Group #23745039 — subgroups

Subgroups — C₁₃×#10624888 #23745039

Order 9477.

764 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 440 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×#6893	C₃	1	9	yes	maximal, complemented
2	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	6	yes	maximal, complemented
3	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	18	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	2	yes	maximal, complemented
5	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
6	C₉×C₁₃×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
7	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
10	C₃×C₁₃×3₋¹⁺²	C₃²	1	18	yes	complemented
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
12	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	6	yes	—
13	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
14	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
15	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
16	C₃²×C₉×C₁₃	C₃²	1	9	yes	complemented
17	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
19	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
20	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
21	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
22	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	complemented
23	C₁₃×C₃²⋊C₉	C₃²	1	36	yes	complemented
24	#10624888	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃³×C₁₃	—	3	3	no	—
26	C₃³×C₁₃	—	9	1	no	—
27	C₃³×C₁₃	—	9	2	no	—
28	C₃³×C₁₃	C₃³	1	1	yes	characteristic
29	C₃³×C₁₃	C₃³	1	2	yes	—
30	C₃³×C₁₃	C₃³	1	9	yes	—
31	C₃³×C₁₃	C₃³	1	1	yes	characteristic
32	C₁₃×3₋¹⁺²	—	9	6	no	—
33	C₁₃×3₋¹⁺²	—	9	18	no	—
34	C₁₃×H(3,𝔽₃)	—	3	9	no	—
35	C₁₃×H(3,𝔽₃)	—	9	3	no	—
36	C₁₃×H(3,𝔽₃)	—	9	6	no	—
37	C₃×C₉×C₁₃	—	9	1	no	—
38	C₃×C₉×C₁₃	—	9	2	no	—
39	C₃×C₉×C₁₃	—	9	9	no	—
40	C₃×C₉×C₁₃	C₃³	1	3	yes	—
41	C₃×C₉×C₁₃	C₃³	1	6	yes	—
42	C₃×C₉×C₁₃	C₃³	1	18	yes	—
43	#6893	C₃×C₁₃	1	9	yes	complemented
44	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	6	yes	complemented
45	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	18	yes	complemented
46	#6891	C₃×C₁₃	1	2	yes	complemented
47	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
48	C₉×H(3,𝔽₃)	C₃×C₁₃	1	3	yes	complemented
49	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
50	C₃²×C₁₃	—	3	1	no	—
51	C₃²×C₁₃	—	3	2	no	—
52	C₃²×C₁₃	—	3	9	no	—
53	C₃²×C₁₃	—	3	1	no	—
54	C₃²×C₁₃	—	3	2	no	—
55	C₃²×C₁₃	—	3	9	no	—
56	C₃²×C₁₃	—	3	1	no	—
57	C₃²×C₁₃	—	3	2	no	—
58	C₃²×C₁₃	—	3	2	no	—
59	C₃²×C₁₃	—	3	18	no	—
60	C₃²×C₁₃	—	3	2	no	—
61	C₃²×C₁₃	—	3	2	no	—
62	C₃²×C₁₃	—	9	9	no	—
63	C₃²×C₁₃	#737	1	3	yes	—
64	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
65	C₉×C₁₃	—	3	3	no	—
66	C₉×C₁₃	—	3	6	no	—
67	C₉×C₁₃	—	3	18	no	—
68	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
69	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
70	C₃×3₋¹⁺²	C₃²×C₁₃	1	18	yes	complemented
71	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
72	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	6	yes	—
73	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
74	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
75	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
76	C₃²×C₉	C₃²×C₁₃	1	9	yes	complemented
77	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
78	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
79	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
80	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
81	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
82	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	complemented
83	C₃²⋊C₉	C₃²×C₁₃	1	36	yes	complemented
84	C₃×C₁₃	—	3	3	no	—
85	C₃×C₁₃	—	9	9	no	—
86	C₃×C₁₃	—	9	1	no	—
87	C₃×C₁₃	—	9	2	no	—
88	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
89	C₃×C₁₃	H(5,𝔽₃)	1	1	yes	characteristic
90	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
91	C₃³	—	3	3	no	—
92	C₃³	—	9	1	no	—
93	C₃³	—	9	2	no	—
94	C₃³	C₃³×C₁₃	1	1	yes	characteristic
95	C₃³	C₃³×C₁₃	1	2	yes	—
96	C₃³	C₃³×C₁₃	1	9	yes	—
97	C₃³	C₃³×C₁₃	1	1	yes	characteristic
98	3₋¹⁺²	—	9	6	no	—
99	3₋¹⁺²	—	9	18	no	—
100	H(3,𝔽₃)	—	3	9	no	—
101	H(3,𝔽₃)	—	9	3	no	—
102	H(3,𝔽₃)	—	9	6	no	—
103	C₃×C₉	—	9	1	no	—
104	C₃×C₉	—	9	2	no	—
105	C₃×C₉	—	9	9	no	—
106	C₃×C₉	C₃³×C₁₃	1	3	yes	—
107	C₃×C₉	C₃³×C₁₃	1	6	yes	—
108	C₃×C₉	C₃³×C₁₃	1	18	yes	—
109	C₁₃	#10624888	1	1	yes	characteristic, direct product factor, Sylow
110	C₃²	—	3	1	no	—
111	C₃²	—	3	2	no	—
112	C₃²	—	3	9	no	—
113	C₃²	—	3	1	no	—
114	C₃²	—	3	2	no	—
115	C₃²	—	3	9	no	—
116	C₃²	—	3	1	no	—
117	C₃²	—	3	2	no	—
118	C₃²	—	3	2	no	—
119	C₃²	—	3	18	no	—
120	C₃²	—	3	2	no	—
121	C₃²	—	3	2	no	—
122	C₃²	—	9	9	no	—
123	C₃²	C₁₃×#737	1	3	yes	—
124	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
125	C₉	—	3	3	no	—
126	C₉	—	3	6	no	—
127	C₉	—	3	18	no	—
128	C₃	—	3	3	no	—
129	C₃	—	9	1	no	—
130	C₃	—	9	2	no	—
131	C₃	—	9	9	no	—
132	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
133	C₃	C₁₃×H(5,𝔽₃)	1	1	yes	characteristic
134	C₃	C₁₃×3₋¹⁺⁴	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6893

