Group #13111151 — subgroups

Subgroups — C₁₃×#2093 #13111151

Order 1664.

290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 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×C₁₃×#107	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#102	C₂	1	2	yes	maximal
3	C₁₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
9	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
12	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#107	—	2	4	no	—
14	C₁₃×#102	—	2	4	no	—
15	C₂⁴×C₁₃	—	2	1	no	—
16	C₂×D₄×C₁₃	—	2	2	no	—
17	C₂×D₄×C₁₃	—	2	2	no	—
18	C₂×D₄×C₁₃	—	2	1	no	—
19	C₂×D₄×C₁₃	Q₈	1	2	yes	—
20	C₂²×C₄×C₁₃	—	2	1	no	—
21	C₂²×C₄×C₁₃	—	2	2	no	—
22	C₂²×C₄×C₁₃	D₄	1	2	yes	—
23	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₁₃	—	2	2	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	D₄	1	4	yes	—
27	C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₁₃×C₄⋊C₄	—	4	4	no	—
31	C₁₃×C₂²⋊C₄	—	4	4	no	—
32	C₄²×C₁₃	—	2	2	no	—
33	#2093	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₁₃	—	2	2	no	—
35	C₂³×C₁₃	—	4	1	no	—
36	C₂³×C₁₃	—	4	1	no	—
37	C₂³×C₁₃	—	4	2	no	—
38	C₂³×C₁₃	—	4	2	no	—
39	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
40	D₄×C₁₃	—	2	4	no	—
41	D₄×C₁₃	—	4	2	no	—
42	C₂×C₄×C₁₃	—	2	2	no	—
43	C₂×C₄×C₁₃	—	2	2	no	—
44	C₂×C₄×C₁₃	—	4	2	no	—
45	C₂×C₄×C₁₃	—	4	1	no	—
46	C₂×C₄×C₁₃	—	4	2	no	—
47	C₂×C₄×C₁₃	—	4	4	no	—
48	C₂×C₄×C₁₃	D₈	1	4	yes	—
49	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×C₁₃	#41	1	2	yes	—
52	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
53	C₈×C₁₃	—	2	4	no	—
54	C₂×#107	C₂×C₁₃	1	2	yes	complemented
55	C₂×#102	C₂×C₁₃	1	2	yes	—
56	#390	C₂×C₁₃	1	1	yes	characteristic
57	#384	C₂×C₁₃	1	1	yes	characteristic, complemented
58	#336	C₂×C₁₃	1	1	yes	characteristic, complemented
59	C₂²×C₁₃	—	4	2	no	—
60	C₂²×C₁₃	—	4	4	no	—
61	C₂²×C₁₃	—	8	2	no	—
62	C₂²×C₁₃	—	8	1	no	—
63	C₂²×C₁₃	—	8	1	no	—
64	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂²×C₁₃	#123	1	1	yes	characteristic
66	C₂²×C₁₃	#127	1	1	yes	characteristic
67	C₂²×C₁₃	C₂×D₈	1	2	yes	—
68	C₂²×C₁₃	#137	1	2	yes	—
69	C₄×C₁₃	—	2	4	no	—
70	C₄×C₁₃	—	8	1	no	—
71	C₄×C₁₃	—	8	2	no	—
72	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
73	C₄×C₁₃	#123	1	2	yes	—
74	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
75	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
76	C₂×C₄⋊C₄	—	2	2	no	—
77	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
78	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
79	C₂×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
81	#107	—	2	4	no	—
82	#102	—	2	4	no	—
83	C₂×C₁₃	—	8	2	no	—
84	C₂×C₁₃	#399	1	1	yes	characteristic
85	C₂×C₁₃	#474	1	2	yes	—
86	C₂×C₁₃	#480	1	2	yes	—
87	C₂×C₁₃	#493	1	1	yes	characteristic
88	C₂×C₁₃	#497	1	1	yes	characteristic
89	C₂⁴	—	2	1	no	—
90	C₂×D₄	—	2	2	no	—
91	C₂×D₄	—	2	2	no	—
92	C₂×D₄	—	2	1	no	—
93	C₂×D₄	Q₈×C₁₃	1	2	yes	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	D₄×C₁₃	1	2	yes	—
97	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	D₄×C₁₃	1	4	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	4	4	no	—
105	C₂²⋊C₄	—	4	4	no	—
106	C₄²	—	2	2	no	—
107	C₁₃	#2093	1	1	yes	characteristic, direct product factor, Sylow
108	C₂³	—	2	2	no	—
109	C₂³	—	4	1	no	—
110	C₂³	—	4	1	no	—
111	C₂³	—	4	2	no	—
112	C₂³	—	4	2	no	—
113	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
114	D₄	—	2	4	no	—
115	D₄	—	4	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	4	4	no	—
122	C₂×C₄	C₁₃×D₈	1	4	yes	—
123	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
124	C₂×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
125	C₂×C₄	C₁₃×#41	1	2	yes	—
126	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
127	C₈	—	2	4	no	—
128	C₂²	—	4	2	no	—
129	C₂²	—	4	4	no	—
130	C₂²	—	8	2	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
134	C₂²	C₁₃×#123	1	1	yes	characteristic
135	C₂²	C₁₃×#127	1	1	yes	characteristic
136	C₂²	C₂×C₁₃×D₈	1	2	yes	—
137	C₂²	C₁₃×#137	1	2	yes	—
138	C₄	—	2	4	no	—
139	C₄	—	8	1	no	—
140	C₄	—	8	2	no	—
141	C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
142	C₄	C₁₃×#123	1	2	yes	—
143	C₂	—	8	2	no	—
144	C₂	C₁₃×#399	1	1	yes	characteristic
145	C₂	C₁₃×#474	1	2	yes	—
146	C₂	C₁₃×#480	1	2	yes	—
147	C₂	C₁₃×#493	1	1	yes	characteristic
148	C₂	C₁₃×#497	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#107

