Group #13130941 — subgroups

Subgroups — #13130941

Order 1664.

240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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×#88101	C₂	1	1	yes	maximal, characteristic
2	C₂×#88100	C₂	1	1	yes	maximal, characteristic
3	#11719083	C₂	1	2	yes	maximal
4	D₁₃×#107	C₂	1	1	yes	maximal, characteristic
5	#11718246	C₂	1	2	yes	maximal
6	C₂×C₄⋊#261	—	2	2	no	—
7	C₂×C₄⋊#261	C₂²	1	2	yes	—
8	C₂×C₄×#261	C₂²	1	1	yes	characteristic
9	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
12	(C₂×#261)⋊C₄	—	2	2	no	—
13	#88101	—	2	2	no	—
14	#88100	—	2	2	no	—
15	C₁₃×#107	C₄	1	1	yes	characteristic, complemented
16	#88058	C₄	1	1	yes	characteristic, complemented
17	#88047	C₄	1	2	yes	complemented
18	C₂²×#261	—	2	2	no	—
19	C₂²×#261	D₄	1	2	yes	—
20	C₂×C₄×D₁₃	—	2	2	no	—
21	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
22	C₂×#1057	—	2	1	no	—
23	C₄⋊#261	—	2	2	no	—
24	C₄⋊#261	—	2	2	no	—
25	C₄⋊#261	—	4	4	no	—
26	C₄×#261	—	2	1	no	—
27	C₄×#261	—	2	1	no	—
28	D₁₃⋊C₈	—	2	1	no	—
29	D₁₃⋊C₈	Q₈	1	2	yes	—
30	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
32	C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
33	#6101	—	2	2	no	—
34	C₂×#1055	C₂×C₄	1	1	yes	characteristic
35	C₈×D₁₃	D₄	1	2	yes	—
36	C₈×D₁₃	Q₈	1	2	yes	—
37	#1943	—	13	1	no	maximal, Sylow
38	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×#261	—	2	2	no	—
40	C₂×#261	—	2	2	no	—
41	C₂×#261	—	2	2	no	—
42	C₂×#261	—	4	2	no	—
43	C₂×#261	—	4	2	no	—
44	C₂×#261	—	4	2	no	—
45	C₂×C₄×C₁₃	—	2	2	no	—
46	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₁₃	—	2	2	no	—
48	C₂×Dic₁₃	#41	1	1	yes	characteristic
49	C₄×D₁₃	—	4	2	no	—
50	C₄×D₁₃	—	4	2	no	—
51	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
52	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₄×D₁₃	#41	1	1	yes	characteristic
55	#1057	—	2	2	no	—
56	C₈×C₁₃	C₄⋊C₄	1	2	yes	complemented
57	#1055	C₄⋊C₄	1	2	yes	complemented
58	C₂×#107	—	13	1	no	—
59	C₂×#106	—	13	1	no	—
60	C₂×#97	—	13	1	no	—
61	#389	—	13	2	no	—
62	#340	—	13	2	no	—
63	C₂²×C₁₃	C₄×D₄	1	1	yes	characteristic
64	C₂×D₁₃	#121	1	1	yes	characteristic
65	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
67	C₂×D₁₃	#137	1	2	yes	—
68	#261	—	4	2	no	—
69	#261	—	8	2	no	—
70	C₄×C₁₃	—	4	2	no	—
71	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
73	Dic₁₃	—	4	2	no	—
74	Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
75	Dic₁₃	#125	1	1	yes	characteristic
76	C₂²×C₈	—	13	1	no	—
77	C₂²×C₈	—	13	1	no	—
78	C₂×C₄⋊C₄	—	13	2	no	—
79	C₂×C₄⋊C₄	—	13	2	no	—
80	C₂×C₄⋊C₄	—	26	2	no	—
81	C₂×C₄²	—	13	1	no	—
82	#107	—	13	1	no	—
83	#107	—	13	2	no	—
84	#107	#261	1	1	yes	characteristic, complemented
85	#106	—	26	2	no	—
86	#97	—	26	2	no	—
87	#95	—	26	2	no	—
88	C₂×C₁₃	#389	1	1	yes	characteristic
89	C₂×C₁₃	#441	1	1	yes	characteristic
90	C₂×C₁₃	#442	1	1	yes	characteristic
91	D₁₃	#468	1	2	yes	—
92	D₁₃	#501	1	2	yes	—
93	C₂²×C₄	—	13	1	no	—
94	C₂²×C₄	—	13	2	no	—
95	C₂²×C₄	—	26	2	no	—
96	C₂²×C₄	—	26	2	no	—
97	C₂×C₈	—	13	1	no	—
98	C₂×C₈	—	13	2	no	—
99	C₂×C₈	—	13	2	no	—
100	C₂×C₈	—	13	2	no	—
101	C₂×C₈	—	26	1	no	—
102	C₂×C₈	—	26	1	no	—
103	C₂×C₈	C₂×#261	1	1	yes	characteristic
104	C₄⋊C₄	—	13	2	no	—
105	C₄⋊C₄	—	26	2	no	—
106	C₄⋊C₄	—	26	2	no	—
107	C₄⋊C₄	—	26	2	no	—
108	C₄⋊C₄	—	52	4	no	—
109	C₄⋊C₄	C₂×#261	1	2	yes	—
110	C₄²	—	26	1	no	—
111	C₄²	—	26	1	no	—
112	C₁₃	#1943	1	1	yes	characteristic, complemented, Sylow
113	C₂³	—	13	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	13	1	no	—
116	C₂×C₄	—	13	1	no	—
117	C₂×C₄	—	13	1	no	—
118	C₂×C₄	—	13	1	no	—
119	C₂×C₄	—	13	1	no	—
120	C₂×C₄	—	26	2	no	—
121	C₂×C₄	—	26	2	no	—
122	C₂×C₄	—	26	2	no	—
123	C₂×C₄	—	26	2	no	—
124	C₂×C₄	—	52	2	no	—
125	C₂×C₄	—	52	2	no	—
126	C₂×C₄	—	52	2	no	—
127	C₂×C₄	—	52	2	no	—
128	C₂×C₄	—	52	2	no	—
129	C₂×C₄	C₂²×#261	1	1	yes	characteristic
130	C₈	—	13	2	no	—
131	C₈	—	26	2	no	—
132	C₈	C₄⋊#261	1	2	yes	complemented
133	C₂²	—	13	1	no	—
134	C₂²	—	13	1	no	—
135	C₂²	—	13	2	no	—
136	C₂²	—	13	2	no	—
137	C₂²	D₄×#261	1	1	yes	characteristic
138	C₄	—	4	2	no	—
139	C₄	—	13	1	no	—
140	C₄	—	13	1	no	—
141	C₄	—	52	2	no	—
142	C₄	—	52	2	no	—
143	C₄	—	104	2	no	—
144	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
145	C₄	Q₈×#261	1	1	yes	characteristic
146	C₂	—	13	2	no	—
147	C₂	—	13	2	no	—
148	C₂	#11719083	1	1	yes	characteristic
149	C₂	#11719102	1	1	yes	characteristic
150	C₂	#11719110	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88101