C₃

yes

maximal, complemented

C₁₃×C₉⋊H(3,𝔽₃)

C₃

yes

maximal, complemented

C₁₃×C₉⋊H(3,𝔽₃)

C₃

yes

maximal, complemented

C₁₃×#6891

C₃

yes

maximal, complemented

C₁₃×C₃²⋊H(3,𝔽₃)

C₃

yes

maximal, characteristic

C₉×C₁₃×H(3,𝔽₃)

C₃

yes

maximal, complemented

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

complemented

C₃×C₁₃×H(3,𝔽₃)

C₃²

yes

—

C₃×C₁₃×H(3,𝔽₃)

C₃²

yes

—

C₃×C₁₃×H(3,𝔽₃)

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

complemented

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

complemented

C₁₃×C₃²⋊C₉

C₃²

yes

complemented

#10624888

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃³

yes

characteristic

C₃³×C₁₃

C₃³

yes

—

C₃³×C₁₃

C₃³

yes

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×H(3,𝔽₃)

—

C₁₃×H(3,𝔽₃)

—

C₁₃×H(3,𝔽₃)

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

#6893

C₃×C₁₃

yes

complemented

C₉⋊H(3,𝔽₃)

C₃×C₁₃

yes

complemented

C₉⋊H(3,𝔽₃)

C₃×C₁₃

yes

complemented

#6891

C₃×C₁₃

yes

complemented

C₃²⋊H(3,𝔽₃)

C₃×C₁₃

yes

characteristic

C₉×H(3,𝔽₃)

C₃×C₁₃

yes

complemented

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic, 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

#737

yes

—

C₃²×C₁₃

C₃⁴

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

complemented

C₃×H(3,𝔽₃)

C₃²×C₁₃

yes

—

C₃×H(3,𝔽₃)

C₃²×C₁₃

yes

—

C₃×H(3,𝔽₃)