C₂

yes

maximal, complemented

C₂×C₁₃×#102

C₂

yes

maximal

C₁₃×#390

C₂

yes

maximal, characteristic

C₁₃×#384

C₂

yes

maximal, characteristic, complemented

C₁₃×#336

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₃

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₁₃×#107

—

C₁₃×#102

—

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

Q₈

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

#2093

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×D₄

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

D₈

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

characteristic

C₈×C₁₃

—

C₂×#107

C₂×C₁₃

yes

complemented

C₂×#102

C₂×C₁₃

yes

—

#390

C₂×C₁₃

yes

characteristic

#384

C₂×C₁₃

yes

characteristic, complemented

#336

C₂×C₁₃

yes

characteristic, complemented

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊Q₈

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

C₂×D₈

yes

—

C₂²×C₁₃

#137

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

C₄×C₁₃

#123

yes

—

C₂²×D₄

C₂²×C₁₃

yes

characteristic

C₂²×C₈

C₂²×C₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²×C₁₃

yes

—

C₂×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂²×C₁₃

yes

characteristic

#107

—

#102

—

C₂×C₁₃

—

C₂×C₁₃

#399

yes

characteristic

C₂×C₁₃

#474

yes

—

C₂×C₁₃

#480

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

Q₈×C₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₁₃

yes

—

C₂²×C₄

C₂³×C₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

D₄×C₁₃

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₁₃

#2093

yes

characteristic, direct product factor, Sylow

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

C₂×D₄×C₁₃

yes

characteristic

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₁₃×D₈

yes

—

123

C₂×C₄

C₂×D₄×C₁₃

yes

—

124

C₂×C₄

C₂×Q₈×C₁₃

yes

characteristic

125

C₂×C₄

C₁₃×#41

yes

—

126

C₂×C₄

C₁₃×#41

yes

characteristic

127

C₈

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₁₃×C₂²⋊Q₈

yes

characteristic

134

C₂²

C₁₃×#123

yes

characteristic

135

C₂²

C₁₃×#127

yes

characteristic

136

C₂²

C₂×C₁₃×D₈

yes

—

137

C₂²

C₁₃×#137

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

C₁₃×C₂²⋊Q₈

yes

—

142

C₄

C₁₃×#123

yes

—

143

C₂

—

144

C₂

C₁₃×#399

yes

characteristic

145

C₂

C₁₃×#474

yes

—

146

C₂

C₁₃×#480

yes

—

147

C₂

C₁₃×#493

yes

characteristic

148

C₂

C₁₃×#497

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

C₂×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₃

prime radical

C₂²×D₄×C₁₃

C₂²

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₃×#107	C₂	semidirect
4. C₁₃×#384	C₂	semidirect
5. C₁₃×#336	C₂	semidirect
33. #2093	C₁₃	direct (N × H)
54. C₂×#107	C₂×C₁₃	semidirect
57. #384	C₂×C₁₃	semidirect
58. #336	C₂×C₁₃	semidirect
107. C₁₃	#2093	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₃×#107

C₂

semidirect

4. C₁₃×#384

C₂

semidirect

5. C₁₃×#336

C₂

semidirect

33. #2093

C₁₃

direct (N × H)

54. C₂×#107

C₂×C₁₃

semidirect

57. #384

C₂×C₁₃

semidirect

58. #336

C₂×C₁₃

semidirect

107. C₁₃

#2093

direct (N × H)

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

subgroup	index
C₂×C₁₃×#107	2
C₂×C₁₃×#102	2
C₁₃×#390	2
C₁₃×#384	2
C₁₃×#336	2
#2093	13

subgroup

index

C₂×C₁₃×#107

C₂×C₁₃×#102

C₁₃×#390

C₁₃×#384

C₁₃×#336

#2093

Subgroups — C₁₃×#2093 #13111151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#2093 #13111151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2093 #13111151