Group #23744707 — subgroups

Subgroups — C₁₃×#10624556 #23744707

Order 9477.

554 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 206 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	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₉⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₁₃×#6855	C₃	1	6	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	—	3	3	no	—
8	C₃²×C₉×C₁₃	—	3	3	no	—
9	C₃²×C₉×C₁₃	—	3	6	no	—
10	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
14	C₁₃×C₉⋊C₉	—	3	9	no	—
15	C₁₃×C₃²⋊C₉	—	3	6	no	—
16	C₁₃×C₃²⋊C₉	C₉	1	9	yes	complemented
17	#10624556	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	—	3	1	no	—
19	C₃³×C₁₃	—	3	2	no	—
20	C₃³×C₁₃	—	3	2	no	—
21	C₃³×C₁₃	—	3	4	no	—
22	C₃³×C₁₃	C₃×C₉	1	3	yes	—
23	C₃³×C₁₃	3₋¹⁺²	1	6	yes	—
24	C₃³×C₁₃	3₋¹⁺²	1	3	yes	—
25	C₃³×C₁₃	C₃³	1	1	yes	characteristic
26	C₃×C₉×C₁₃	—	3	27	no	—
27	C₃×C₉×C₁₃	—	3	3	no	—
28	C₃×C₉×C₁₃	—	3	2	no	—
29	C₃×C₉×C₁₃	—	3	1	no	—
30	C₃×C₉×C₁₃	—	3	2	no	—
31	C₃×C₉×C₁₃	—	3	2	no	—
32	C₃×C₉×C₁₃	—	3	2	no	—
33	C₃×C₉×C₁₃	—	3	6	no	—
34	C₃×C₉×C₁₃	—	3	6	no	—
35	C₃×C₉×C₁₃	—	3	6	no	—
36	C₃×C₉×C₁₃	—	3	12	no	—
37	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	complemented
38	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
39	C₃×C₉×C₁₃	3₋¹⁺²	1	6	yes	—
40	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
41	C₃×C₉⋊C₉	C₃×C₁₃	1	3	yes	complemented
42	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
43	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
44	#6855	C₃×C₁₃	1	6	yes	complemented
45	C₃²×C₁₃	—	3	3	no	—
46	C₃²×C₁₃	—	3	6	no	—
47	C₃²×C₁₃	—	3	3	no	—
48	C₃²×C₁₃	—	3	6	no	—
49	C₃²×C₁₃	—	3	12	no	—
50	C₃²×C₁₃	—	3	6	no	—
51	C₃²×C₁₃	C₉⋊C₉	1	9	yes	complemented
52	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
53	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
55	C₃²×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
56	C₃²×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
57	C₃²×C₁₃	#737	1	2	yes	—
58	C₃²×C₁₃	#737	1	4	yes	—
59	C₉×C₁₃	—	3	9	no	—
60	C₉×C₁₃	—	3	3	no	—
61	C₉×C₁₃	—	3	6	no	—
62	C₉×C₁₃	—	9	6	no	—
63	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
64	C₃²×C₉	—	3	3	no	—
65	C₃²×C₉	—	3	3	no	—
66	C₃²×C₉	—	3	6	no	—
67	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
68	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
69	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
70	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
71	C₉⋊C₉	—	3	9	no	—
72	C₃²⋊C₉	—	3	6	no	—
73	C₃²⋊C₉	C₉×C₁₃	1	9	yes	complemented
74	C₃×C₁₃	—	3	9	no	—
75	C₃×C₁₃	C₃×C₉⋊C₉	1	1	yes	characteristic
76	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
77	C₃×C₁₃	C₉×3₋¹⁺²	1	2	yes	—
78	C₃×C₁₃	#6891	1	1	yes	characteristic
79	C₃×C₁₃	C₉⋊H(3,𝔽₃)	1	2	yes	—
80	C₃×C₁₃	#6894	1	4	yes	—
81	C₃×C₁₃	#6895	1	2	yes	—
82	C₃³	—	3	1	no	—
83	C₃³	—	3	2	no	—
84	C₃³	—	3	2	no	—
85	C₃³	—	3	4	no	—
86	C₃³	C₃×C₉×C₁₃	1	3	yes	—
87	C₃³	C₁₃×3₋¹⁺²	1	6	yes	—
88	C₃³	C₁₃×3₋¹⁺²	1	3	yes	—
89	C₃³	C₃³×C₁₃	1	1	yes	characteristic
90	C₃×C₉	—	3	27	no	—
91	C₃×C₉	—	3	3	no	—
92	C₃×C₉	—	3	2	no	—
93	C₃×C₉	—	3	1	no	—
94	C₃×C₉	—	3	2	no	—
95	C₃×C₉	—	3	2	no	—
96	C₃×C₉	—	3	2	no	—
97	C₃×C₉	—	3	6	no	—
98	C₃×C₉	—	3	6	no	—
99	C₃×C₉	—	3	6	no	—
100	C₃×C₉	—	3	12	no	—
101	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	complemented
102	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
103	C₃×C₉	C₁₃×3₋¹⁺²	1	6	yes	—
104	C₁₃	#10624556	1	1	yes	characteristic, direct product factor, Sylow
105	C₃²	—	3	3	no	—
106	C₃²	—	3	6	no	—
107	C₃²	—	3	3	no	—
108	C₃²	—	3	6	no	—
109	C₃²	—	3	12	no	—
110	C₃²	—	3	6	no	—
111	C₃²	C₁₃×C₉⋊C₉	1	9	yes	complemented
112	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
113	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
114	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
115	C₃²	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
116	C₃²	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
117	C₃²	C₁₃×#737	1	2	yes	—
118	C₃²	C₁₃×#737	1	4	yes	—
119	C₉	—	3	9	no	—
120	C₉	—	3	3	no	—
121	C₉	—	3	6	no	—
122	C₉	—	9	6	no	—
123	C₃	—	3	9	no	—
124	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic
125	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
126	C₃	C₉×C₁₃×3₋¹⁺²	1	2	yes	—
127	C₃	C₁₃×#6891	1	1	yes	characteristic
128	C₃	C₁₃×C₉⋊H(3,𝔽₃)	1	2	yes	—
129	C₃	C₁₃×#6894	1	4	yes	—
130	C₃	C₁₃×#6895	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃³×C₉×C₁₃

