Group #15779335 — subgroups

Subgroups — #15779335

Order 3328.

382 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 167 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×#11718103	C₂	1	4	yes	maximal
2	#13116592	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
9	C₂×#88052	C₂²	1	2	yes	—
10	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×#1055	C₄	1	1	yes	characteristic
12	C₁₃×C₄⋊C₁₆	—	2	2	no	—
13	#11718103	—	2	8	no	—
14	C₄⋊#6090	—	2	2	no	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₃	—	2	2	no	—
19	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
20	C₂²×#1055	C₂×C₄	1	2	yes	—
21	C₁₃×M₃₂	—	2	4	no	—
22	C₂×C₁₃×C₁₆	—	2	2	no	—
23	C₄×C₈×C₁₃	D₄	1	2	yes	—
24	C₄×C₈×C₁₃	Q₈	1	2	yes	—
25	C₈×Dic₁₃	—	2	4	no	—
26	C₈×Dic₁₃	D₄	1	4	yes	—
27	C₈×Dic₁₃	Q₈	1	4	yes	—
28	#88052	—	2	4	no	—
29	C₂×#6090	—	2	2	no	—
30	C₄×#1055	C₈	1	2	yes	—
31	C₄×#1055	C₈	1	2	yes	—
32	#12900	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×Dic₁₃	—	2	2	no	—
36	C₂×C₈×C₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
39	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
42	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
43	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
44	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₄×Dic₁₃	—	2	8	no	—
46	C₄×Dic₁₃	—	2	2	no	—
47	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
48	C₂×#1055	C₄⋊C₄	1	4	yes	—
49	C₂×#1055	C₂×C₈	1	4	yes	—
50	C₂×#1055	M₁₆	1	4	yes	—
51	C₁₃×C₁₆	—	4	2	no	—
52	#6090	—	4	2	no	—
53	C₂×#364	—	13	4	no	—
54	#2150	—	13	1	no	—
55	#2150	D₁₃	1	1	yes	characteristic
56	C₄²×C₈	—	13	1	no	—
57	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
58	C₂×C₄×C₁₃	—	2	4	no	—
59	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
60	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
65	C₂×Dic₁₃	—	2	8	no	—
66	C₂×Dic₁₃	—	2	4	no	—
67	C₈×C₁₃	—	2	2	no	—
68	C₈×C₁₃	#127	1	1	yes	characteristic
69	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
70	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
71	#1055	C₄⋊C₈	1	8	yes	—
72	C₂×M₃₂	—	13	2	no	—
73	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
74	C₂×C₄×C₈	—	13	2	no	—
75	C₂×C₄×C₈	—	13	1	no	—
76	C₂×C₄×C₈	—	13	2	no	—
77	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
78	C₄³	—	13	1	no	—
79	#364	—	26	8	no	—
80	C₄⋊C₁₆	—	2	2	no	—
81	C₄⋊C₁₆	—	26	2	no	—
82	C₂²×C₁₃	—	2	2	no	—
83	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
84	C₂²×C₁₃	#423	1	2	yes	—
85	C₄×C₁₃	—	2	2	no	—
86	C₄×C₁₃	#364	1	4	yes	complemented
87	C₄×C₁₃	#384	1	1	yes	characteristic
88	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
89	C₄×C₁₃	#423	1	1	yes	characteristic
90	Dic₁₃	—	2	8	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	—	26	2	no	—
96	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
97	M₃₂	—	2	4	no	—
98	M₃₂	—	26	4	no	—
99	C₂×C₁₆	—	2	2	no	—
100	C₂×C₁₆	—	26	2	no	—
101	C₄×C₈	—	13	4	no	—
102	C₄×C₈	—	13	4	no	—
103	C₄×C₈	—	13	2	no	—
104	C₄×C₈	—	13	2	no	—
105	C₄×C₈	—	26	4	no	—
106	C₄×C₈	Dic₂₆	1	2	yes	—
107	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
108	C₂×C₁₃	—	2	2	no	—
109	C₂×C₁₃	#1842	1	1	yes	characteristic
110	C₂×C₁₃	C₂×#364	1	2	yes	—
111	C₂²×C₄	—	26	2	no	—
112	C₂²×C₄	#6094	1	2	yes	—
113	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
114	C₂×C₈	—	2	2	no	—
115	C₂×C₈	—	13	4	no	—
116	C₂×C₈	—	13	4	no	—
117	C₂×C₈	—	13	4	no	—
118	C₂×C₈	#6101	1	2	yes	—
119	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
120	C₂×C₈	D₄×D₁₃	1	2	yes	—
121	C₂×C₈	Q₈×D₁₃	1	2	yes	—
122	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
123	C₄²	—	13	4	no	—
124	C₄²	—	26	8	no	—
125	C₄²	—	26	2	no	—
126	C₄²	C₈×D₁₃	1	1	yes	characteristic
127	C₄²	C₈×D₁₃	1	1	yes	characteristic
128	C₄²	#6101	1	2	yes	—
129	C₁₆	—	4	2	no	—
130	C₁₆	—	52	2	no	—
131	C₁₃	#12900	1	1	yes	characteristic, complemented, Sylow
132	C₂³	C₂×#6094	1	1	yes	characteristic
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	26	8	no	—
135	C₂×C₄	—	26	4	no	—
136	C₂×C₄	#88054	1	2	yes	—
137	C₂×C₄	#88054	1	2	yes	—
138	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
139	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
140	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
141	C₂×C₄	C₂×#6101	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	13	8	no	—
144	C₈	#88142	1	2	yes	—
145	C₈	#88194	1	1	yes	characteristic
146	C₈	#88198	1	1	yes	characteristic
147	C₂²	—	2	2	no	—
148	C₂²	#11718498	1	2	yes	—
149	C₂²	C₂×#88054	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	26	8	no	—
152	C₄	#11718103	1	4	yes	complemented
153	C₄	D₁₃×C₄⋊C₈	1	2	yes	—
154	C₄	#11718637	1	1	yes	characteristic
155	C₄	#11718779	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	#13114987	1	1	yes	characteristic
158	C₂	C₂×#11718103	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718103