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

complemented

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

complemented

C₃²⋊C₉

C₃²×C₁₃

yes

complemented

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃×C₁₃

3₋¹⁺⁴

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃³×C₁₃

yes

characteristic

C₃³

C₃³×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

100

H(3,𝔽₃)

—

101

H(3,𝔽₃)

—

102

H(3,𝔽₃)

—

103

C₃×C₉

—

104

C₃×C₉

—

105

C₃×C₉

—

106

C₃×C₉

C₃³×C₁₃

yes

—

107

C₃×C₉

C₃³×C₁₃

yes

—

108

C₃×C₉

C₃³×C₁₃

yes

—

109

C₁₃

#10624888

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

—

123

C₃²

C₁₃×#737

yes

—

124

C₃²

C₃⁴×C₁₃

yes

characteristic

125

C₉

—

126

C₉

—

127

C₉

—

128

C₃

—

129

C₃

—

130

C₃

—

131

C₃

—

132

C₃

C₃×C₁₃×#737

yes

characteristic

133

C₃

C₁₃×H(5,𝔽₃)

yes

characteristic

134

C₃

C₁₃×3₋¹⁺⁴

yes

—

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

subgroup

G/H

center, socle

C₃²×C₁₃

C₃⁴

commutator, Frattini, cosocle

C₃²

C₃⁴×C₁₃

prime radical

C₁₃×C₃²⋊H(3,𝔽₃)

C₃

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#6893	C₃	semidirect
2. C₁₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
3. C₁₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
4. C₁₃×#6891	C₃	semidirect
6. C₉×C₁₃×H(3,𝔽₃)	C₃	semidirect
7. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
10. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
16. C₃²×C₉×C₁₃	C₃²	semidirect
22. C₁₃×C₃²⋊C₉	C₃²	semidirect
23. C₁₃×C₃²⋊C₉	C₃²	semidirect
24. #10624888	C₁₃	direct (N × H)
43. #6893	C₃×C₁₃	semidirect
44. C₉⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
45. C₉⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
46. #6891	C₃×C₁₃	semidirect
48. C₉×H(3,𝔽₃)	C₃×C₁₃	semidirect
49. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
70. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
76. C₃²×C₉	C₃²×C₁₃	semidirect
82. C₃²⋊C₉	C₃²×C₁₃	semidirect
83. C₃²⋊C₉	C₃²×C₁₃	semidirect
109. C₁₃	#10624888	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6893

C₃

semidirect

2. C₁₃×C₉⋊H(3,𝔽₃)

C₃

semidirect

3. C₁₃×C₉⋊H(3,𝔽₃)

C₃

semidirect

4. C₁₃×#6891

C₃

semidirect

6. C₉×C₁₃×H(3,𝔽₃)

C₃

semidirect

7. C₃×C₁₃×C₃²⋊C₉

C₃

semidirect

10. C₃×C₁₃×3₋¹⁺²

C₃²

semidirect

16. C₃²×C₉×C₁₃

C₃²

semidirect

22. C₁₃×C₃²⋊C₉

C₃²

semidirect

23. C₁₃×C₃²⋊C₉

C₃²

semidirect

24. #10624888

C₁₃

direct (N × H)

43. #6893

C₃×C₁₃

semidirect

44. C₉⋊H(3,𝔽₃)

C₃×C₁₃

semidirect

45. C₉⋊H(3,𝔽₃)

C₃×C₁₃

semidirect

46. #6891

C₃×C₁₃

semidirect

48. C₉×H(3,𝔽₃)

C₃×C₁₃

semidirect

49. C₃×C₃²⋊C₉

C₃×C₁₃

semidirect

70. C₃×3₋¹⁺²

C₃²×C₁₃

semidirect

76. C₃²×C₉

C₃²×C₁₃

semidirect

82. C₃²⋊C₉

C₃²×C₁₃

semidirect

83. C₃²⋊C₉

C₃²×C₁₃

semidirect

109. C₁₃

#10624888

direct (N × H)

Subgroups — C₁₃×#10624888 #23745039

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624888 #23745039

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624888 #23745039