Group #15783401 — subgroups

Subgroups — #15783401

Order 3328.

218 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 127 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×#11718091	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13113031	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	1	yes	characteristic
8	C₁₃×M₆₄	—	2	2	no	—
9	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
10	C₁₆×Dic₁₃	C₄	1	2	yes	—
11	C₁₆×Dic₁₃	C₂²	1	2	yes	—
12	#11718091	—	2	2	no	—
13	C₂×#88034	C₂²	1	2	yes	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
16	C₂²×#1055	C₈	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
21	C₈×Dic₁₃	C₈	1	2	yes	—
22	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×#6090	—	2	2	no	—
24	C₂×#6090	C₂×C₄	1	2	yes	—
25	C₁₃×C₃₂	—	2	2	no	—
26	#88034	—	2	2	no	—
27	#13627	—	13	1	no	maximal, Sylow
28	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂²×Dic₁₃	C₁₆	1	2	yes	—
30	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
33	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
35	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
36	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
37	C₂×#1055	—	2	2	no	—
38	C₂×#1055	C₂×C₈	1	2	yes	—
39	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
40	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
41	C₁₃×C₁₆	C₂×Q₈	1	1	yes	characteristic
42	#6090	—	2	2	no	—
43	C₂×M₆₄	—	13	1	no	—
44	C₂×M₆₄	D₁₃	1	1	yes	characteristic
45	C₂×C₄×C₁₆	—	13	1	no	—
46	C₄⋊C₃₂	—	13	4	no	—
47	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
49	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
51	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₂×Dic₁₃	—	2	4	no	—
53	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
54	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
55	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
56	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
58	#1055	—	2	2	no	—
59	C₂²×C₁₆	—	13	1	no	—
60	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
61	C₂×C₄×C₈	—	13	1	no	—
62	M₆₄	—	2	2	no	—
63	M₆₄	—	26	2	no	—
64	C₂×C₃₂	—	13	2	no	—
65	C₂×C₃₂	C₂×D₁₃	1	2	yes	—
66	C₄×C₁₆	—	13	2	no	—
67	C₄×C₁₆	—	13	2	no	—
68	C₂²×C₁₃	—	2	2	no	—
69	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
70	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
71	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
72	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
74	Dic₁₃	—	2	2	no	—
75	Dic₁₃	M₆₄	1	4	yes	complemented
76	C₂²×C₈	—	13	1	no	—
77	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
78	C₂×C₄²	—	13	1	no	—
79	C₂×C₁₆	—	13	2	no	—
80	C₂×C₁₆	—	26	2	no	—
81	C₂×C₁₆	Dic₂₆	1	2	yes	—
82	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
83	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
84	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
85	C₄×C₈	—	13	2	no	—
86	C₄×C₈	—	13	2	no	—
87	C₃₂	—	2	2	no	—
88	C₃₂	—	26	2	no	—
89	C₂×C₁₃	—	2	2	no	—
90	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
91	C₂×C₁₃	C₂×M₆₄	1	2	yes	—
92	C₂²×C₄	—	13	2	no	—
93	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
94	C₂×C₈	—	13	2	no	—
95	C₂×C₈	—	26	2	no	—
96	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
97	C₂×C₈	#6094	1	2	yes	—
98	C₂×C₈	#6101	1	2	yes	—
99	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
100	C₄²	—	13	2	no	—
101	C₄²	—	13	1	no	—
102	C₄²	—	13	1	no	—
103	C₁₆	—	26	2	no	—
104	C₁₆	#6101	1	2	yes	—
105	C₁₆	C₂×Dic₂₆	1	1	yes	characteristic
106	C₁₆	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
107	C₁₃	#13627	1	1	yes	characteristic, complemented, Sylow
108	C₂³	C₁₆×D₁₃	1	1	yes	characteristic
109	C₂×C₄	—	13	2	no	—
110	C₂×C₄	—	13	2	no	—
111	C₂×C₄	—	26	4	no	—
112	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
113	C₂×C₄	#88038	1	2	yes	—
114	C₂×C₄	#88054	1	2	yes	—
115	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
116	C₈	—	26	2	no	—
117	C₈	#88054	1	2	yes	—
118	C₈	C₂×#6094	1	1	yes	characteristic
119	C₈	C₂×#6101	1	1	yes	characteristic
120	C₂²	—	2	2	no	—
121	C₂²	#11718093	1	2	yes	—
122	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
123	C₄	—	13	4	no	—
124	C₄	—	26	2	no	—
125	C₄	#11718093	1	2	yes	—
126	C₄	C₂×#88038	1	1	yes	characteristic
127	C₄	C₂×#88054	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	C₂×#11718093	1	1	yes	characteristic
130	C₂	D₁₃×M₆₄	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718091

