Group #15779307 — subgroups

Subgroups — #15779307

Order 3328.

282 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 119 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×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	#13115006	C₂	1	2	yes	maximal
3	#13112930	C₂	1	1	yes	maximal, characteristic
4	#13112929	C₂	1	2	yes	maximal
5	C₁₃×#1381	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	C₂²	1	2	yes	—
8	C₂×#88062	—	2	2	no	—
9	#11718779	—	2	2	no	—
10	C₂×#88059	C₂²	1	2	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₁₆×Dic₁₃	C₄	1	2	yes	—
14	C₁₆×Dic₁₃	C₄	1	2	yes	—
15	C₂×C₁₃×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
18	C₂×#6099	—	2	2	no	—
19	C₂²×#1055	D₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	—	2	2	no	—
21	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
22	C₁₃×#108	—	2	2	no	—
23	C₁₃×#108	—	2	2	no	—
24	#88062	—	4	4	no	—
25	#88059	—	2	2	no	—
26	#88059	—	2	2	no	—
27	#88054	—	4	4	no	—
28	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
31	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
32	C₂×#6090	—	2	2	no	—
33	C₂×#6090	C₂×C₄	1	2	yes	—
34	#12891	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₃	Q₁₆	1	2	yes	—
37	C₁₃×M₁₆	—	4	2	no	—
38	C₁₃×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₃	—	4	2	no	—
40	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	#41	1	2	yes	—
43	C₂×C₈×C₁₃	#41	1	2	yes	—
44	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
46	C₄×Dic₁₃	D₈	1	2	yes	—
47	#6099	—	4	2	no	—
48	#6099	—	4	2	no	—
49	C₂×#1055	—	4	2	no	—
50	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
51	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
52	C₂×#1055	SD₁₆	1	4	yes	—
53	C₁₃×C₁₆	—	2	2	no	—
54	#6090	—	2	2	no	—
55	C₂×C₄×C₁₆	—	13	1	no	—
56	#1848	—	13	2	no	—
57	#1381	—	13	1	no	—
58	#1381	—	13	2	no	—
59	#1381	D₁₃	1	1	yes	characteristic
60	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₃	#124	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
65	C₂×Dic₁₃	—	2	4	no	—
66	C₂×Dic₁₃	#107	1	2	yes	—
67	C₂×Dic₁₃	#107	1	2	yes	—
68	C₈×C₁₃	—	8	2	no	—
69	C₈×C₁₃	#117	1	1	yes	characteristic
70	C₈×C₁₃	#117	1	1	yes	characteristic
71	C₈×C₁₃	#125	1	2	yes	—
72	#1055	—	8	2	no	—
73	#1055	#106	1	2	yes	—
74	#1055	#106	1	2	yes	—
75	C₂²×C₁₆	—	13	1	no	—
76	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
77	C₂×#108	—	13	2	no	—
78	C₂×#108	—	26	2	no	—
79	C₂×#108	C₂×D₁₃	1	2	yes	—
80	#423	—	26	2	no	—
81	C₂×C₄×C₈	—	13	1	no	—
82	C₄×C₁₆	—	13	2	no	—
83	C₄×C₁₆	—	13	2	no	—
84	C₂²×C₁₃	—	2	2	no	—
85	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
86	C₂²×C₁₃	#487	1	2	yes	—
87	C₄×C₁₃	#382	1	1	yes	characteristic
88	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
89	C₄×C₁₃	#486	1	2	yes	—
90	Dic₁₃	—	2	2	no	—
91	Dic₁₃	#368	1	4	yes	—
92	C₂×M₁₆	—	2	2	no	—
93	C₂×M₁₆	—	26	2	no	—
94	C₂²×C₈	—	13	1	no	—
95	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
96	C₂×C₄²	—	13	1	no	—
97	C₂×C₁₆	—	2	2	no	—
98	C₂×C₁₆	—	13	2	no	—
99	C₂×C₁₆	—	26	2	no	—
100	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
101	#108	—	2	2	no	—
102	#108	—	2	2	no	—
103	#108	—	26	2	no	—
104	#108	—	26	2	no	—
105	#108	—	52	4	no	—
106	C₄⋊C₈	—	52	4	no	—
107	C₄×C₈	—	13	1	no	—
108	C₄×C₈	—	13	1	no	—
109	C₄×C₈	—	13	1	no	—
110	C₄×C₈	—	13	1	no	—
111	C₂×C₁₃	—	2	2	no	—
112	C₂×C₁₃	#1834	1	1	yes	characteristic
113	C₂×C₁₃	C₂×#368	1	2	yes	—
114	C₂²×C₄	—	13	2	no	—
115	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
116	M₁₆	—	4	2	no	—
117	M₁₆	—	4	2	no	—
118	M₁₆	—	52	2	no	—
119	M₁₆	—	52	2	no	—
120	C₂×C₈	—	4	2	no	—
121	C₂×C₈	—	13	1	no	—
122	C₂×C₈	—	13	1	no	—
123	C₂×C₈	—	13	4	no	—
124	C₂×C₈	—	52	2	no	—
125	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
126	C₂×C₈	#6127	1	2	yes	—
127	C₂×C₈	#6129	1	2	yes	—
128	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
129	C₄²	—	13	1	no	—
130	C₄²	—	13	1	no	—
131	C₄²	—	13	2	no	—
132	C₁₆	—	2	2	no	—
133	C₁₆	—	26	2	no	—
134	C₁₃	#12891	1	1	yes	characteristic, complemented, Sylow
135	C₂³	Q₁₆×D₁₃	1	1	yes	characteristic
136	C₂×C₄	—	13	2	no	—
137	C₂×C₄	—	13	2	no	—
138	C₂×C₄	—	26	4	no	—
139	C₂×C₄	#88139	1	2	yes	—
140	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
141	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
142	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
143	C₈	—	8	2	no	—
144	C₈	—	13	2	no	—
145	C₈	—	13	2	no	—
146	C₈	—	104	2	no	—
147	C₈	#88126	1	1	yes	characteristic
148	C₈	#88131	1	1	yes	characteristic
149	C₈	#88143	1	2	yes	—
150	C₂²	—	2	2	no	—
151	C₂²	#11718453	1	2	yes	—
152	C₂²	D₁₃×#107	1	1	yes	characteristic
153	C₄	—	13	4	no	—
154	C₄	—	26	2	no	—
155	C₄	#11718311	1	1	yes	characteristic
156	C₄	#11718421	1	2	yes	—
157	C₄	D₁₃×#106	1	1	yes	characteristic
158	C₂	—	2	2	no	—
159	C₂	#13114962	1	1	yes	characteristic
160	C₂	D₁₃×#368	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×Dic₁₃

