Group #13120815 — subgroups

Subgroups — #13120815

Order 1664.

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

normal subgroups only

This group has 360 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	C₁₃×#382	C₂	1	1	yes	maximal, characteristic
2	#11718646	C₂	1	2	yes	maximal
3	#11718634	C₂	1	2	yes	maximal
4	#11718596	C₂	1	1	yes	maximal, characteristic
5	#11718593	C₂	1	1	yes	maximal, characteristic
6	#11718322	C₂	1	4	yes	maximal
7	#11718321	C₂	1	4	yes	maximal
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
12	C₂×C₄⋊Dic₁₃	C₂²	1	4	yes	—
13	C₂×#6101	C₂²	1	4	yes	—
14	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#95	C₂²	1	4	yes	—
17	#88071	C₂²	1	2	yes	—
18	#88071	C₂²	1	4	yes	—
19	#88071	C₂²	1	4	yes	—
20	#88071	C₂²	1	2	yes	—
21	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
22	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₃	C₂³	1	2	yes	—
26	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₃	C₂³	1	4	yes	—
28	C₁₃×C₄⋊C₄	—	2	4	no	—
29	C₄²×C₁₃	Q₈	1	4	yes	—
30	C₄⋊Dic₁₃	—	2	4	no	—
31	C₄⋊Dic₁₃	—	4	4	no	—
32	C₄⋊Dic₁₃	—	4	4	no	—
33	#6101	—	4	4	no	—
34	C₄×Dic₁₃	—	2	2	no	—
35	C₄×Dic₁₃	—	2	2	no	—
36	#2647	—	13	1	no	maximal, Sylow
37	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
38	C₂×C₄×C₁₃	—	2	2	no	—
39	C₂×C₄×C₁₃	—	2	2	no	—
40	C₂×C₄×C₁₃	—	2	4	no	—
41	C₂×C₄×C₁₃	—	2	4	no	—
42	C₂×C₄×C₁₃	—	2	4	no	—
43	C₂×C₄×C₁₃	C₂×Q₈	1	4	yes	—
44	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₁₃	#41	1	2	yes	—
46	C₂×C₄×C₁₃	#41	1	2	yes	—
47	C₂×Dic₁₃	—	2	1	no	—
48	C₂×Dic₁₃	—	2	1	no	—
49	C₂×Dic₁₃	—	2	2	no	—
50	C₂×Dic₁₃	—	2	4	no	—
51	C₂×Dic₁₃	—	2	2	no	—
52	C₂×Dic₁₃	—	2	4	no	—
53	C₂×Dic₁₃	—	2	2	no	—
54	C₂×Dic₁₃	—	2	4	no	—
55	C₂×Dic₁₃	—	2	2	no	—
56	C₂×Dic₁₃	—	2	2	no	—
57	#400	—	13	4	no	—
58	#398	—	13	4	no	—
59	#389	—	13	2	no	—
60	#389	—	13	2	no	—
61	#384	—	13	1	no	—
62	#382	D₁₃	1	1	yes	characteristic
63	#376	—	13	1	no	—
64	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
65	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
66	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
67	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
68	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
69	C₄×C₁₃	—	2	4	no	—
70	C₄×C₁₃	—	4	4	no	—
71	C₄×C₁₃	#125	1	4	yes	—
72	Dic₁₃	—	4	1	no	—
73	Dic₁₃	—	4	4	no	—
74	Dic₁₃	—	4	1	no	—
75	Dic₁₃	—	4	2	no	—
76	C₂×C₄⋊C₄	—	13	2	no	—
77	C₂×C₄⋊C₄	—	13	4	no	—
78	C₂×C₄⋊C₄	—	13	4	no	—
79	C₂×C₄⋊C₄	—	13	4	no	—
80	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
81	C₂×C₄²	—	13	1	no	—
82	C₂×C₄²	—	13	1	no	—
83	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
84	#95	—	13	2	no	—
85	#95	—	13	2	no	—
86	#95	—	13	4	no	—
87	#95	—	13	4	no	—
88	#95	C₂×D₁₃	1	4	yes	—
89	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
90	C₂×C₁₃	#540	1	1	yes	characteristic
91	C₂×C₁₃	#541	1	1	yes	characteristic
92	C₂×C₁₃	#542	1	2	yes	—
93	C₂×C₁₃	#544	1	2	yes	—
94	C₂²×C₄	—	13	1	no	—
95	C₂²×C₄	—	13	2	no	—
96	C₂²×C₄	—	13	1	no	—
97	C₂²×C₄	—	13	4	no	—
98	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
99	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
100	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
101	C₄⋊C₄	—	2	4	no	—
102	C₄⋊C₄	—	26	4	no	—
103	C₄⋊C₄	—	52	4	no	—
104	C₄⋊C₄	—	52	4	no	—
105	C₄⋊C₄	—	52	4	no	—
106	C₄²	—	26	2	no	—
107	C₄²	—	26	2	no	—
108	C₄²	Dic₂₆	1	4	yes	—
109	C₁₃	#2647	1	1	yes	characteristic, complemented, Sylow
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	—	26	2	no	—
117	C₂×C₄	—	26	1	no	—
118	C₂×C₄	—	26	1	no	—
119	C₂×C₄	—	26	4	no	—
120	C₂×C₄	—	26	2	no	—
121	C₂×C₄	—	26	4	no	—
122	C₂×C₄	—	26	2	no	—
123	C₂×C₄	—	26	4	no	—
124	C₂×C₄	—	26	2	no	—
125	C₂×C₄	—	26	2	no	—
126	C₂×C₄	C₂×Dic₂₆	1	4	yes	—
127	C₂×C₄	C₂×Dic₂₆	1	2	yes	—
128	C₂×C₄	#6129	1	2	yes	—
129	C₂×C₄	#6131	1	2	yes	—
130	C₂²	C₂²×Dic₂₆	1	1	yes	characteristic
131	C₂²	C₂×#6129	1	1	yes	characteristic
132	C₂²	C₂×#6131	1	1	yes	characteristic
133	C₂²	#88256	1	2	yes	—
134	C₂²	#88257	1	2	yes	—
135	C₄	—	2	4	no	—
136	C₄	—	4	4	no	—
137	C₄	—	52	2	no	—
138	C₄	—	52	1	no	—
139	C₄	—	52	1	no	—
140	C₄	—	52	4	no	—
141	C₄	#88144	1	4	yes	—
142	C₂	C₂×#88144	1	1	yes	characteristic
143	C₂	#11719224	1	2	yes	—
144	C₂	#11719387	1	2	yes	—
145	C₂	#11719402	1	1	yes	characteristic
146	C₂	#11719403	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#382

