Group #23744933 — subgroups

Subgroups — C₁₃×#10624782 #23744933

Order 9477.

368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 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	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6891	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6891	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₁₃×3₋¹⁺²⋊C₉	C₃	1	9	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
9	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
10	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
11	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
12	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
13	C₃²×C₉×C₁₃	—	3	1	no	—
14	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
15	C₁₃×C₃²⋊C₉	—	3	1	no	—
16	C₁₃×C₃²⋊C₉	—	3	1	no	—
17	C₁₃×C₃²⋊C₉	—	3	1	no	—
18	C₁₃×C₃²⋊C₉	—	3	1	no	—
19	C₁₃×C₃²⋊C₉	—	3	1	no	—
20	C₁₃×C₃²⋊C₉	—	3	1	no	—
21	C₁₃×C₃²⋊C₉	—	3	1	no	—
22	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
23	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
24	#10624782	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃³×C₁₃	—	3	3	no	—
26	C₃³×C₁₃	—	3	3	no	—
27	C₃³×C₁₃	—	9	1	no	—
28	C₃³×C₁₃	—	9	1	no	—
29	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
32	C₃³×C₁₃	C₃³	1	1	yes	characteristic
33	C₁₃×3₋¹⁺²	—	3	9	no	—
34	C₁₃×3₋¹⁺²	—	3	9	no	—
35	C₁₃×3₋¹⁺²	—	3	6	no	—
36	C₁₃×3₋¹⁺²	—	9	3	no	—
37	C₁₃×3₋¹⁺²	—	9	3	no	—
38	C₁₃×3₋¹⁺²	3₋¹⁺²	1	9	yes	complemented
39	C₃×C₉×C₁₃	—	3	9	no	—
40	C₃×C₉×C₁₃	—	3	3	no	—
41	C₃×C₉×C₁₃	—	3	3	no	—
42	C₃×C₉×C₁₃	—	3	3	no	—
43	C₃×C₉×C₁₃	—	3	3	no	—
44	C₃×C₉×C₁₃	—	9	3	no	—
45	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
46	#6891	C₃×C₁₃	1	1	yes	characteristic
47	#6891	C₃×C₁₃	1	1	yes	characteristic
48	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
49	3₋¹⁺²⋊C₉	C₃×C₁₃	1	9	yes	complemented
50	C₃²×C₁₃	—	3	1	no	—
51	C₃²×C₁₃	—	3	1	no	—
52	C₃²×C₁₃	—	3	1	no	—
53	C₃²×C₁₃	—	3	1	no	—
54	C₃²×C₁₃	—	3	1	no	—
55	C₃²×C₁₃	—	3	1	no	—
56	C₃²×C₁₃	—	3	1	no	—
57	C₃²×C₁₃	—	3	1	no	—
58	C₃²×C₁₃	—	3	1	no	—
59	C₃²×C₁₃	—	3	1	no	—
60	C₃²×C₁₃	—	3	1	no	—
61	C₃²×C₁₃	—	3	1	no	—
62	C₃²×C₁₃	—	3	1	no	—
63	C₃²×C₁₃	—	3	1	no	—
64	C₃²×C₁₃	—	9	9	no	—
65	C₃²×C₁₃	#733	1	3	yes	—
66	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
67	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
68	C₉×C₁₃	—	3	9	no	—
69	C₉×C₁₃	—	9	3	no	—
70	C₉×C₁₃	—	9	3	no	—
71	C₉×C₁₃	—	9	3	no	—
72	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
73	C₃×3₋¹⁺²	—	3	1	no	—
74	C₃×3₋¹⁺²	—	3	1	no	—
75	C₃×3₋¹⁺²	—	3	9	no	—
76	C₃×3₋¹⁺²	—	3	1	no	—
77	C₃×3₋¹⁺²	—	3	1	no	—
78	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
79	C₃²×C₉	—	3	1	no	—
80	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
81	C₃²⋊C₉	—	3	1	no	—
82	C₃²⋊C₉	—	3	1	no	—
83	C₃²⋊C₉	—	3	1	no	—
84	C₃²⋊C₉	—	3	1	no	—
85	C₃²⋊C₉	—	3	1	no	—
86	C₃²⋊C₉	—	3	1	no	—
87	C₃²⋊C₉	—	3	1	no	—
88	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
89	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
90	C₃×C₁₃	—	3	3	no	—
91	C₃×C₁₃	—	3	3	no	—
92	C₃×C₁₃	—	9	1	no	—
93	C₃×C₁₃	—	9	1	no	—
94	C₃×C₁₃	#6891	1	1	yes	characteristic
95	C₃×C₁₃	C₃×#733	1	1	yes	characteristic
96	C₃×C₁₃	#6909	1	1	yes	characteristic
97	C₃×C₁₃	#6910	1	1	yes	characteristic
98	C₃³	—	3	3	no	—
99	C₃³	—	3	3	no	—
100	C₃³	—	9	1	no	—
101	C₃³	—	9	1	no	—
102	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
103	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
104	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
105	C₃³	C₃³×C₁₃	1	1	yes	characteristic
106	3₋¹⁺²	—	3	9	no	—
107	3₋¹⁺²	—	3	9	no	—
108	3₋¹⁺²	—	3	6	no	—
109	3₋¹⁺²	—	9	3	no	—
110	3₋¹⁺²	—	9	3	no	—
111	3₋¹⁺²	C₁₃×3₋¹⁺²	1	9	yes	complemented
112	C₃×C₉	—	3	9	no	—
113	C₃×C₉	—	3	3	no	—
114	C₃×C₉	—	3	3	no	—
115	C₃×C₉	—	3	3	no	—
116	C₃×C₉	—	3	3	no	—
117	C₃×C₉	—	9	3	no	—
118	C₁₃	#10624782	1	1	yes	characteristic, direct product factor, Sylow
119	C₃²	—	3	1	no	—
120	C₃²	—	3	1	no	—
121	C₃²	—	3	1	no	—
122	C₃²	—	3	1	no	—
123	C₃²	—	3	1	no	—
124	C₃²	—	3	1	no	—
125	C₃²	—	3	1	no	—
126	C₃²	—	3	1	no	—
127	C₃²	—	3	1	no	—
128	C₃²	—	3	1	no	—
129	C₃²	—	3	1	no	—
130	C₃²	—	3	1	no	—
131	C₃²	—	3	1	no	—
132	C₃²	—	3	1	no	—
133	C₃²	—	9	9	no	—
134	C₃²	C₁₃×#733	1	3	yes	—
135	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
136	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
137	C₉	—	3	9	no	—
138	C₉	—	9	3	no	—
139	C₉	—	9	3	no	—
140	C₉	—	9	3	no	—
141	C₃	—	3	3	no	—
142	C₃	—	3	3	no	—
143	C₃	—	9	1	no	—
144	C₃	—	9	1	no	—
145	C₃	C₁₃×#6891	1	1	yes	characteristic
146	C₃	C₃×C₁₃×#733	1	1	yes	characteristic
147	C₃	C₁₃×#6909	1	1	yes	characteristic
148	C₃	C₁₃×#6910	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₁₃×#6891