C₂

yes

maximal, characteristic

#13115006

C₂

yes

maximal

#13112930

C₂

yes

maximal, characteristic

#13112929

C₂

yes

maximal

C₁₃×#1381

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂×C₁₃×#108

C₂²

yes

—

C₂×#88062

—

#11718779

—

C₂×#88059

C₂²

yes

—

C₂×C₈×Dic₁₃

C₂²

yes

characteristic

C₂²×#6090

C₂²

yes

characteristic

C₁₆×Dic₁₃

C₄

yes

—

C₁₆×Dic₁₃

C₄

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄×Dic₁₃

D₄

yes

characteristic

C₂×#6099

—

C₂²×#1055

D₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₁₃×#108

—

C₁₃×#108

—

—

—

—

—

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

Q₈

yes

characteristic

C₈×Dic₁₃

Q₈

yes

characteristic

C₂×#6090

—

C₂×#6090

C₂×C₄

yes

—

#12891

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

Q₁₆

yes

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₂×C₈×C₁₃

#41

yes

—

C₄×Dic₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

D₈

yes

—

—

—

—

C₄⋊C₄

yes

characteristic

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

SD₁₆

yes

—

C₁₃×C₁₆

—

#6090

—

C₂×C₄×C₁₆

—

—

—

—

D₁₃

yes

characteristic

C₂³×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#107

yes

—

C₂×Dic₁₃

#107

yes

—

C₈×C₁₃

—

C₈×C₁₃

yes

C₈×C₁₃

yes

C₈×C₁₃

yes

—

#1055

—

#1055

#106

yes

—

#1055

#106

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₃

yes

—

—

C₂×D₁₃

yes

—

#423

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×#107

yes

characteristic

C₂²×C₁₃

#487

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

Dic₁₃

#368

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

C₂×C₁₆

C₄×D₁₃

yes

—

101

#108

—

102

#108

—

103

#108

—

104

#108

—

105

#108

—

106

C₄⋊C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

111

C₂×C₁₃

—

112

C₂×C₁₃

#1834

yes

characteristic

113

C₂×C₁₃

C₂×#368

yes

—

114

C₂²×C₄

—

115

C₂²×C₄

D₄×D₁₃

yes

characteristic

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

126

C₂×C₈

#6127

yes

—

127

C₂×C₈

#6129

yes

—

128

C₂×C₈

Q₈×D₁₃

yes

characteristic

129

C₄²

—

130

C₄²

—

131

C₄²

—

132

C₁₆

—

133

C₁₆

—

134

C₁₃

#12891

yes

characteristic, complemented, Sylow

135

C₂³

Q₁₆×D₁₃

yes

characteristic

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

#88139

yes

—

140

C₂×C₄

C₄⋊C₄×D₁₃

yes

characteristic

141

C₂×C₄

D₈×D₁₃

yes

characteristic

142

C₂×C₄

SD₁₆×D₁₃

yes

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

104

—

147

C₈

#88126

yes

characteristic

148

C₈

#88131

yes

characteristic

149

C₈

#88143

yes

—

150

C₂²

—

151

C₂²

#11718453

yes

—

152

C₂²

D₁₃×#107

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

#11718311

yes

characteristic

156

C₄

#11718421

yes

—

157

C₄

D₁₃×#106

yes

characteristic

158

C₂

—

159

C₂

#13114962

yes

characteristic

160

C₂

D₁₃×#368

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₃
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1381	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1381	D₁₃
hypocenter	C₁₃	#12891
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂×C₄

D₈×D₁₃

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#1381

C₂

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂³×C₁₃

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
134. C₁₃	#12891	semidirect

H ≅ G/N

type

134. C₁₃

#12891

semidirect

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

subgroup	index
C₂×C₁₆×Dic₁₃	2
#13115006	2
#13112930	2
#13112929	2
C₁₃×#1381	2
#12891	13

subgroup

index

C₂×C₁₆×Dic₁₃

C₁₃×#1381

Subgroups — #15779307

Conjugacy classes of subgroups

Complements

Maximal subgroups