Group #15774482 — subgroups

Subgroups — #15774482

Order 3328.

220 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 99 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	D₁₃×#364	C₂	1	2	yes	maximal
2	#13116429	C₂	1	1	yes	maximal, characteristic
3	#13112904	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112903	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1369	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₃×M₃₂	—	2	2	no	—
7	C₂×#88038	C₄	1	1	yes	characteristic
8	C₂×#88038	C₄	1	1	yes	characteristic
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#364	C₂²	1	2	yes	—
11	C₁₃×#346	C₂²	1	1	yes	characteristic
12	#11718103	—	2	2	no	—
13	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
14	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
15	#11718055	C₂²	1	2	yes	—
16	#11718053	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
19	C₄²×D₁₃	Q₈	1	1	yes	characteristic
20	C₁₃×M₃₂	—	2	2	no	—
21	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₈×Dic₁₃	D₄	1	1	yes	characteristic
26	#88052	—	2	2	no	—
27	C₂×#6090	C₂×C₄	1	1	yes	characteristic
28	C₂×#6090	C₂×C₄	1	1	yes	characteristic
29	C₄×#1055	Q₈	1	1	yes	characteristic
30	#88038	—	2	2	no	—
31	#88038	—	4	2	no	—
32	#88038	C₈	1	4	yes	—
33	C₁₆×D₁₃	—	4	2	no	—
34	#12002	—	13	1	no	maximal, Sylow
35	C₂×C₄×D₁₃	—	2	1	no	—
36	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
40	C₄×Dic₁₃	—	2	1	no	—
41	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
42	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
43	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
44	C₈×D₁₃	C₂×C₈	1	2	yes	—
45	C₈×D₁₃	M₁₆	1	2	yes	—
46	C₈×D₁₃	SD₁₆	1	2	yes	—
47	C₈×D₁₃	SD₁₆	1	2	yes	—
48	C₁₃×C₁₆	—	2	1	no	—
49	C₁₃×C₁₆	—	4	2	no	—
50	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
51	#6090	—	2	1	no	—
52	#6090	—	4	2	no	—
53	#6090	C₂×C₈	1	2	yes	—
54	C₂×#364	—	13	2	no	—
55	C₄×M₃₂	—	13	1	no	—
56	#1369	—	13	2	no	—
57	#1369	—	13	1	no	—
58	#1369	D₁₃	1	1	yes	characteristic, complemented
59	C₂²×D₁₃	#108	1	1	yes	characteristic
60	C₂×C₄×C₁₃	—	2	1	no	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×Dic₁₃	—	2	1	no	—
63	C₂×Dic₁₃	#108	1	1	yes	characteristic
64	C₄×D₁₃	—	4	2	no	—
65	C₄×D₁₃	C₄⋊C₈	1	2	yes	—
66	C₄×D₁₃	#106	1	2	yes	—
67	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
68	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
69	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
70	#1055	C₄⋊C₈	1	2	yes	—
71	#1055	#106	1	1	yes	characteristic