C₂

yes

maximal

#13116592

C₂

yes

maximal, characteristic

C₄×C₈×Dic₁₃

C₂

yes

maximal, characteristic

C₁₃×#2150

C₂

yes

maximal, characteristic

C₂×C₁₃×M₃₂

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×C₈×Dic₁₃

C₄

yes

—

C₂×C₈×Dic₁₃

C₂²

yes

—

C₂×#88052

C₂²

yes

—

C₄²×Dic₁₃

C₄

yes

characteristic

C₂×C₄×#1055

C₄

yes

characteristic

C₁₃×C₄⋊C₁₆

—

#11718103

—

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×Dic₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₈×Dic₁₃

—

C₈×Dic₁₃

D₄

yes

—

C₈×Dic₁₃

Q₈

yes

—

#88052

—

C₂×#6090

—

C₄×#1055

C₈

yes

—

C₄×#1055

C₈

yes

—

#12900

—

maximal, Sylow

C₂²×C₄×C₁₃

M₁₆

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

C₂×C₈

yes

characteristic

C₄²×C₁₃

C₂×C₈

yes

characteristic

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₄⋊C₄

yes

—

C₂×#1055

C₄⋊C₄

yes

—

C₂×#1055

C₂×C₈

yes

—

C₂×#1055

M₁₆

yes

—

C₁₃×C₁₆

—

—

—

—

D₁₃

yes

characteristic

C₄²×C₈

—

C₂³×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#127

yes

characteristic

C₈×C₁₃

C₄⋊Q₈

yes

—

C₈×C₁₃

C₄⋊Q₈

yes

characteristic

#1055

C₄⋊C₈

yes

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₃

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

C₄³

—

#364

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₃

#423

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

C₂×C₄⋊C₈

yes

—

C₄×C₁₃

#423

yes

characteristic

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₃

yes

characteristic

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

100

C₂×C₁₆

—

101

C₄×C₈

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

Dic₂₆

yes

—

107

C₄×C₈

C₂²⋊D₁₃

yes

—

108

C₂×C₁₃

—

109

C₂×C₁₃

#1842

yes

characteristic

110

C₂×C₁₃

C₂×#364

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

#6094

yes

—

113

C₂²×C₄

C₂×C₄×D₁₃

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

#6101

yes

—

119

C₂×C₈

C₂×Dic₂₆

yes

characteristic

120

C₂×C₈

D₄×D₁₃

yes

—

121

C₂×C₈

Q₈×D₁₃

yes

—

122

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

123

C₄²

—

124

C₄²

—

125

C₄²

—

126

C₄²

C₈×D₁₃

yes

characteristic

127

C₄²

C₈×D₁₃

yes

characteristic

128

C₄²

#6101

yes

—

129

C₁₆

—

130

C₁₆

—

131

C₁₃

#12900

yes

characteristic, complemented, Sylow

132

C₂³

C₂×#6094

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#88054

yes

—

137

C₂×C₄

#88054

yes

—

138

C₂×C₄

C₄⋊C₄×D₁₃

yes

—

139

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

140

C₂×C₄

M₁₆×D₁₃

yes

—

141

C₂×C₄

C₂×#6101

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

#88142

yes

—

145

C₈

#88194

yes

characteristic

146

C₈

#88198

yes

characteristic

147

C₂²

—

148

C₂²

#11718498

yes

—

149

C₂²

C₂×#88054

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

#11718103

yes

complemented

153

C₄

D₁₃×C₄⋊C₈

yes

—

154

C₄

#11718637

yes

characteristic

155

C₄

#11718779

yes

characteristic

156

C₂

—

157

C₂

#13114987

yes

characteristic

158

C₂

C₂×#11718103

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#2150	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#12900
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#2150

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₈

prime radical

C₂³×C₁₃

C₂×M₁₆

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
86. C₄×C₁₃	#364	semidirect
131. C₁₃	#12900	semidirect
152. C₄	#11718103	semidirect

H ≅ G/N

type

86. C₄×C₁₃

#364

semidirect

131. C₁₃

#12900

semidirect

152. C₄

#11718103

semidirect

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

subgroup	index
C₂×#11718103	2
#13116592	2
C₄×C₈×Dic₁₃	2
C₁₃×#2150	2
#12900	13

subgroup

index

C₂×#11718103

#13116592

C₄×C₈×Dic₁₃

C₁₃×#2150

#12900

Subgroups — #15779335

Conjugacy classes of subgroups

Complements

Maximal subgroups