	semidirect
97. C₁₃	#11412	semidirect

H ≅ G/N

type

3. #13112755

C₂

semidirect

4. C₈×#6090

C₂

semidirect

5. C₁₃×#1311

C₂

semidirect

42. #1311

D₁₃

semidirect

97. C₁₃

#11412

semidirect

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

subgroup	index
#13116633	2
#13113118	2
#13112755	2
C₈×#6090	2
C₁₃×#1311	2
#11412	13

subgroup

index

C₁₃×#1311

Subgroups — #15771957

Conjugacy classes of subgroups

Complements

Maximal subgroups