Group #23744757 — subgroups

Subgroups — C₁₃×#10624606 #23744757

Order 9477.

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

normal subgroups only

This group has 204 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	C₁₃×#6894	C₃	1	2	yes	maximal, complemented
2	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6862	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#6861	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#6859	C₃	1	2	yes	maximal
7	C₁₃×#6858	C₃	1	2	yes	maximal, complemented
8	C₁₃×#6858	C₃	1	2	yes	maximal, complemented
9	C₁₃×#6857	C₃	1	1	yes	maximal, characteristic
10	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₃	—	3	1	no	—
13	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
14	C₁₃×C₉⋊C₉	—	3	1	no	—
15	C₁₃×C₉⋊C₉	—	3	1	no	—
16	C₁₃×C₉⋊C₉	—	3	2	no	—
17	C₁₃×C₉⋊C₉	—	3	2	no	—
18	C₁₃×C₉⋊C₉	—	3	2	no	—
19	C₁₃×C₃²⋊C₉	—	3	1	no	—
20	C₁₃×C₃²⋊C₉	—	3	1	no	—
21	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
22	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
23	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
24	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
25	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
26	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
27	C₉²×C₁₃	—	3	1	no	—
28	#10624606	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₃³×C₁₃	—	3	1	no	—
30	C₃³×C₁₃	C₃³	1	1	yes	characteristic
31	C₁₃×3₋¹⁺²	—	9	2	no	—
32	C₁₃×H(3,𝔽₃)	—	3	3	no	—
33	C₃×C₉×C₁₃	—	3	3	no	—
34	C₃×C₉×C₁₃	—	3	2	no	—
35	C₃×C₉×C₁₃	—	3	1	no	—
36	C₃×C₉×C₁₃	—	3	1	no	—
37	C₃×C₉×C₁₃	—	3	1	no	—
38	C₃×C₉×C₁₃	—	3	2	no	—
39	C₃×C₉×C₁₃	—	3	2	no	—
40	C₃×C₉×C₁₃	—	3	2	no	—
41	C₃×C₉×C₁₃	—	9	3	no	—
42	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
43	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
44	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
45	#6894	C₃×C₁₃	1	2	yes	complemented
46	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
47	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
48	#6862	C₃×C₁₃	1	1	yes	characteristic, complemented
49	#6861	C₃×C₁₃	1	1	yes	characteristic, complemented
50	#6859	C₃×C₁₃	1	2	yes	—
51	#6858	C₃×C₁₃	1	2	yes	complemented
52	#6858	C₃×C₁₃	1	2	yes	complemented
53	#6857	C₃×C₁₃	1	1	yes	characteristic
54	C₃²×C₁₃	—	3	2	no	—
55	C₃²×C₁₃	—	3	1	no	—
56	C₃²×C₁₃	—	3	1	no	—
57	C₃²×C₁₃	—	3	3	no	—
58	C₃²×C₁₃	—	9	2	no	—
59	C₃²×C₁₃	—	9	1	no	—
60	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
61	C₉×C₁₃	—	3	1	no	—
62	C₉×C₁₃	—	3	1	no	—
63	C₉×C₁₃	—	9	2	no	—
64	C₉×C₁₃	—	9	2	no	—
65	C₉×C₁₃	—	9	2	no	—
66	C₉×C₁₃	—	9	1	no	—
67	C₉×C₁₃	—	9	1	no	—
68	C₉×C₁₃	—	9	1	no	—
69	C₉×C₁₃	—	9	2	no	—
70	C₉×C₁₃	#731	1	3	yes	—
71	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
72	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
73	C₃²×C₉	—	3	1	no	—
74	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
75	C₉⋊C₉	—	3	1	no	—
76	C₉⋊C₉	—	3	1	no	—
77	C₉⋊C₉	—	3	2	no	—
78	C₉⋊C₉	—	3	2	no	—
79	C₉⋊C₉	—	3	2	no	—
80	C₃²⋊C₉	—	3	1	no	—
81	C₃²⋊C₉	—	3	1	no	—
82	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
83	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
84	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
85	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
86	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
87	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
88	C₉²	—	3	1	no	—
89	C₃×C₁₃	—	9	1	no	—
90	C₃×C₁₃	—	9	3	no	—
91	C₃×C₁₃	C₃×#731	1	1	yes	characteristic
92	C₃×C₁₃	#6908	1	1	yes	characteristic
93	C₃×C₁₃	#6913	1	2	yes	—
94	C₃³	—	3	1	no	—
95	C₃³	C₃³×C₁₃	1	1	yes	characteristic
96	3₋¹⁺²	—	9	2	no	—
97	H(3,𝔽₃)	—	3	3	no	—
98	C₃×C₉	—	3	3	no	—
99	C₃×C₉	—	3	1	no	—
100	C₃×C₉	—	3	2	no	—
101	C₃×C₉	—	3	1	no	—
102	C₃×C₉	—	3	1	no	—
103	C₃×C₉	—	3	2	no	—
104	C₃×C₉	—	3	2	no	—
105	C₃×C₉	—	3	2	no	—
106	C₃×C₉	—	9	3	no	—
107	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
108	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
109	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
110	C₁₃	#10624606	1	1	yes	characteristic, direct product factor, Sylow
111	C₃²	—	3	1	no	—
112	C₃²	—	3	1	no	—
113	C₃²	—	3	3	no	—
114	C₃²	—	3	2	no	—
115	C₃²	—	9	1	no	—
116	C₃²	—	9	2	no	—
117	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
118	C₉	—	3	1	no	—
119	C₉	—	3	1	no	—
120	C₉	—	9	1	no	—
121	C₉	—	9	1	no	—
122	C₉	—	9	1	no	—
123	C₉	—	9	2	no	—
124	C₉	—	9	2	no	—
125	C₉	—	9	2	no	—
126	C₉	—	9	2	no	—
127	C₉	C₁₃×#731	1	3	yes	—
128	C₃	—	9	1	no	—
129	C₃	—	9	3	no	—
130	C₃	C₃×C₁₃×#731	1	1	yes	characteristic
131	C₃	C₁₃×#6908	1	1	yes	characteristic
132	C₃	C₁₃×#6913	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6894