72	#1055	#106	1	1	yes	characteristic
73	C₂×M₃₂	—	13	1	no	—
74	C₂×M₃₂	—	13	1	no	—
75	C₂×M₃₂	—	26	2	no	—
76	C₂×C₄×C₈	—	13	1	no	—
77	#364	—	13	2	no	—
78	#364	—	26	2	no	—
79	#364	C₂×D₁₃	1	2	yes	—
80	#346	—	13	1	no	—
81	#346	C₂×D₁₃	1	1	yes	characteristic
82	C₄×C₁₆	—	13	1	no	—
83	C₄×C₁₆	—	13	1	no	—
84	C₂²×C₁₃	C₂×#108	1	1	yes	characteristic
85	C₂×D₁₃	—	4	1	no	—
86	C₂×D₁₃	#334	1	2	yes	—
87	C₄×C₁₃	—	4	1	no	—
88	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
89	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
90	Dic₁₃	—	2	2	no	—
91	Dic₁₃	#334	1	2	yes	—
92	C₂²×C₈	—	13	1	no	—
93	C₂²×C₈	—	13	1	no	—
94	C₂×C₄²	—	13	1	no	—
95	M₃₂	—	2	2	no	—
96	M₃₂	—	13	4	no	—
97	M₃₂	—	26	2	no	—
98	M₃₂	—	26	2	no	—
99	M₃₂	—	52	2	no	—
100	C₂×C₁₆	—	13	1	no	—
101	C₂×C₁₆	—	13	1	no	—
102	C₂×C₁₆	—	52	2	no	—
103	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
104	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
105	C₄×C₈	—	13	1	no	—
106	C₄×C₈	—	13	1	no	—
107	C₄×C₈	—	13	1	no	—
108	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
109	C₂×C₁₃	—	2	1	no	—
110	C₂×C₁₃	C₂×#334	1	1	yes	characteristic
111	D₁₃	—	2	2	no	—
112	C₂²×C₄	—	13	1	no	—
113	C₂²×C₄	—	26	1	no	—
114	C₂×C₈	—	13	1	no	—
115	C₂×C₈	—	13	1	no	—
116	C₂×C₈	—	13	2	no	—
117	C₂×C₈	—	13	2	no	—
118	C₂×C₈	—	13	2	no	—
119	C₂×C₈	—	13	2	no	—
120	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
121	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
122	C₄²	—	13	1	no	—
123	C₄²	—	26	1	no	—
124	C₄²	Q₈×D₁₃	1	1	yes	characteristic
125	C₁₆	—	2	1	no	—
126	C₁₆	—	4	2	no	—
127	C₁₆	—	13	2	no	—
128	C₁₆	—	26	1	no	—
129	C₁₆	—	52	2	no	—
130	C₁₆	C₈×D₁₃	1	2	yes	—
131	C₁₃	#12002	1	1	yes	characteristic, complemented, Sylow
132	C₂³	—	13	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	13	1	no	—
135	C₂×C₄	—	13	2	no	—
136	C₂×C₄	—	13	2	no	—
137	C₂×C₄	—	26	1	no	—
138	C₂×C₄	—	52	2	no	—
139	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
140	C₈	—	13	2	no	—
141	C₈	—	13	1	no	—
142	C₈	—	13	1	no	—
143	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
144	C₈	M₁₆×D₁₃	1	1	yes	characteristic
145	C₈	SD₁₆×D₁₃	1	2	yes	—
146	C₂²	—	13	2	no	—
147	C₂²	—	52	1	no	—
148	C₂²	D₁₃×#108	1	1	yes	characteristic
149	C₄	—	4	1	no	—
150	C₄	—	13	2	no	—
151	C₄	—	26	2	no	—
152	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
153	C₄	D₁₃×#106	1	1	yes	characteristic
154	C₂	—	2	1	no	—
155	C₂	—	26	2	no	—
156	C₂	D₁₃×#334	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₃×#364