C₂

yes

maximal, characteristic

#11718646

C₂

yes

maximal

#11718634

C₂

yes

maximal

#11718596

C₂

yes

maximal, characteristic

#11718593

C₂

yes

maximal, characteristic

#11718322

C₂

yes

maximal

#11718321

C₂

yes

maximal

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6101

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₁₃×#95

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

#88071

C₂²

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

Q₈

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

#2647

—

maximal, Sylow

C₂³×C₁₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic

#376

—

C₂²×C₁₃

C₂²×Q₈

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

characteristic

C₂²×C₁₃

C₂×#41

yes

characteristic

C₂²×C₁₃

H(5,𝔽₂)

yes

—

C₂²×C₁₃

2₋¹⁺⁴

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#125

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

—

—

—

—

C₂×D₁₃

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

C₂×C₁₃

#544

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

—

C₂²×C₄

C₂²×D₁₃

yes

—

100

C₂²×C₄

C₂²×D₁₃

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

Dic₂₆

yes

—

109

C₁₃

#2647

yes

characteristic, complemented, Sylow

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

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₂₆

yes

—

127

C₂×C₄

C₂×Dic₂₆

yes

—

128

C₂×C₄

#6129

yes

—

129

C₂×C₄

#6131

yes

—

130

C₂²

C₂²×Dic₂₆

yes

characteristic

131

C₂²

C₂×#6129

yes

characteristic

132

C₂²

C₂×#6131

yes

characteristic

133

C₂²

#88256

yes

—

134

C₂²

#88257

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

#88144

yes

—

142

C₂

C₂×#88144

yes

characteristic

143

C₂

#11719224

yes

—

144

C₂

#11719387

yes

—

145

C₂

#11719402

yes

characteristic

146

C₂

#11719403

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃
commutator, socle, prime radical, cosocle	C₂³×C₁₃	C₂⁴
Fitting	C₁₃×#382	C₂
hypercenter	#382	D₁₃
hypocenter	C₁₃	#2647
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃

commutator, socle, prime radical, cosocle

C₂³×C₁₃

C₂⁴

Fitting

C₁₃×#382

C₂

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
109. C₁₃	#2647	semidirect

H ≅ G/N

type

109. C₁₃

#2647

semidirect

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

subgroup	index
C₁₃×#382	2
#11718646	2
#11718634	2
#11718596	2
#11718593	2
#11718322	2
#11718321	2
#2647	13

subgroup

index

C₁₃×#382

Subgroups — #13120815

Conjugacy classes of subgroups

Complements

Maximal subgroups