C₃

yes

maximal, complemented

C₉×C₁₃×H(3,𝔽₃)

C₃

yes

maximal, characteristic

C₁₃×#6887

C₃

yes

maximal, characteristic, complemented

C₁₃×#6862

C₃

yes

maximal, characteristic, complemented

C₁₃×#6861

C₃

yes

maximal, characteristic, complemented

C₁₃×#6859

C₃

yes

maximal

C₁₃×#6858

C₃

yes

maximal, complemented

C₁₃×#6858

C₃

yes

maximal, complemented

C₁₃×#6857

C₃

yes

maximal, characteristic

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×H(3,𝔽₃)

C₃²

yes

characteristic

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

C₃²

yes

characteristic

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

characteristic

C₁₃×C₃²⋊C₉

C₃²

yes

characteristic

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₃

—

#10624606

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×H(3,𝔽₃)

—

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

yes

C₃×C₉×C₁₃

yes

C₃×C₉×C₁₃

yes

C₃×C₁₃

yes

complemented

C₉×H(3,𝔽₃)

C₃×C₁₃

yes

characteristic

#6887

C₃×C₁₃

yes

characteristic, complemented

#6862

C₃×C₁₃

yes

characteristic, complemented

#6861

C₃×C₁₃

yes

characteristic, complemented

#6859

C₃×C₁₃

yes

—

#6858

C₃×C₁₃

yes

complemented

#6858

C₃×C₁₃

yes

complemented

#6857

C₃×C₁₃

yes

characteristic

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

#731

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×H(3,𝔽₃)

C₃²×C₁₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃²×C₁₃

yes

characteristic

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

characteristic

C₃²⋊C₉

C₃²×C₁₃

yes

characteristic

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₉²

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

—

C₃³

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

H(3,𝔽₃)

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

—

101

C₃×C₉

—

102

C₃×C₉

—

103

C₃×C₉

—

104

C₃×C₉

—

105

C₃×C₉

—

106

C₃×C₉

—

107

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

108

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

109

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

110

C₁₃

#10624606

yes

characteristic, direct product factor, Sylow

111

C₃²

—

112

C₃²

—

113

C₃²

—

114

C₃²

—

115

C₃²

—

116

C₃²

—

117

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

118

C₉

—

119

C₉

—

120

C₉

—

121

C₉

—

122

C₉

—

123

C₉

—

124

C₉

—

125

C₉

—

126

C₉

—

127

C₉

C₁₃×#731

yes

—

128

C₃

—

129

C₃

—

130

C₃

C₃×C₁₃×#731

yes

characteristic

131

C₃

C₁₃×#6908

yes

characteristic

132

C₃

C₁₃×#6913

yes

—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃²×C₁₃

C₃×H(3,𝔽₃)

commutator, Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃×C₁₃×H(3,𝔽₃)

C₃²

LCS

G ▷ C₃³ ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#6894	C₃	semidirect
3. C₁₃×#6887	C₃	semidirect
4. C₁₃×#6862	C₃	semidirect
5. C₁₃×#6861	C₃	semidirect
7. C₁₃×#6858	C₃	semidirect
8. C₁₃×#6858	C₃	semidirect
28. #10624606	C₁₃	direct (N × H)
45. #6894	C₃×C₁₃	semidirect
47. #6887	C₃×C₁₃	semidirect
48. #6862	C₃×C₁₃	semidirect
49. #6861	C₃×C₁₃	semidirect
51. #6858	C₃×C₁₃	semidirect
52. #6858	C₃×C₁₃	semidirect
110. C₁₃	#10624606	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6894

C₃

semidirect

3. C₁₃×#6887

C₃

semidirect

4. C₁₃×#6862

C₃

semidirect

5. C₁₃×#6861

C₃

semidirect

7. C₁₃×#6858

C₃

semidirect

8. C₁₃×#6858

C₃

semidirect

28. #10624606

C₁₃

direct (N × H)

45. #6894

C₃×C₁₃

semidirect

47. #6887

C₃×C₁₃

semidirect

48. #6862

C₃×C₁₃

semidirect

49. #6861

C₃×C₁₃

semidirect

51. #6858

C₃×C₁₃

semidirect

52. #6858

C₃×C₁₃

semidirect

110. C₁₃

#10624606

direct (N × H)

Subgroups — C₁₃×#10624606 #23744757

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624606 #23744757

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624606 #23744757