Group #13115627 — subgroups

Subgroups — #13115627

Order 1664.

184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 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×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
2	#11718786	C₂	1	2	yes	maximal
3	C₂×#88059	C₂	1	1	yes	maximal, characteristic
4	#11718762	C₂	1	1	yes	maximal, characteristic
5	#11718151	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	#88180	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂×#6099	C₂²	1	1	yes	characteristic
11	C₁₃×#108	C₄	1	4	yes	complemented
12	#88059	—	2	1	no	—
13	#88059	—	2	1	no	—
14	#88059	—	2	4	no	—
15	#88055	—	2	1	no	—
16	C₈×Dic₁₃	—	2	1	no	—
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×M₁₆	—	2	2	no	—
19	C₁₃×M₁₆	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₃	—	2	2	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₃	Q₈	1	2	yes	—
25	C₂²⋊Dic₁₃	Q₈	1	2	yes	—
26	C₄⋊Dic₁₃	—	2	1	no	—
27	C₄×Dic₁₃	—	2	1	no	—
28	#6099	—	2	1	no	—
29	#6099	—	2	2	no	—
30	#6099	—	2	2	no	—
31	#6099	D₄	1	2	yes	—
32	C₂×#1055	—	2	1	no	—
33	C₂×#1055	—	2	2	no	—
34	#1953	—	13	1	no	maximal, Sylow
35	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
41	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
42	C₂×Dic₁₃	—	2	2	no	—
43	C₈×C₁₃	—	2	4	no	—
44	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
46	#1055	—	2	2	no	—
47	#1055	—	4	2	no	—
48	#430	—	13	2	no	—
49	C₂×#108	—	13	1	no	—
50	C₂×#108	D₁₃	1	1	yes	characteristic
51	#405	—	13	1	no	—
52	#344	—	13	2	no	—
53	C₂²×C₁₃	—	4	1	no	—
54	C₂²×C₁₃	C₄×Q₈	1	1	yes	characteristic
55	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
56	C₂²×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
57	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
59	C₄×C₁₃	#121	1	1	yes	characteristic
60	C₄×C₁₃	#125	1	1	yes	characteristic
61	Dic₁₃	—	4	2	no	—
62	C₂×M₁₆	—	13	1	no	—
63	C₂×M₁₆	—	13	2	no	—
64	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
65	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
66	#117	—	13	1	no	—
67	#108	—	26	4	no	—
68	#108	—	26	1	no	—
69	#108	—	26	1	no	—
70	#108	Dic₁₃	1	4	yes	complemented
71	#97	—	26	1	no	—
72	C₄×C₈	—	26	1	no	—
73	C₂×C₁₃	—	2	1	no	—
74	C₂×C₁₃	—	2	1	no	—
75	C₂×C₁₃	—	2	1	no	—
76	C₂×C₁₃	#389	1	1	yes	characteristic
77	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
78	M₁₆	—	2	2	no	—
79	M₁₆	—	13	2	no	—
80	M₁₆	—	26	1	no	—
81	M₁₆	—	26	2	no	—
82	M₁₆	—	26	2	no	—
83	M₁₆	C₂×Dic₁₃	1	4	yes	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	26	1	no	—
86	C₂×C₈	—	26	2	no	—
87	C₂×C₈	Dic₂₆	1	2	yes	—
88	C₂×C₈	D₅₂	1	1	yes	characteristic
89	C₂×C₈	D₅₂	1	1	yes	characteristic
90	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
91	C₄⋊C₄	—	26	1	no	—
92	C₂²⋊C₄	—	13	2	no	—
93	C₄²	—	26	1	no	—
94	C₁₃	#1953	1	1	yes	characteristic, complemented, Sylow
95	C₂³	Q₈×D₁₃	1	1	yes	characteristic
96	C₂×C₄	—	26	2	no	—
97	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
98	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
99	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
100	C₂×C₄	#6129	1	1	yes	characteristic
101	C₂×C₄	#6131	1	1	yes	characteristic
102	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₈	—	26	2	no	—
105	C₈	—	52	2	no	—
106	C₈	C₄⋊Dic₁₃	1	2	yes	—
107	C₈	C₄⋊Dic₁₃	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#88142	1	1	yes	characteristic
110	C₂²	#88151	1	1	yes	characteristic
111	C₂²	Q₈×Dic₁₃	1	1	yes	characteristic
112	C₄	—	52	2	no	—
113	C₄	#88144	1	1	yes	characteristic
114	C₄	#88149	1	1	yes	characteristic
115	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
116	C₄	D₄×Dic₁₃	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#11718646	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#108

C₂

yes

maximal, characteristic

#11718786

C₂

yes

maximal

C₂×#88059

C₂

yes

maximal, characteristic

#11718762

C₂

yes

maximal, characteristic

#11718151

C₂

yes

maximal

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

#88180

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

C₂×#6099

C₂²

yes

characteristic

C₁₃×#108

C₄

yes

—

—

—

—

C₈×Dic₁₃

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

D₄

yes

characteristic

C₂×C₈×C₁₃

D₄

yes

characteristic

C₂×C₈×C₁₃

Q₈

yes

—

C₂²⋊Dic₁₃

Q₈

yes

—

C₄⋊Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

D₄

yes

—

—

—

—

C₂³×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

C₄⋊C₄

yes

—

—

—

—

—

D₁₃

yes

characteristic

#405

—

#344

—

C₂²×C₁₃

—

C₂²×C₁₃

C₄×Q₈

yes

characteristic

C₂²×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₃

C₄⋊Q₈

yes

characteristic

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₄×D₄

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

C₂×D₁₃

yes

—

—

—

—

Dic₁₃

yes

complemented

#97

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#389

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₂₆

yes

—

C₂×C₈

D₅₂

yes

characteristic

C₂×C₈

D₅₂

yes

characteristic

C₂×C₈

C₂×Dic₁₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₃

#1953

yes

characteristic, complemented, Sylow

C₂³

Q₈×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×Dic₂₆

yes

characteristic

C₂×C₄

C₂×D₅₂

yes

characteristic

C₂×C₄

D₄×D₁₃

yes

characteristic

100

C₂×C₄

#6129

yes

characteristic

101

C₂×C₄

#6131

yes

characteristic

102

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

C₄⋊Dic₁₃

yes

—

107

C₈

C₄⋊Dic₁₃

yes

—

108

C₂²

—

109

C₂²

#88142

yes

characteristic

110

C₂²

#88151

yes

characteristic

111

C₂²

Q₈×Dic₁₃

yes

characteristic

112

C₄

—

113

C₄

#88144

yes

characteristic

114

C₄

#88149

yes

characteristic

115

C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

116

C₄

D₄×Dic₁₃

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#11718646

yes

characteristic

	subgroup	G/H
center	C₄	#88149
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#108	C₂
socle	C₂×C₁₃	#389
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×#108	D₁₃
hypocenter	C₁₃	#1953
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₄

#88149

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#108

C₂

socle

C₂×C₁₃

#389

prime radical

C₂³×C₁₃

C₂×Q₈

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₁₃×#108	C₄	semidirect
70. #108	Dic₁₃	semidirect
94. C₁₃	#1953	semidirect

H ≅ G/N

type

11. C₁₃×#108

C₄

semidirect

70. #108

Dic₁₃

semidirect

94. C₁₃

#1953

semidirect

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

subgroup	index
C₂×C₁₃×#108	2
#11718786	2
C₂×#88059	2
#11718762	2
#11718151	2
#1953	13

subgroup

index

C₂×C₁₃×#108

Subgroups — #13115627

Conjugacy classes of subgroups

Complements

Maximal subgroups