C₂

yes

maximal, characteristic

C₂×C₁₆×Dic₁₃

C₂

yes

maximal, characteristic

#13113031

C₂

yes

maximal, complemented

C₂×C₁₃×M₆₄

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂×C₈×Dic₁₃

C₄

yes

characteristic

C₂²×#6090

C₄

yes

characteristic

C₁₃×M₆₄

—

C₂×C₁₃×C₃₂

C₂²

yes

—

C₁₆×Dic₁₃

C₄

yes

—

C₁₆×Dic₁₃

C₂²

yes

—

#11718091

—

C₂×#88034

C₂²

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₈

yes

characteristic

C₂²×#1055

C₈

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

D₄

yes

—

C₂×C₁₃×C₁₆

Q₈

yes

—

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₈×Dic₁₃

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₂×#6090

—

C₂×#6090

C₂×C₄

yes

—

C₁₃×C₃₂

—

#88034

—

#13627

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂²×Dic₁₃

C₁₆

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₁₆

yes

characteristic

C₄×Dic₁₃

C₁₆

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

—

C₂×#1055

C₂×C₈

yes

—

C₁₃×C₁₆

C₄⋊C₄

yes

—

C₁₃×C₁₆

C₂×D₄

yes

characteristic

C₁₃×C₁₆

C₂×Q₈

yes

characteristic

#6090

—

C₂×M₆₄

—

C₂×M₆₄

D₁₃

yes

characteristic

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₂³×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

M₃₂

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₈×C₁₃

C₄⋊C₈

yes

—

C₈×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

#1055

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

C₂×C₄×C₈

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₁₃

yes

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₄⋊C₁₆

yes

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₄×C₁₃

C₄⋊C₁₆

yes

—

C₄×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₃

C₂×M₃₂

yes

characteristic

Dic₁₃

—

Dic₁₃

M₆₄

yes

complemented

C₂²×C₈

—

C₂²×C₈

C₄×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

Dic₂₆

yes

—

C₂×C₁₆

C₄×D₁₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₃

yes

—

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₁₃

C₂×M₆₄

yes

—

C₂²×C₄

—

C₂²×C₄

C₈×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₃

yes

characteristic

C₂×C₈

#6094

yes

—

C₂×C₈

#6101

yes

—

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₁₆

—

104

C₁₆

#6101

yes

—

105

C₁₆

C₂×Dic₂₆

yes

characteristic

106

C₁₆

C₂×C₂²⋊D₁₃

yes

characteristic

107

C₁₃

#13627

yes

characteristic, complemented, Sylow

108

C₂³

C₁₆×D₁₃

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₁₆×D₁₃

yes

characteristic

113

C₂×C₄

#88038

yes

—

114

C₂×C₄

#88054

yes

—

115

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

116

C₈

—

117

C₈

#88054

yes

—

118

C₈

C₂×#6094

yes

characteristic

119

C₈

C₂×#6101

yes

characteristic

120

C₂²

—

121

C₂²

#11718093

yes

—

122

C₂²

C₂×C₁₆×D₁₃

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

#11718093

yes

—

126

C₄

C₂×#88038

yes

characteristic

127

C₄

C₂×#88054

yes

characteristic

128

C₂

—

129

C₂

C₂×#11718093

yes

characteristic

130

C₂

D₁₃×M₆₄

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂×C₁₃×M₆₄	C₂
prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂×M₆₄	D₁₃
hypocenter	C₁₃	#13627
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂²×C₁₆

Fitting

C₂×C₁₃×M₆₄

C₂

prime radical

C₂³×C₁₃

C₂×C₁₆

cosocle

C₂×C₁₃×C₁₆

C₂³

hypercenter

C₂×M₆₄

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

N	H ≅ G/N	type
3. #13113031	C₂	semidirect
75. Dic₁₃	M₆₄	semidirect
107. C₁₃	#13627	semidirect

H ≅ G/N

type

3. #13113031

C₂

semidirect

75. Dic₁₃

M₆₄

semidirect

107. C₁₃

#13627

semidirect

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

subgroup	index
C₂×#11718091	2
C₂×C₁₆×Dic₁₃	2
#13113031	2
C₂×C₁₃×M₆₄	2
#13627	13

subgroup

index

C₂×#11718091

C₂×C₁₆×Dic₁₃

#13113031

C₂×C₁₃×M₆₄

#13627

Subgroups — #15783401

Conjugacy classes of subgroups

Complements

Maximal subgroups