C₂

yes

maximal

#13116429

C₂

yes

maximal, characteristic

#13112904

C₂

yes

maximal, characteristic, complemented

#13112903

C₂

yes

maximal, complemented

C₁₃×#1369

C₂

yes

maximal, characteristic, complemented

D₁₃×M₃₂

—

C₂×#88038

C₄

yes

characteristic

C₂×#88038

C₄

yes

characteristic

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₁₃×#364

C₂²

yes

—

C₁₃×#346

C₂²

yes

characteristic

#11718103

—

C₁₆×Dic₁₃

C₄

yes

characteristic

C₁₆×Dic₁₃

C₄

yes

characteristic

#11718055

C₂²

yes

—

#11718053

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×D₁₃

D₄

yes

characteristic

C₄²×D₁₃

Q₈

yes

characteristic

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂³

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

D₄

yes

characteristic

#88052

—

C₂×#6090

C₂×C₄

yes

characteristic

C₂×#6090

C₂×C₄

yes

characteristic

C₄×#1055

Q₈

yes

—

—

C₈

yes

—

C₁₆×D₁₃

—

#12002

—

maximal, Sylow

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄×Dic₁₃

—

C₄×Dic₁₃

C₄⋊C₄

yes

characteristic

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

C₄⋊C₄

yes

characteristic

C₈×D₁₃

C₂×C₈

yes

—

C₈×D₁₃

M₁₆

yes

—

C₈×D₁₃

SD₁₆

yes

—

C₈×D₁₃

SD₁₆

yes

—

C₁₃×C₁₆

—

C₁₃×C₁₆

—

C₁₃×C₁₆

C₂×C₈

yes

—

#6090

—

#6090

—

#6090

C₂×C₈

yes

—

C₂×#364

—

C₄×M₃₂

—

#1369

—

#1369

—

#1369

D₁₃

yes

characteristic, complemented

C₂²×D₁₃

#108

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

#108

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₄⋊C₈

yes

—

C₄×D₁₃

#106

yes

—

C₈×C₁₃

C₂²×C₈

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

C₈×C₁₃

C₂×SD₁₆

yes

—

#1055

C₄⋊C₈

yes

—

yes

yes

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×C₄×C₈

—

#364

—

#364

—

#364

C₂×D₁₃

yes

—

#346

—

#346

C₂×D₁₃

yes

characteristic

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₁₃

C₂×#108

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

#334

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₃

C₂×#106

yes

characteristic

Dic₁₃

—

Dic₁₃

#334

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

100

C₂×C₁₆

—

101

C₂×C₁₆

—

102

C₂×C₁₆

—

103

C₂×C₁₆

C₄×D₁₃

yes

characteristic

104

C₂×C₁₆

C₄×D₁₃

yes

characteristic

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

C₂²×D₁₃

yes

characteristic

109

C₂×C₁₃

—

110

C₂×C₁₃

C₂×#334

yes

characteristic

111

D₁₃

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

121

C₂×C₈

D₄×D₁₃

yes

characteristic

122

C₄²

—

123

C₄²

—

124

C₄²

Q₈×D₁₃

yes

characteristic

125

C₁₆

—

126

C₁₆

—

127

C₁₆

—

128

C₁₆

—

129

C₁₆

—

130

C₁₆

C₈×D₁₃

yes

—

131

C₁₃

#12002

yes

characteristic, complemented, Sylow

132

C₂³

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₄⋊C₄×D₁₃

yes

characteristic

140

C₈

—

141

C₈

—

142

C₈

—

143

C₈

C₂×C₈×D₁₃

yes

characteristic

144

C₈

M₁₆×D₁₃

yes

characteristic

145

C₈

SD₁₆×D₁₃

yes

—

146

C₂²

—

147

C₂²

—

148

C₂²

D₁₃×#108

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

D₁₃×C₄⋊C₈

yes

characteristic

153

C₄

D₁₃×#106

yes

characteristic

154

C₂

—

155

C₂

—

156

C₂

D₁₃×#334

yes

characteristic

	subgroup	G/H
center	C₄	D₁₃×#106
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₁₃×#1369	C₂
socle	C₂×C₁₃	C₂×#334
prime radical	C₂²×D₁₃	#108
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1369	D₁₃
hypocenter	C₁₃	#12002
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

subgroup

G/H

center

C₄

D₁₃×#106

commutator

C₈×C₁₃

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₁₃

Fitting

C₁₃×#1369

C₂

C₂×C₁₃

C₂²×D₁₃

C₄×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

N	H ≅ G/N	type
3. #13112904	C₂	semidirect
4. #13112903	C₂	semidirect
5. C₁₃×#1369	C₂	semidirect
58. #1369	D₁₃	semidirect
131. C₁₃	#12002	semidirect

H ≅ G/N

type

3. #13112904

C₂

semidirect

4. #13112903

C₂

semidirect

5. C₁₃×#1369

C₂

semidirect

58. #1369

D₁₃

semidirect

131. C₁₃

#12002

semidirect

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

subgroup	index
D₁₃×#364	2
#13116429	2
#13112904	2
#13112903	2
C₁₃×#1369	2
#12002	13

subgroup

index

D₁₃×#364

C₁₃×#1369

Subgroups — #15774482

Conjugacy classes of subgroups

Complements

Maximal subgroups