Group #15779268 — subgroups

Subgroups — #15779268

Order 3328.

322 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 151 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×C₄⋊#6090	C₂	1	1	yes	maximal, characteristic
2	#13114522	C₂	1	1	yes	maximal, characteristic
3	#13112913	C₂	1	4	yes	maximal
4	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88055	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
9	C₂²×#6090	C₂²	1	2	yes	—
10	#11718593	C₄	1	1	yes	characteristic
11	C₂×#88043	C₄	1	1	yes	characteristic
12	C₁₃×C₄⋊C₁₆	—	2	2	no	—
13	C₄⋊#6090	—	2	2	no	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
18	C₂²×#1055	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	—	2	2	no	—
20	C₂×C₁₃×C₁₆	—	2	4	no	—
21	C₄×C₈×C₁₃	D₄	1	2	yes	—
22	C₄×C₈×C₁₃	Q₈	1	2	yes	—
23	#88071	C₈	1	2	yes	—
24	#88071	C₈	1	2	yes	—
25	#88055	—	2	4	no	—
26	C₈×Dic₁₃	—	2	2	no	—
27	C₈×Dic₁₃	—	2	2	no	—
28	C₂×#6090	—	2	2	no	—
29	C₂×#6090	—	2	4	no	—
30	#88043	—	2	2	no	—
31	#12880	—	13	1	no	maximal, Sylow
32	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
36	C₂×C₈×C₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₈×C₁₃	#41	1	2	yes	—
41	C₂×C₈×C₁₃	#41	1	2	yes	—
42	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
43	C₄²×C₁₃	M₁₆	1	2	yes	—
44	C₄×Dic₁₃	—	2	2	no	—
45	C₄×Dic₁₃	—	2	2	no	—
46	C₂×#1055	—	2	2	no	—
47	C₂×#1055	—	2	2	no	—
48	C₂×#1055	M₁₆	1	4	yes	—
49	C₁₃×C₁₆	—	4	2	no	—
50	#6090	—	4	2	no	—
51	C₂×C₄⋊C₁₆	—	13	1	no	—
52	C₂×C₄⋊C₁₆	D₁₃	1	1	yes	characteristic
53	#1726	—	13	1	no	—
54	#1374	—	13	4	no	—
55	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	—	2	2	no	—
57	C₂×C₄×C₁₃	—	2	2	no	—
58	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
59	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
60	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₃	#117	1	2	yes	—
62	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₂×Dic₁₃	—	2	4	no	—
65	C₂×Dic₁₃	—	2	4	no	—
66	C₂×Dic₁₃	—	2	4	no	—
67	C₈×C₁₃	—	2	2	no	—
68	C₈×C₁₃	#124	1	1	yes	characteristic
69	C₈×C₁₃	#124	1	1	yes	characteristic
70	C₈×C₁₃	#125	1	2	yes	—
71	#1055	—	2	4	no	—
72	C₂²×C₁₆	—	13	2	no	—
73	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
74	C₂×#97	—	13	2	no	—
75	C₂×#97	—	13	1	no	—
76	C₂×C₄×C₈	—	13	2	no	—
77	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
78	#376	—	13	1	no	—
79	C₄⋊C₁₆	—	2	2	no	—
80	C₄⋊C₁₆	—	26	2	no	—
81	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
82	C₂²×C₁₃	#431	1	2	yes	—
83	C₂²×C₁₃	#504	1	2	yes	—
84	C₂²×C₁₃	#504	1	2	yes	—
85	C₄×C₁₃	—	2	2	no	—
86	C₄×C₁₃	—	2	2	no	—
87	C₄×C₁₃	#382	1	1	yes	characteristic
88	C₄×C₁₃	#423	1	1	yes	characteristic
89	C₄×C₁₃	#432	1	2	yes	—
90	Dic₁₃	—	4	4	no	—
91	C₂²×C₈	—	13	2	no	—
92	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
93	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
94	C₂×C₄²	—	13	2	no	—
95	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
96	C₂×C₁₆	—	2	4	no	—
97	C₂×C₁₆	—	2	2	no	—
98	C₂×C₁₆	—	26	4	no	—
99	C₂×C₁₆	—	26	2	no	—
100	#97	—	26	4	no	—
101	#97	—	26	2	no	—
102	C₄×C₈	—	26	2	no	—
103	C₄×C₈	—	26	2	no	—
104	C₄×C₈	Dic₂₆	1	2	yes	—
105	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
106	#95	—	13	2	no	—
107	#95	—	13	2	no	—
108	C₂×C₁₃	#1831	1	1	yes	characteristic
109	C₂×C₁₃	#2151	1	1	yes	characteristic
110	C₂×C₁₃	#2151	1	1	yes	characteristic
111	C₂×C₁₃	#2164	1	4	yes	—
112	C₂²×C₄	—	13	4	no	—
113	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
114	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
115	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	13	4	no	—
118	C₂×C₈	—	26	2	no	—
119	C₂×C₈	—	26	2	no	—
120	C₂×C₈	#6101	1	2	yes	—
121	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
122	C₂×C₈	#6129	1	2	yes	—
123	C₂×C₈	#6131	1	2	yes	—
124	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
125	C₄²	—	26	2	no	—
126	C₄²	—	26	2	no	—
127	C₄²	#6094	1	2	yes	—
128	C₄²	#6101	1	2	yes	—
129	C₁₆	—	4	2	no	—
130	C₁₆	—	52	2	no	—
131	C₁₃	#12880	1	1	yes	characteristic, complemented, Sylow
132	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	26	4	no	—
136	C₂×C₄	—	26	4	no	—
137	C₂×C₄	—	26	4	no	—
138	C₂×C₄	#88054	1	2	yes	—
139	C₂×C₄	#88054	1	2	yes	—
140	C₂×C₄	#88146	1	2	yes	—
141	C₂×C₄	C₂×#6094	1	1	yes	characteristic
142	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
143	C₂×C₄	C₂×#6101	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	—	26	4	no	—
146	C₈	#88144	1	2	yes	—
147	C₈	#88190	1	1	yes	characteristic
148	C₈	#88201	1	1	yes	characteristic
149	C₂²	#11718494	1	2	yes	—
150	C₂²	#11718562	1	2	yes	—
151	C₂²	#11718568	1	2	yes	—
152	C₂²	C₂×#88054	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	52	4	no	—
156	C₄	#11718496	1	2	yes	—
157	C₄	#11718638	1	1	yes	characteristic
158	C₄	#11718779	1	1	yes	characteristic
159	C₂	#13114952	1	1	yes	characteristic
160	C₂	#13116594	1	1	yes	characteristic
161	C₂	#13116596	1	1	yes	characteristic
162	C₂	#13116642	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#6090

