Group #13120806 — subgroups

Subgroups — #13120806

Order 1664.

436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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×#95	C₂	1	1	yes	maximal, characteristic
2	#11718873	C₂	1	2	yes	maximal
3	#11718871	C₂	1	4	yes	maximal
4	#11718321	C₂	1	4	yes	maximal, complemented
5	#11718318	C₂	1	4	yes	maximal, complemented
6	C₂³×C₄×C₁₃	C₂²	1	2	yes	—
7	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊Dic₁₃	C₂²	1	4	yes	—
9	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×#6101	C₂²	1	4	yes	—
12	C₂×#6101	C₂²	1	4	yes	—
13	C₁₃×#95	C₂²	1	4	yes	—
14	#88071	C₂²	1	4	yes	—
15	#88071	C₂²	1	4	yes	—
16	#88071	C₂²	1	4	yes	—
17	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₃	—	2	4	no	—
19	C₂²×C₄×C₁₃	—	4	2	no	—
20	C₂²×C₄×C₁₃	—	4	2	no	—
21	C₂²×C₄×C₁₃	—	4	2	no	—
22	C₂²×C₄×C₁₃	Q₈	1	4	yes	—
23	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
24	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
25	C₂²×Dic₁₃	C₂³	1	4	yes	—
26	C₂²×Dic₁₃	C₂³	1	4	yes	—
27	C₂²⋊Dic₁₃	—	2	8	no	—
28	C₄⋊Dic₁₃	—	4	2	no	—
29	C₄⋊Dic₁₃	—	4	2	no	—
30	#6101	—	4	4	no	—
31	#6101	—	4	4	no	—
32	#2646	—	13	1	no	maximal, Sylow
33	C₂³×C₁₃	—	2	1	no	—
34	C₂³×C₁₃	—	2	2	no	—
35	C₂³×C₁₃	—	2	1	no	—
36	C₂³×C₁₃	C₂×Q₈	1	2	yes	—
37	C₂³×C₁₃	#41	1	4	yes	—
38	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₁₃	—	2	2	no	—
40	C₂×C₄×C₁₃	—	2	2	no	—
41	C₂×C₄×C₁₃	—	2	4	no	—
42	C₂×C₄×C₁₃	—	2	4	no	—
43	C₂×C₄×C₁₃	—	2	4	no	—
44	C₂×C₄×C₁₃	—	4	4	no	—
45	C₂×C₄×C₁₃	—	4	8	no	—
46	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
47	C₂×Dic₁₃	—	2	4	no	—
48	C₂×Dic₁₃	—	2	4	no	—
49	C₂×Dic₁₃	—	2	4	no	—
50	C₂×Dic₁₃	—	2	4	no	—
51	C₂×Dic₁₃	—	2	4	no	—
52	C₂×Dic₁₃	—	2	4	no	—
53	#400	—	13	4	no	—
54	#398	—	13	4	no	—
55	#385	—	13	4	no	—
56	#380	—	13	2	no	—
57	C₂×#95	D₁₃	1	1	yes	characteristic
58	C₂²×C₁₃	—	2	4	no	—
59	C₂²×C₁₃	—	2	4	no	—
60	C₂²×C₁₃	—	2	2	no	—
61	C₂²×C₁₃	—	2	2	no	—
62	C₂²×C₁₃	#125	1	4	yes	—
63	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
64	C₂²×C₁₃	C₂×#41	1	2	yes	—
65	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
66	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
67	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
68	C₄×C₁₃	—	2	4	no	—
69	C₄×C₁₃	—	4	4	no	—
70	Dic₁₃	—	4	4	no	—
71	Dic₁₃	—	4	4	no	—
72	C₂³×C₄	C₂×D₁₃	1	2	yes	—
73	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
74	C₂×C₄⋊C₄	—	13	4	no	—
75	C₂×C₄⋊C₄	—	13	4	no	—
76	C₂×C₄⋊C₄	—	13	2	no	—
77	C₂×C₄⋊C₄	—	13	2	no	—
78	C₂×C₂²⋊C₄	—	13	4	no	—
79	#95	—	13	4	no	—
80	#95	—	13	4	no	—
81	#95	—	13	4	no	—
82	#95	C₂×D₁₃	1	4	yes	—
83	C₂×C₁₃	—	2	4	no	—
84	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
85	C₂×C₁₃	#538	1	2	yes	—
86	C₂×C₁₃	#539	1	2	yes	—
87	C₂×C₁₃	#543	1	1	yes	characteristic
88	C₂×C₁₃	#544	1	1	yes	characteristic
89	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
90	C₂²×C₄	—	2	4	no	—
91	C₂²×C₄	—	4	2	no	—
92	C₂²×C₄	—	4	2	no	—
93	C₂²×C₄	—	4	2	no	—
94	C₂²×C₄	—	13	4	no	—
95	C₂²×C₄	—	13	4	no	—
96	C₂²×C₄	Dic₂₆	1	4	yes	—
97	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
98	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
99	C₄⋊C₄	—	52	4	no	—
100	C₄⋊C₄	—	52	4	no	—
101	C₄⋊C₄	—	52	2	no	—
102	C₄⋊C₄	—	52	2	no	—
103	C₂²⋊C₄	—	26	8	no	—
104	C₁₃	#2646	1	1	yes	characteristic, complemented, Sylow
105	C₂³	—	2	2	no	—
106	C₂³	—	2	1	no	—
107	C₂³	—	2	1	no	—
108	C₂³	C₂×Dic₂₆	1	2	yes	—
109	C₂³	#6127	1	4	yes	—
110	C₂³	C₂³×D₁₃	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	4	8	no	—
118	C₂×C₄	—	26	4	no	—
119	C₂×C₄	—	26	4	no	—
120	C₂×C₄	—	26	4	no	—
121	C₂×C₄	—	26	4	no	—
122	C₂×C₄	—	26	4	no	—
123	C₂×C₄	—	26	4	no	—
124	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	4	no	—
127	C₂²	—	2	2	no	—
128	C₂²	—	2	4	no	—
129	C₂²	#88124	1	4	yes	—
130	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
131	C₂²	C₂×#6127	1	2	yes	—
132	C₂²	#88251	1	2	yes	—
133	C₂²	#88251	1	1	yes	characteristic
134	C₂²	#88254	1	1	yes	characteristic
135	C₄	—	2	4	no	—
136	C₄	—	4	4	no	—
137	C₄	—	52	4	no	—
138	C₄	—	52	4	no	—
139	C₂	—	2	4	no	—
140	C₂	C₂×#88124	1	1	yes	characteristic
141	C₂	#11719188	1	1	yes	characteristic
142	C₂	#11719199	1	2	yes	—
143	C₂	#11719205	1	1	yes	characteristic
144	C₂	#11719220	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#95

