Group #13115006 — subgroups

Subgroups — #13115006

Order 1664.

220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₂×#88062	C₂	1	2	yes	maximal
3	#11718779	C₂	1	2	yes	maximal
4	C₂×#88059	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	2	yes	—
10	C₂²×#1055	C₂²	1	1	yes	characteristic
11	C₁₃×#108	—	2	2	no	—
12	#88062	—	2	4	no	—
13	#88059	—	2	2	no	—
14	#88054	—	2	4	no	—
15	C₈×Dic₁₃	C₄	1	2	yes	—
16	C₈×Dic₁₃	C₄	1	2	yes	—
17	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₃	Q₈	1	2	yes	—
19	C₁₃×M₁₆	—	2	2	no	—
20	C₁₃×M₁₆	—	2	2	no	—
21	C₂×C₈×C₁₃	—	2	2	no	—
22	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₁₃	D₄	1	2	yes	—
24	C₂×C₈×C₁₃	Q₈	1	2	yes	—
25	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₁₃	D₄	1	2	yes	—
28	#6099	—	2	2	no	—
29	#6099	—	2	2	no	—
30	C₂×#1055	—	2	2	no	—
31	C₂×#1055	C₂×C₄	1	2	yes	—
32	C₂×#1055	D₄	1	2	yes	—
33	C₂×#1055	Q₈	1	2	yes	—
34	#1848	—	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×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×Dic₁₃	—	2	4	no	—
43	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
45	C₈×C₁₃	—	4	2	no	—
46	C₈×C₁₃	C₄⋊C₄	1	4	yes	—
47	#1055	—	4	2	no	—
48	#1055	C₄⋊C₄	1	4	yes	—
49	C₂×#108	—	13	2	no	—
50	C₂×#108	—	13	1	no	—
51	C₂×#108	D₁₃	1	1	yes	characteristic
52	#423	—	13	2	no	—
53	C₂×C₄×C₈	—	13	1	no	—
54	C₂²×C₁₃	—	2	2	no	—
55	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
57	C₂²×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
58	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₄×C₁₃	#127	1	1	yes	characteristic
61	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
62	Dic₁₃	—	2	2	no	—
63	Dic₁₃	#108	1	4	yes	complemented
64	C₂×M₁₆	—	13	2	no	—
65	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
66	C₂²×C₈	—	13	1	no	—
67	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
68	C₂×C₄²	—	13	1	no	—
69	#108	—	2	2	no	—
70	#108	—	26	4	no	—
71	#108	—	26	2	no	—
72	C₄⋊C₈	—	26	4	no	—
73	C₄×C₈	—	13	2	no	—
74	C₄×C₈	—	13	2	no	—
75	C₂×C₁₃	—	2	1	no	—
76	C₂×C₁₃	—	2	1	no	—
77	C₂×C₁₃	#384	1	1	yes	characteristic
78	C₂×C₁₃	C₂×#108	1	2	yes	—
79	C₂²×C₄	—	13	2	no	—
80	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
81	M₁₆	—	2	2	no	—
82	M₁₆	—	2	2	no	—
83	M₁₆	—	26	2	no	—
84	M₁₆	—	26	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	—	13	2	no	—
88	C₂×C₈	—	13	2	no	—
89	C₂×C₈	—	26	2	no	—
90	C₂×C₈	Dic₂₆	1	2	yes	—
91	C₂×C₈	C₄×D₁₃	1	2	yes	—
92	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
93	C₄²	—	13	1	no	—
94	C₄²	—	13	1	no	—
95	C₄²	—	13	2	no	—
96	C₁₃	#1848	1	1	yes	characteristic, complemented, Sylow
97	C₂³	Q₈×D₁₃	1	1	yes	characteristic
98	C₂×C₄	—	13	2	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	26	4	no	—
101	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
102	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
103	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
104	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
105	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
106	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	13	4	no	—
109	C₈	—	52	2	no	—
110	C₈	#6101	1	4	yes	—
111	C₂²	—	2	2	no	—
112	C₂²	#88142	1	1	yes	characteristic
113	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
114	C₂²	#88198	1	1	yes	characteristic
115	C₄	—	13	4	no	—
116	C₄	—	26	2	no	—
117	C₄	#88142	1	1	yes	characteristic
118	C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
119	C₄	C₂×#6101	1	1	yes	characteristic
120	C₄	#88194	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	2	1	no	—
123	C₂	D₁₃×#108	1	2	yes	—
124	C₂	#11718637	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#108

C₂

yes

maximal, characteristic

C₂×#88062

C₂

yes

maximal

#11718779

C₂

yes

maximal

C₂×#88059

C₂

yes

maximal, characteristic

C₂×C₈×Dic₁₃

C₂

yes

maximal, characteristic

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

C₂²×#1055

C₂²

yes

characteristic

C₁₃×#108

—

#88062

—

#88059

—

#88054

—

C₈×Dic₁₃

C₄

yes

—

C₈×Dic₁₃

C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

Q₈

yes

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

D₄

yes

—

C₂×C₈×C₁₃

Q₈

yes

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#1055

D₄

yes

—

C₂×#1055

Q₈

yes

—

#1848

—

maximal, Sylow

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×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄⋊C₄

yes

—

#1055

—

#1055

C₄⋊C₄

yes

—

C₂×#108

—

C₂×#108

—

C₂×#108

D₁₃

yes

characteristic

#423

—

C₂×C₄×C₈

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

C₄⋊Q₈

yes

characteristic

C₂²×C₁₃

C₄⋊Q₈

yes

characteristic

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

#127

yes

characteristic

C₄×C₁₃

C₄⋊Q₈

yes

characteristic

Dic₁₃

—

Dic₁₃

#108

yes

complemented

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#384

yes

characteristic

C₂×C₁₃

C₂×#108

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₂₆

yes

—

C₂×C₈

C₄×D₁₃

yes

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1848

yes

characteristic, complemented, Sylow

C₂³

Q₈×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂×Dic₂₆

yes

characteristic

102

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

103

C₂×C₄

D₄×D₁₃

yes

characteristic

104

C₂×C₄

D₄×D₁₃

yes

characteristic

105

C₂×C₄

Q₈×D₁₃

yes

characteristic

106

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

#6101

yes

—

111

C₂²

—

112

C₂²

#88142

yes

characteristic

113

C₂²

C₄⋊C₄×D₁₃

yes

characteristic

114

C₂²

#88198

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

#88142

yes

characteristic

118

C₄

C₄⋊C₄×D₁₃

yes

characteristic

119

C₄

C₂×#6101

yes

characteristic

120

C₄

#88194

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

D₁₃×#108

yes

—

124

C₂

#11718637

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#108	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×#108	D₁₃
hypocenter	C₁₃	#1848
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₂×C₁₃×#108

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂³×C₁₃

C₂×Q₈

cosocle

C₂²×C₄×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
63. Dic₁₃	#108	semidirect
96. C₁₃	#1848	semidirect

H ≅ G/N

type

63. Dic₁₃

#108

semidirect

96. C₁₃

#1848

semidirect

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

subgroup	index
C₂×C₁₃×#108	2
C₂×#88062	2
#11718779	2
C₂×#88059	2
C₂×C₈×Dic₁₃	2
#1848	13

subgroup

index

C₂×C₁₃×#108

C₂×C₈×Dic₁₃

Subgroups — #13115006

Conjugacy classes of subgroups

Complements

Maximal subgroups