C₂

yes

maximal, characteristic

#13114522

C₂

yes

maximal, characteristic

#13112913

C₂

yes

maximal

C₂×C₁₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88055

C₄

yes

—

C₂×C₈×Dic₁₃

C₂²

yes

—

C₂²×#6090

C₂²

yes

—

#11718593

C₄

yes

characteristic

C₂×#88043

C₄

yes

characteristic

C₁₃×C₄⋊C₁₆

—

C₄⋊#6090

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#88071

C₈

yes

—

#88071

C₈

yes

—

#88055

—

C₈×Dic₁₃

—

C₈×Dic₁₃

—

—

—

—

—

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

M₁₆

yes

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₂×#1055

—

C₂×#1055

—

C₂×#1055

M₁₆

yes

—

C₁₃×C₁₆

—

#6090

—

C₂×C₄⋊C₁₆

—

C₂×C₄⋊C₁₆

D₁₃

yes

characteristic

#1726

—

#1374

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

yes

C₈×C₁₃

yes

C₈×C₁₃

yes

—

#1055

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₃

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#376

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₃

#431

yes

—

C₂²×C₁₃

#504

yes

—

C₂²×C₁₃

#504

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₃

yes

characteristic

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

100

#97

—

101

#97

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

Dic₂₆

yes

—

105

C₄×C₈

C₂²⋊D₁₃

yes

—

106

#95

—

107

#95

—

108

C₂×C₁₃

#1831

yes

characteristic

109

C₂×C₁₃

#2151

yes

characteristic

110

C₂×C₁₃

#2151

yes

characteristic

111

C₂×C₁₃

#2164

yes

—

112

C₂²×C₄

—

113

C₂²×C₄

C₈×D₁₃

yes

characteristic

114

C₂²×C₄

C₈×D₁₃

yes

characteristic

115

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

#6101

yes

—

121

C₂×C₈

C₂×Dic₂₆

yes

characteristic

122

C₂×C₈

#6129

yes

—

123

C₂×C₈

#6131

yes

—

124

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

125

C₄²

—

126

C₄²

—

127

C₄²

#6094

yes

—

128

C₄²

#6101

yes

—

129

C₁₆

—

130

C₁₆

—

131

C₁₃

#12880

yes

characteristic, complemented, Sylow

132

C₂³

C₂×C₈×D₁₃

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

#88054

yes

—

139

C₂×C₄

#88054

yes

—

140

C₂×C₄

#88146

yes

—

141

C₂×C₄

C₂×#6094

yes

characteristic

142

C₂×C₄

M₁₆×D₁₃

yes

—

143

C₂×C₄

C₂×#6101

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

#88144

yes

—

147

C₈

#88190

yes

characteristic

148

C₈

#88201

yes

characteristic

149

C₂²

#11718494

yes

—

150

C₂²

#11718562

yes

—

151

C₂²

#11718568

yes

—

152

C₂²

C₂×#88054

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

#11718496

yes

—

157

C₄

#11718638

yes

characteristic

158

C₄

#11718779

yes

characteristic

159

C₂

#13114952

yes

characteristic

160

C₂

#13116594

yes

characteristic

161

C₂

#13116596

yes

characteristic

162

C₂

#13116642

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₈
Fitting	C₂×C₁₃×C₄⋊C₁₆	C₂
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₁₃
hypocenter	C₁₃	#12880
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₁₃

commutator, socle, prime radical

C₂³×C₁₃

C₂²×C₈

Fitting

C₂×C₁₃×C₄⋊C₁₆

C₂

cosocle

C₂²×C₈×C₁₃

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
131. C₁₃	#12880	semidirect

H ≅ G/N

type

131. C₁₃

#12880

semidirect

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

subgroup	index
C₂×C₄⋊#6090	2
#13114522	2
#13112913	2
C₂×C₁₃×C₄⋊C₁₆	2
#12880	13

subgroup

index

C₂×C₄⋊#6090

#13114522

#13112913

C₂×C₁₃×C₄⋊C₁₆

#12880

Subgroups — #15779268

Conjugacy classes of subgroups

Complements

Maximal subgroups