Group #23744784 — subgroups

Subgroups — C₁₃×#10624633 #23744784

Order 9477.

344 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 80 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	C₁₃×#6891	C₃	1	1	yes	maximal, characteristic
5	C₁₃×#6860	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	1	no	—
10	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
11	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
12	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
13	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
14	C₃²×C₉×C₁₃	—	3	1	no	—
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	#10624633	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃³×C₁₃	—	3	3	no	—
26	C₃³×C₁₃	—	9	2	no	—
27	C₃³×C₁₃	—	9	1	no	—
28	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
29	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃³×C₁₃	C₃³	1	1	yes	characteristic
32	C₁₃×3₋¹⁺²	—	3	9	no	—
33	C₁₃×3₋¹⁺²	—	3	9	no	—
34	C₁₃×3₋¹⁺²	—	3	9	no	—
35	C₁₃×3₋¹⁺²	—	9	3	no	—
36	C₁₃×3₋¹⁺²	—	9	3	no	—
37	C₁₃×3₋¹⁺²	—	9	3	no	—
38	C₃×C₉×C₁₃	—	3	9	no	—
39	C₃×C₉×C₁₃	—	3	3	no	—
40	C₃×C₉×C₁₃	—	3	3	no	—
41	C₃×C₉×C₁₃	—	3	3	no	—
42	C₃×C₉×C₁₃	—	3	3	no	—
43	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
44	#6891	C₃×C₁₃	1	1	yes	characteristic
45	#6891	C₃×C₁₃	1	1	yes	characteristic
46	#6891	C₃×C₁₃	1	1	yes	characteristic
47	#6860	C₃×C₁₃	1	9	yes	complemented
48	C₃²×C₁₃	—	3	2	no	—
49	C₃²×C₁₃	—	3	1	no	—
50	C₃²×C₁₃	—	3	2	no	—
51	C₃²×C₁₃	—	3	2	no	—
52	C₃²×C₁₃	—	3	2	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	—	9	9	no	—
60	C₃²×C₁₃	AΣL(1,𝔽₂₇)	1	3	yes	—
61	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
62	C₉×C₁₃	—	3	9	no	—
63	C₉×C₁₃	—	9	3	no	—
64	C₉×C₁₃	—	9	3	no	—
65	C₉×C₁₃	—	9	3	no	—
66	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
67	C₃×3₋¹⁺²	—	3	1	no	—
68	C₃×3₋¹⁺²	—	3	1	no	—
69	C₃×3₋¹⁺²	—	3	1	no	—
70	C₃×3₋¹⁺²	—	3	1	no	—
71	C₃×3₋¹⁺²	—	3	9	no	—
72	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
73	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
74	C₃²×C₉	—	3	1	no	—
75	C₃²⋊C₉	—	3	1	no	—
76	C₃²⋊C₉	—	3	1	no	—
77	C₃²⋊C₉	—	3	1	no	—
78	C₃²⋊C₉	—	3	1	no	—
79	C₃²⋊C₉	—	3	1	no	—
80	C₃²⋊C₉	—	3	1	no	—
81	C₃²⋊C₉	—	3	1	no	—
82	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
83	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
84	C₃×C₁₃	—	3	3	no	—
85	C₃×C₁₃	—	9	1	no	—
86	C₃×C₁₃	—	9	1	no	—
87	C₃×C₁₃	—	9	1	no	—
88	C₃×C₁₃	C₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
89	C₃×C₁₃	#6909	1	1	yes	characteristic
90	C₃×C₁₃	#6912	1	2	yes	—
91	C₃³	—	3	3	no	—
92	C₃³	—	9	1	no	—
93	C₃³	—	9	2	no	—
94	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
95	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
96	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
97	C₃³	C₃³×C₁₃	1	1	yes	characteristic
98	3₋¹⁺²	—	3	9	no	—
99	3₋¹⁺²	—	3	9	no	—
100	3₋¹⁺²	—	3	9	no	—
101	3₋¹⁺²	—	9	3	no	—
102	3₋¹⁺²	—	9	3	no	—
103	3₋¹⁺²	—	9	3	no	—
104	C₃×C₉	—	3	9	no	—
105	C₃×C₉	—	3	3	no	—
106	C₃×C₉	—	3	3	no	—
107	C₃×C₉	—	3	3	no	—
108	C₃×C₉	—	3	3	no	—
109	C₁₃	#10624633	1	1	yes	characteristic, direct product factor, Sylow
110	C₃²	—	3	1	no	—
111	C₃²	—	3	2	no	—
112	C₃²	—	3	1	no	—
113	C₃²	—	3	1	no	—
114	C₃²	—	3	1	no	—
115	C₃²	—	3	1	no	—
116	C₃²	—	3	1	no	—
117	C₃²	—	3	1	no	—
118	C₃²	—	3	2	no	—
119	C₃²	—	3	2	no	—
120	C₃²	—	3	2	no	—
121	C₃²	—	9	9	no	—
122	C₃²	C₁₃×AΣL(1,𝔽₂₇)	1	3	yes	—
123	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
124	C₉	—	3	9	no	—
125	C₉	—	9	3	no	—
126	C₉	—	9	3	no	—
127	C₉	—	9	3	no	—
128	C₃	—	3	3	no	—
129	C₃	—	9	1	no	—
130	C₃	—	9	1	no	—
131	C₃	—	9	1	no	—
132	C₃	C₃×C₁₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
133	C₃	C₁₃×#6909	1	1	yes	characteristic
134	C₃	C₁₃×#6912	1	2	yes	—

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

C₁₃×#6891

C₃

yes

maximal, characteristic

C₁₃×#6860

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

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₃

—

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

—

#10624633

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

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

—

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

#6891

C₃×C₁₃

yes

characteristic

#6860

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

AΣL(1,𝔽₂₇)

yes

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

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

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃²×C₉

—

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

C₃×AΣL(1,𝔽₂₇)

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

100

3₋¹⁺²

—

101

3₋¹⁺²

—

102

3₋¹⁺²

—

103

3₋¹⁺²

—

104

C₃×C₉

—

105

C₃×C₉

—

106

C₃×C₉

—

107

C₃×C₉

—

108

C₃×C₉

—

109

C₁₃

#10624633

yes

characteristic, direct product factor, Sylow

110

C₃²

—

111

C₃²

—

112

C₃²

—

113

C₃²

—

114

C₃²

—

115

C₃²

—

116

C₃²

—

117

C₃²

—

118

C₃²

—

119

C₃²

—

120

C₃²

—

121

C₃²

—

122

C₃²

C₁₃×AΣL(1,𝔽₂₇)

yes

—

123

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

124

C₉

—

125

C₉

—

126

C₉

—

127

C₉

—

128

C₃

—

129

C₃

—

130

C₃

—

131

C₃

—

132

C₃

C₃×C₁₃×AΣL(1,𝔽₂₇)

yes

characteristic

133

C₃

C₁₃×#6909

yes

characteristic

134

C₃

C₁₃×#6912

yes

—

	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 ▷ C₃² ▷ 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 ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

N	H ≅ G/N	type
5. C₁₃×#6860	C₃	semidirect
24. #10624633	C₁₃	direct (N × H)
47. #6860	C₃×C₁₃	semidirect
109. C₁₃	#10624633	direct (N × H)

H ≅ G/N

type

5. C₁₃×#6860

C₃

semidirect

24. #10624633

C₁₃

direct (N × H)

47. #6860

C₃×C₁₃

semidirect

109. C₁₃

#10624633

direct (N × H)

Subgroups — C₁₃×#10624633 #23744784

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624633 #23744784

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624633 #23744784