Group #23744751 — subgroups

Subgroups — C₁₃×#10624600 #23744751

Order 9477.

260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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×#6891	C₃	1	2	yes	maximal
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#6861	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
7	C₃²×C₉×C₁₃	—	3	1	no	—
8	C₃²×C₉×C₁₃	—	3	1	no	—
9	C₁₃×C₃²⋊C₉	—	3	1	no	—
10	C₁₃×C₃²⋊C₉	—	3	1	no	—
11	C₁₃×C₃²⋊C₉	—	3	1	no	—
12	C₁₃×C₃²⋊C₉	—	3	1	no	—
13	C₁₃×C₃²⋊C₉	—	3	2	no	—
14	C₁₃×C₃²⋊C₉	—	3	2	no	—
15	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
16	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
17	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
18	#10624600	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃³×C₁₃	—	3	3	no	—
20	C₃³×C₁₃	—	3	3	no	—
21	C₃³×C₁₃	—	9	1	no	—
22	C₃³×C₁₃	—	9	1	no	—
23	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃³×C₁₃	C₃³	1	1	yes	characteristic
27	C₁₃×3₋¹⁺²	—	9	6	no	—
28	C₃×C₉×C₁₃	—	3	3	no	—
29	C₃×C₉×C₁₃	—	3	3	no	—
30	C₃×C₉×C₁₃	—	3	6	no	—
31	C₃×C₉×C₁₃	—	9	3	no	—
32	C₃×C₉×C₁₃	—	9	3	no	—
33	#6891	C₃×C₁₃	1	2	yes	—
34	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
35	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
36	#6861	C₃×C₁₃	1	9	yes	complemented
37	C₃²×C₁₃	—	3	1	no	—
38	C₃²×C₁₃	—	3	1	no	—
39	C₃²×C₁₃	—	3	1	no	—
40	C₃²×C₁₃	—	3	1	no	—
41	C₃²×C₁₃	—	3	1	no	—
42	C₃²×C₁₃	—	3	1	no	—
43	C₃²×C₁₃	—	3	1	no	—
44	C₃²×C₁₃	—	3	1	no	—
45	C₃²×C₁₃	—	3	1	no	—
46	C₃²×C₁₃	—	3	1	no	—
47	C₃²×C₁₃	—	3	1	no	—
48	C₃²×C₁₃	—	3	1	no	—
49	C₃²×C₁₃	—	3	1	no	—
50	C₃²×C₁₃	—	3	1	no	—
51	C₃²×C₁₃	—	9	9	no	—
52	C₃²×C₁₃	#732	1	3	yes	—
53	C₃²×C₁₃	#733	1	3	yes	—
54	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
55	C₉×C₁₃	—	9	3	no	—
56	C₉×C₁₃	—	9	6	no	—
57	C₉×C₁₃	—	9	3	no	—
58	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
59	C₃×3₋¹⁺²	—	3	2	no	—
60	C₃²×C₉	—	3	1	no	—
61	C₃²×C₉	—	3	1	no	—
62	C₃²⋊C₉	—	3	1	no	—
63	C₃²⋊C₉	—	3	1	no	—
64	C₃²⋊C₉	—	3	1	no	—
65	C₃²⋊C₉	—	3	1	no	—
66	C₃²⋊C₉	—	3	2	no	—
67	C₃²⋊C₉	—	3	2	no	—
68	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
69	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
70	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
71	C₃×C₁₃	—	3	3	no	—
72	C₃×C₁₃	—	3	3	no	—
73	C₃×C₁₃	—	9	1	no	—
74	C₃×C₁₃	—	9	1	no	—
75	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
76	C₃×C₁₃	C₃×#733	1	1	yes	characteristic
77	C₃×C₁₃	#6910	1	1	yes	characteristic
78	C₃×C₁₃	#6912	1	1	yes	characteristic
79	C₃³	—	3	3	no	—
80	C₃³	—	3	3	no	—
81	C₃³	—	9	1	no	—
82	C₃³	—	9	1	no	—
83	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
84	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
85	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
86	C₃³	C₃³×C₁₃	1	1	yes	characteristic
87	3₋¹⁺²	—	9	6	no	—
88	C₃×C₉	—	3	3	no	—
89	C₃×C₉	—	3	3	no	—
90	C₃×C₉	—	3	6	no	—
91	C₃×C₉	—	9	3	no	—
92	C₃×C₉	—	9	3	no	—
93	C₁₃	#10624600	1	1	yes	characteristic, direct product factor, Sylow
94	C₃²	—	3	1	no	—
95	C₃²	—	3	1	no	—
96	C₃²	—	3	1	no	—
97	C₃²	—	3	1	no	—
98	C₃²	—	3	1	no	—
99	C₃²	—	3	1	no	—
100	C₃²	—	3	1	no	—
101	C₃²	—	3	1	no	—
102	C₃²	—	3	1	no	—
103	C₃²	—	3	1	no	—
104	C₃²	—	3	1	no	—
105	C₃²	—	3	1	no	—
106	C₃²	—	3	1	no	—
107	C₃²	—	3	1	no	—
108	C₃²	—	9	9	no	—
109	C₃²	C₁₃×#732	1	3	yes	—
110	C₃²	C₁₃×#733	1	3	yes	—
111	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
112	C₉	—	9	3	no	—
113	C₉	—	9	6	no	—
114	C₉	—	9	3	no	—
115	C₃	—	3	3	no	—
116	C₃	—	3	3	no	—
117	C₃	—	9	1	no	—
118	C₃	—	9	1	no	—
119	C₃	C₃×C₁₃×#732	1	1	yes	characteristic
120	C₃	C₃×C₁₃×#733	1	1	yes	characteristic
121	C₃	C₁₃×#6910	1	1	yes	characteristic
122	C₃	C₁₃×#6912	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6891

C₃

yes

maximal

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₁₃×#6861

C₃

yes

maximal, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

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

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

#10624600

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

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

#6891

C₃×C₁₃

yes

—

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic

#6861

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

#732

yes

—

C₃²×C₁₃

#733

yes

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

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

—

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

—

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

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₁₃

#10624600

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

100

C₃²

—

101

C₃²

—

102

C₃²

—

103

C₃²

—

104

C₃²

—

105

C₃²

—

106

C₃²

—

107

C₃²

—

108

C₃²

—

109

C₃²

C₁₃×#732

yes

—

110

C₃²

C₁₃×#733

yes

—

111

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

112

C₉

—

113

C₉

—

114

C₉

—

115

C₃

—

116

C₃

—

117

C₃

—

118

C₃

—

119

C₃

C₃×C₁₃×#732

yes

characteristic

120

C₃

C₃×C₁₃×#733

yes

characteristic

121

C₃

C₁₃×#6910

yes

characteristic

122

C₃

C₁₃×#6912

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 ▷ 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
4. C₁₃×#6861	C₃	semidirect
18. #10624600	C₁₃	direct (N × H)
36. #6861	C₃×C₁₃	semidirect
93. C₁₃	#10624600	direct (N × H)

H ≅ G/N

type

4. C₁₃×#6861

C₃

semidirect

18. #10624600

C₁₃

direct (N × H)

36. #6861

C₃×C₁₃

semidirect

93. C₁₃

#10624600

direct (N × H)

Subgroups — C₁₃×#10624600 #23744751

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624600 #23744751

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624600 #23744751