Group #15719140 — subgroups

Subgroups — C₁₃×#32801 #15719140

Order 3328.

762 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 238 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	C₁₃×#2868	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2863	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2043	C₂	1	6	yes	maximal
4	C₁₃×#2016	C₂	1	6	yes	maximal
5	C₁₃×#1839	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
8	C₂×C₁₃×#103	C₂²	1	12	yes	—
9	C₁₃×#391	C₂²	1	3	yes	—
10	C₁₃×#389	C₂²	1	3	yes	—
11	C₁₃×#387	—	2	3	no	—
12	C₁₃×#384	—	2	3	no	—
13	C₁₃×#384	—	2	1	no	—
14	C₁₃×#383	—	2	1	no	—
15	C₄³×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#336	C₂²	1	6	yes	—
17	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
19	C₂×C₁₃×Q₁₆	—	4	12	no	—
20	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
21	C₁₃×C₄⋊Q₈	—	4	12	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
23	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
25	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
26	C₂×C₄²×C₁₃	D₄	1	3	yes	—
27	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
29	C₁₃×#103	—	4	12	no	—
30	C₁₃×#95	—	2	3	no	—
31	C₁₃×#95	—	2	3	no	—
32	C₁₃×#95	—	2	3	no	—
33	#32801	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂×Q₈×C₁₃	—	2	12	no	—
35	C₂×Q₈×C₁₃	—	2	12	no	—
36	C₂×Q₈×C₁₃	—	2	6	no	—
37	C₂²×C₄×C₁₃	—	2	1	no	—
38	C₂²×C₄×C₁₃	—	2	3	no	—
39	C₂²×C₄×C₁₃	—	2	4	no	—
40	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
41	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
42	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
43	C₁₃×Q₁₆	—	4	16	no	—
44	C₂×C₈×C₁₃	—	2	12	no	—
45	C₁₃×C₄⋊C₄	—	2	6	no	—
46	C₁₃×C₄⋊C₄	—	4	12	no	—
47	C₁₃×C₄⋊C₄	—	4	12	no	—
48	C₁₃×C₄⋊C₄	—	4	6	no	—
49	C₄²×C₁₃	—	2	6	no	—
50	C₄²×C₁₃	—	2	6	no	—
51	C₄²×C₁₃	Q₁₆	1	4	yes	complemented
52	#2868	C₂×C₁₃	1	1	yes	characteristic
53	#2863	C₂×C₁₃	1	1	yes	characteristic
54	#2043	C₂×C₁₃	1	6	yes	—
55	#2016	C₂×C₁₃	1	6	yes	—
56	#1839	C₂×C₁₃	1	1	yes	characteristic
57	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
58	Q₈×C₁₃	—	4	4	no	—
59	Q₈×C₁₃	—	4	4	no	—
60	Q₈×C₁₃	—	4	12	no	—
61	C₂×C₄×C₁₃	—	2	3	no	—
62	C₂×C₄×C₁₃	—	2	3	no	—
63	C₂×C₄×C₁₃	—	2	3	no	—
64	C₂×C₄×C₁₃	—	2	3	no	—
65	C₂×C₄×C₁₃	—	4	3	no	—
66	C₂×C₄×C₁₃	—	4	12	no	—
67	C₂×C₄×C₁₃	—	4	3	no	—
68	C₂×C₄×C₁₃	—	4	6	no	—
69	C₂×C₄×C₁₃	C₂×Q₁₆	1	6	yes	—
70	C₂×C₄×C₁₃	#137	1	6	yes	—
71	C₂×C₄×C₁₃	H(5,𝔽₂)	1	6	yes	—
72	C₈×C₁₃	—	4	4	no	—
73	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