C₂

yes

maximal, characteristic

#11718873

C₂

yes

maximal

#11718871

C₂

yes

maximal

#11718321

C₂

yes

maximal, complemented

#11718318

C₂

yes

maximal, complemented

C₂³×C₄×C₁₃

C₂²

yes

—

C₂³×C₄×C₁₃

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₁₃×#95

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂⁴×C₁₃

C₂³

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

Q₈

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×Q₈

yes

—

C₂³×C₁₃

#41

yes

—

C₂³×C₁₃

C₂⁴

yes

characteristic

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×Q₈

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

—

—

—

—

C₂×#95

D₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#125

yes

—

C₂²×C₁₃

C₂²×Q₈

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

—

C₂²×C₁₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₃

H(5,𝔽₂)

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂³×C₄

C₂×D₁₃

yes

—

C₂³×C₄

C₂×D₁₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

C₂×D₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

C₂×#125

yes

characteristic

C₂×C₁₃

#538

yes

—

C₂×C₁₃

#539

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂⁴

C₂²×D₁₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₂₆

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₁₃

#2646

yes

characteristic, complemented, Sylow

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂×Dic₂₆

yes

—

109

C₂³

#6127

yes

—

110

C₂³

C₂³×D₁₃

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

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

C₂×Dic₂₆

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#88124

yes

—

130

C₂²

C₂²×Dic₂₆

yes

characteristic

131

C₂²

C₂×#6127

yes

—

132

C₂²

#88251

yes

—

133

C₂²

#88251

yes

characteristic

134

C₂²

#88254

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₂

—

140

C₂

C₂×#88124

yes

characteristic

141

C₂

#11719188

yes

characteristic

142

C₂

#11719199

yes

—

143

C₂

#11719205

yes

characteristic

144

C₂

#11719220

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₂×C₁₃×#95	C₂
prime radical	C₂⁴×C₁₃	C₂³
hypercenter	C₂×#95	D₁₃
hypocenter	C₁₃	#2646
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#95

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₂×C₁₃×#95

C₂

prime radical

C₂⁴×C₁₃

C₂³

hypercenter

C₂×#95

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ C₂×#95

N	H ≅ G/N	type
4. #11718321	C₂	semidirect
5. #11718318	C₂	semidirect
104. C₁₃	#2646	semidirect

H ≅ G/N

type

4. #11718321

C₂

semidirect

5. #11718318

C₂

semidirect

104. C₁₃

#2646

semidirect

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

subgroup	index
C₂×C₁₃×#95	2
#11718873	2
#11718871	2
#11718321	2
#11718318	2
#2646	13

subgroup

index

C₂×C₁₃×#95

Subgroups — #13120806

Conjugacy classes of subgroups

Complements

Maximal subgroups