C₃

yes

maximal, characteristic

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, complemented

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₁₃×#6855

C₃

yes

maximal, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

—

C₁₃×C₉⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

C₉

yes

complemented

#10624556

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃×C₉

yes

—

C₃³×C₁₃

3₋¹⁺²

yes

—

C₃³×C₁₃

3₋¹⁺²

yes

—

C₃³×C₁₃

C₃³

yes

characteristic

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

C₃×C₉

yes

complemented

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃³×C₉

C₃×C₁₃

yes

characteristic

C₃×C₉⋊C₉

C₃×C₁₃

yes

complemented

C₃×C₃²⋊C₉

C₃×C₁₃

yes

—

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic

#6855

C₃×C₁₃

yes

complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₉⋊C₉

yes

complemented

C₃²×C₁₃

C₃²×C₉

yes

characteristic

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

#737

yes

—

C₃²×C₁₃

#737

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₉×C₁₃

yes

complemented

C₃×C₁₃

—

C₃×C₁₃

C₃×C₉⋊C₉

yes

characteristic

C₃×C₁₃

C₉×H(3,𝔽₃)

yes

characteristic

C₃×C₁₃

C₉×3₋¹⁺²

yes

—

C₃×C₁₃

#6891

yes

characteristic

C₃×C₁₃

C₉⋊H(3,𝔽₃)

yes

—

C₃×C₁₃

#6894

yes

—

C₃×C₁₃

#6895

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃×C₉×C₁₃

yes

—

C₃³

C₁₃×3₋¹⁺²

yes

—

C₃³

C₁₃×3₋¹⁺²

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

—

101

C₃×C₉

C₃×C₉×C₁₃

yes

complemented

102

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

103

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

104

C₁₃

#10624556

yes

characteristic, direct product factor, Sylow

105

C₃²

—

106

C₃²

—

107

C₃²

—

108

C₃²

—

109

C₃²

—

110

C₃²

—

111

C₃²

C₁₃×C₉⋊C₉

yes

complemented

112

C₃²

C₃²×C₉×C₁₃

yes

characteristic

113

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

114

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

115

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

116

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

117

C₃²

C₁₃×#737

yes

—

118

C₃²

C₁₃×#737

yes

—

119

C₉

—

120

C₉

—

121

C₉

—

122

C₉

—

123

C₃

—

124

C₃

C₃×C₁₃×C₉⋊C₉

yes

characteristic

125

C₃

C₉×C₁₃×H(3,𝔽₃)

yes

characteristic

126

C₃

C₉×C₁₃×3₋¹⁺²

yes

—

127

C₃

C₁₃×#6891

yes

characteristic

128

C₃

C₁₃×C₉⋊H(3,𝔽₃)

yes

—

129

C₃

C₁₃×#6894

yes

—

130

C₃

C₁₃×#6895

yes

—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃³×C₁₃

C₃³

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃³×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
5. C₁₃×#6855	C₃	semidirect
16. C₁₃×C₃²⋊C₉	C₉	semidirect
17. #10624556	C₁₃	direct (N × H)
37. C₃×C₉×C₁₃	C₃×C₉	semidirect
41. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
44. #6855	C₃×C₁₃	semidirect
51. C₃²×C₁₃	C₉⋊C₉	semidirect
73. C₃²⋊C₉	C₉×C₁₃	semidirect
101. C₃×C₉	C₃×C₉×C₁₃	semidirect
104. C₁₃	#10624556	direct (N × H)
111. C₃²	C₁₃×C₉⋊C₉	semidirect

H ≅ G/N

type

2. C₃×C₁₃×C₉⋊C₉

C₃

semidirect

5. C₁₃×#6855

C₃

semidirect

16. C₁₃×C₃²⋊C₉

C₉

semidirect

17. #10624556

C₁₃

direct (N × H)

37. C₃×C₉×C₁₃

C₃×C₉

semidirect

41. C₃×C₉⋊C₉

C₃×C₁₃

semidirect

44. #6855

C₃×C₁₃

semidirect

51. C₃²×C₁₃

C₉⋊C₉

semidirect

73. C₃²⋊C₉

C₉×C₁₃

semidirect

101. C₃×C₉

C₃×C₉×C₁₃

semidirect

104. C₁₃

#10624556

direct (N × H)

111. C₃²

C₁₃×C₉⋊C₉

semidirect

Subgroups — C₁₃×#10624556 #23744707

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624556 #23744707

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624556 #23744707