74	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
75	C₂×#103	C₂²×C₁₃	1	12	yes	—
76	#391	C₂²×C₁₃	1	3	yes	—
77	#389	C₂²×C₁₃	1	3	yes	—
78	#387	—	2	3	no	—
79	#384	—	2	3	no	—
80	#384	—	2	1	no	—
81	#383	—	2	1	no	—
82	C₄³	C₂²×C₁₃	1	1	yes	characteristic
83	#336	C₂²×C₁₃	1	6	yes	—
84	C₂²×C₁₃	#535	1	3	yes	—
85	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
86	C₂²×C₁₃	C₂×#137	1	3	yes	—
87	C₄×C₁₃	—	2	6	no	—
88	C₄×C₁₃	—	2	6	no	—
89	C₄×C₁₃	—	8	4	no	—
90	C₄×C₁₃	—	8	1	no	—
91	C₄×C₁₃	—	8	3	no	—
92	C₄×C₁₃	#560	1	4	yes	—
93	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
94	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
95	C₂×Q₁₆	—	4	12	no	—
96	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
97	C₄⋊Q₈	—	4	12	no	—
98	C₂×C₄⋊C₄	—	2	6	no	—
99	C₂×C₄⋊C₄	—	2	6	no	—
100	C₂×C₄⋊C₄	—	2	3	no	—
101	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
102	C₂×C₄²	D₄×C₁₃	1	3	yes	—
103	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
104	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
105	#103	—	4	12	no	—
106	#95	—	2	3	no	—
107	#95	—	2	3	no	—
108	#95	—	2	3	no	—
109	C₂×C₁₃	#2818	1	1	yes	characteristic
110	C₂×C₁₃	#3209	1	3	yes	—
111	C₂×C₁₃	#3218	1	3	yes	—
112	C₂×Q₈	—	2	12	no	—
113	C₂×Q₈	—	2	12	no	—
114	C₂×Q₈	—	2	6	no	—
115	C₂²×C₄	—	2	1	no	—
116	C₂²×C₄	—	2	3	no	—
117	C₂²×C₄	—	2	4	no	—
118	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
119	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
120	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
121	Q₁₆	—	4	16	no	—
122	C₂×C₈	—	2	12	no	—
123	C₄⋊C₄	—	2	6	no	—
124	C₄⋊C₄	—	4	12	no	—
125	C₄⋊C₄	—	4	12	no	—
126	C₄⋊C₄	—	4	6	no	—
127	C₄²	—	2	6	no	—
128	C₄²	—	2	6	no	—
129	C₄²	C₁₃×Q₁₆	1	4	yes	complemented
130	C₁₃	#32801	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
132	Q₈	—	4	4	no	—
133	Q₈	—	4	4	no	—
134	Q₈	—	4	12	no	—
135	C₂×C₄	—	2	3	no	—
136	C₂×C₄	—	2	3	no	—
137	C₂×C₄	—	2	3	no	—
138	C₂×C₄	—	2	3	no	—
139	C₂×C₄	—	4	3	no	—
140	C₂×C₄	—	4	12	no	—
141	C₂×C₄	—	4	3	no	—
142	C₂×C₄	—	4	6	no	—
143	C₂×C₄	C₂×C₁₃×Q₁₆	1	6	yes	—
144	C₂×C₄	C₁₃×#137	1	6	yes	—
145	C₂×C₄	C₁₃×H(5,𝔽₂)	1	6	yes	—
146	C₈	—	4	4	no	—
147	C₂²	C₁₃×#535	1	3	yes	—
148	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
149	C₂²	C₂×C₁₃×#137	1	3	yes	—
150	C₄	—	2	6	no	—
151	C₄	—	2	6	no	—
152	C₄	—	8	4	no	—
153	C₄	—	8	1	no	—
154	C₄	—	8	3	no	—
155	C₄	C₁₃×#560	1	4	yes	—
156	C₂	C₁₃×#2818	1	1	yes	characteristic
157	C₂	C₁₃×#3209	1	3	yes	—
158	C₂	C₁₃×#3218	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2868