C₃

yes

maximal, characteristic

C₁₃×#6891

C₃

yes

maximal, characteristic

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₁₃×3₋¹⁺²⋊C₉

C₃

yes

maximal, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

#10624782

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

yes

C₃³×C₁₃

yes

C₃³×C₁₃

yes

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

3₋¹⁺²

yes

complemented

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

#6891

C₃×C₁₃

yes

characteristic

#6891

C₃×C₁₃

yes

characteristic

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic

3₋¹⁺²⋊C₉

C₃×C₁₃

yes

complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

#733

yes

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃³

—

C₃³

—

100

C₃³

—

101

C₃³

—

102

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

103

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

104

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

105

C₃³

C₃³×C₁₃

yes

characteristic

106

3₋¹⁺²

—

107

3₋¹⁺²

—

108

3₋¹⁺²

—

109

3₋¹⁺²

—

110

3₋¹⁺²

—

111

3₋¹⁺²

C₁₃×3₋¹⁺²

yes

complemented

112

C₃×C₉

—

113

C₃×C₉

—

114

C₃×C₉

—

115

C₃×C₉

—

116

C₃×C₉

—

117

C₃×C₉

—

118

C₁₃

#10624782

yes

characteristic, direct product factor, Sylow

119

C₃²

—

120

C₃²

—

121

C₃²

—

122

C₃²

—

123

C₃²

—

124

C₃²

—

125

C₃²

—

126

C₃²

—

127

C₃²

—

128

C₃²

—

129

C₃²

—

130

C₃²

—

131

C₃²

—

132

C₃²

—

133

C₃²

—

134

C₃²

C₁₃×#733

yes

—

135

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

136

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

137

C₉

—

138

C₉

—

139

C₉

—

140

C₉

—

141

C₃

—

142

C₃

—

143

C₃

—

144

C₃

—

145

C₃

C₁₃×#6891

yes

characteristic

146

C₃

C₃×C₁₃×#733

yes

characteristic

147

C₃

C₁₃×#6909

yes

characteristic

148

C₃

C₁₃×#6910

yes

characteristic

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃²×C₁₃

C₃×H(3,𝔽₃)

commutator, Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

N	H ≅ G/N	type
5. C₁₃×3₋¹⁺²⋊C₉	C₃	semidirect
24. #10624782	C₁₃	direct (N × H)
38. C₁₃×3₋¹⁺²	3₋¹⁺²	semidirect
49. 3₋¹⁺²⋊C₉	C₃×C₁₃	semidirect
111. 3₋¹⁺²	C₁₃×3₋¹⁺²	semidirect
118. C₁₃	#10624782	direct (N × H)

H ≅ G/N

type

5. C₁₃×3₋¹⁺²⋊C₉

C₃

semidirect

24. #10624782

C₁₃

direct (N × H)

38. C₁₃×3₋¹⁺²

3₋¹⁺²

semidirect

49. 3₋¹⁺²⋊C₉

C₃×C₁₃

semidirect

111. 3₋¹⁺²

C₁₃×3₋¹⁺²

semidirect

118. C₁₃

#10624782

direct (N × H)

Subgroups — C₁₃×#10624782 #23744933

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624782 #23744933

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624782 #23744933