C₂

yes

maximal, characteristic

C₂×#88100

C₂

yes

maximal, characteristic

#11719083

C₂

yes

maximal

D₁₃×#107

C₂

yes

maximal, characteristic

#11718246

C₂

yes

maximal

C₂×C₄⋊#261

—

C₂×C₄⋊#261

C₂²

yes

—

C₂×C₄×#261

C₂²

yes

characteristic

C₂×D₁₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₄⋊C₄×D₁₃

C₂²

yes

—

(C₂×#261)⋊C₄

—

#88101

—

#88100

—

C₁₃×#107

C₄

yes

characteristic, complemented

#88058

C₄

yes

characteristic, complemented

#88047

C₄

yes

complemented

C₂²×#261

—

C₂²×#261

D₄

yes

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₂³

yes

—

—

—

—

—

—

D₁₃⋊C₈

—

D₁₃⋊C₈

Q₈

yes

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₄⋊Dic₁₃

C₂×C₄

yes

—

#6101

—

C₂×#1055

C₂×C₄

yes

characteristic

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

#1943

—

maximal, Sylow

C₂²×D₁₃

C₂×D₄

yes

—

—

—

—

—

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

#41

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

C₄×D₁₃

yes

—

C₈×C₁₃

C₄⋊C₄

yes

complemented

#1055

C₄⋊C₄

yes

complemented

C₂×#107

—

C₂×#106

—

C₂×#97

—

#389

—

#340

—

C₂²×C₁₃

C₄×D₄

yes

characteristic

C₂×D₁₃

#121

yes

characteristic

C₂×D₁₃

C₄⋊Q₈

yes

characteristic

C₂×D₁₃

AGL(1,ℤ/8)

yes

—

C₂×D₁₃

#137

yes

—

#261

—

#261

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₄×Q₈

yes

characteristic

Dic₁₃

—

Dic₁₃

C₂²⋊Q₈

yes

characteristic

Dic₁₃

#125

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#106

—

#97

—

#95

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

D₁₃

yes

—

D₁₃

#501

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

C₂×#261

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

C₂×#261

yes

—

110

C₄²

—

111

C₄²

—

112

C₁₃

#1943

yes

characteristic, complemented, Sylow

113

C₂³

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂²×#261

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

C₄⋊#261

yes

complemented

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

D₄×#261

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

104

—

144

C₄

C₂×C₄⋊#261

yes

characteristic

145

C₄

Q₈×#261

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

#11719083

yes

characteristic

149

C₂

#11719102

yes

characteristic

150

C₂

#11719110

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#107	C₄
socle	C₂²×C₁₃	C₄×D₄
prime radical	C₂²×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#107	#261
hypocenter	C₁₃	#1943
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#107

C₄

socle

C₂²×C₁₃

C₄×D₄

prime radical

C₂²×D₁₃

C₂×D₄

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
15. C₁₃×#107	C₄	semidirect
16. #88058	C₄	semidirect
17. #88047	C₄	semidirect
56. C₈×C₁₃	C₄⋊C₄	semidirect
57. #1055	C₄⋊C₄	semidirect
84. #107	#261	semidirect
112. C₁₃	#1943	semidirect
132. C₈	C₄⋊#261	semidirect

H ≅ G/N

type

15. C₁₃×#107

C₄

semidirect

16. #88058

C₄

semidirect

17. #88047

C₄

semidirect

56. C₈×C₁₃

C₄⋊C₄

semidirect

57. #1055

C₄⋊C₄

semidirect

84. #107

#261

semidirect

112. C₁₃

#1943

semidirect

132. C₈

C₄⋊#261

semidirect

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

subgroup	index
C₂×#88101	2
C₂×#88100	2
#11719083	2
D₁₃×#107	2
#11718246	2
#1943	13

subgroup

index

D₁₃×#107

Subgroups — #13130941

Conjugacy classes of subgroups

Complements

Maximal subgroups