C₂

yes

maximal, characteristic

C₁₃×#2863

C₂

yes

maximal, characteristic

C₁₃×#2043

C₂

yes

maximal

C₁₃×#2016

C₂

yes

maximal

C₁₃×#1839

C₂

yes

maximal, characteristic

C₂²×C₁₃×Q₁₆

C₂²

yes

—

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

—

C₂×C₁₃×#103

C₂²

yes

—

C₁₃×#391

C₂²

yes

—

C₁₃×#389

C₂²

yes

—

C₁₃×#387

—

C₁₃×#384

—

C₁₃×#384

—

C₁₃×#383

—

C₄³×C₁₃

C₂²

yes

characteristic

C₁₃×#336

C₂²

yes

—

C₂²×Q₈×C₁₃

C₂³

yes

characteristic

C₂²×Q₈×C₁₃

C₂³

yes

—

C₂×C₁₃×Q₁₆

—

C₂²×C₈×C₁₃

C₂³

yes

—

C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂³

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

—

C₁₃×#103

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

#32801

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂⁴

yes

characteristic

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

Q₁₆

yes

complemented

#2868

C₂×C₁₃

yes

characteristic

#2863

C₂×C₁₃

yes

characteristic

#2043

C₂×C₁₃

yes

—

#2016

C₂×C₁₃

yes

—

#1839

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

C₂²×D₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×C₄×C₁₃

H(5,𝔽₂)

yes

—

C₈×C₁₃

—

C₂²×Q₁₆

C₂²×C₁₃

yes

—

C₂×C₄⋊Q₈

C₂²×C₁₃

yes

—

C₂×#103

C₂²×C₁₃

yes

—

#391

C₂²×C₁₃

yes

—

#389

C₂²×C₁₃

yes

—

—

—

—

—

C₄³

C₂²×C₁₃

yes

characteristic

#336

C₂²×C₁₃

yes

—

C₂²×C₁₃

#535

yes

—

C₂²×C₁₃

C₂²×Q₁₆

yes

characteristic

C₂²×C₁₃

C₂×#137

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#560

yes

—

C₂²×Q₈

C₂³×C₁₃

yes

—

C₂²×Q₈

C₂³×C₁₃

yes

characteristic

C₂×Q₁₆

—

C₂²×C₈

C₂³×C₁₃

yes

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

C₂³×C₁₃

yes

—

102

C₂×C₄²

D₄×C₁₃

yes

—

103

C₂×C₄²

D₄×C₁₃

yes

characteristic

104

C₂×C₄²

C₂³×C₁₃

yes

—

105

#103

—

106

#95

—

107

#95

—

108

#95

—

109

C₂×C₁₃

#2818

yes

characteristic

110

C₂×C₁₃

#3209

yes

—

111

C₂×C₁₃

#3218

yes

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂×D₄×C₁₃

yes

—

119

C₂²×C₄

C₂×D₄×C₁₃

yes

—

120

C₂²×C₄

C₂⁴×C₁₃

yes

characteristic

121

Q₁₆

—

122

C₂×C₈

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄²

—

128

C₄²

—

129

C₄²

C₁₃×Q₁₆

yes

complemented

130

C₁₃

#32801

yes

characteristic, direct product factor, Sylow

131

C₂³

C₂²×D₄×C₁₃

yes

characteristic

132

Q₈

—

133

Q₈

—

134

Q₈

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

C₂×C₁₃×Q₁₆

yes

—

144

C₂×C₄

C₁₃×#137

yes

—

145

C₂×C₄

C₁₃×H(5,𝔽₂)

yes

—

146

C₈

—

147

C₂²

C₁₃×#535

yes

—

148

C₂²

C₂²×C₁₃×Q₁₆

yes

characteristic

149

C₂²

C₂×C₁₃×#137

yes

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

C₁₃×#560

yes

—

156

C₂

C₁₃×#2818

yes

characteristic

157

C₂

C₁₃×#3209

yes

—

158

C₂

C₁₃×#3218

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₃

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

N	H ≅ G/N	type
33. #32801	C₁₃	direct (N × H)
51. C₄²×C₁₃	Q₁₆	semidirect
129. C₄²	C₁₃×Q₁₆	semidirect
130. C₁₃	#32801	direct (N × H)

H ≅ G/N

type

33. #32801

C₁₃

direct (N × H)

51. C₄²×C₁₃

Q₁₆

semidirect

129. C₄²

C₁₃×Q₁₆

semidirect

130. C₁₃

#32801

direct (N × H)

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

subgroup	index
C₁₃×#2868	2
C₁₃×#2863	2
C₁₃×#2043	2
C₁₃×#2016	2
C₁₃×#1839	2
#32801	13

subgroup

index

C₁₃×#2868

C₁₃×#2863

C₁₃×#2043

C₁₃×#2016

C₁₃×#1839

#32801

Subgroups — C₁₃×#32801 #15719140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#32801 #15719140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32801 #15719140