Group #23745030 — subgroups

Subgroups — C₁₃×#10624879 #23745030

Order 9477.

758 conjugacy classes of subgroups; only the 494 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 494 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	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6900	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6899	C₃	1	6	yes	maximal, complemented
4	C₁₃×#6896	C₃	1	9	yes	maximal, complemented
5	C₁₃×#6894	C₃	1	6	yes	maximal, complemented
6	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	3	yes	maximal
7	C₉×C₁₃×3₋¹⁺²	C₃	1	9	yes	maximal, complemented
8	C₁₃×#6887	C₃	1	2	yes	maximal, complemented
9	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#737	—	3	9	no	—
11	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
12	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
13	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
14	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
15	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
16	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
17	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
18	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
19	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
20	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
21	C₁₃×C₉⋊C₉	C₃²	1	36	yes	—
22	C₁₃×C₉⋊C₉	C₃²	1	18	yes	—
23	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
24	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
25	C₉²×C₁₃	C₃²	1	3	yes	—
26	C₉²×C₁₃	C₃²	1	2	yes	—
27	C₉²×C₁₃	C₃²	1	1	yes	characteristic
28	C₉²×C₁₃	C₃²	1	3	yes	—
29	C₉²×C₁₃	C₃²	1	6	yes	—
30	#10624879	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₃³×C₁₃	C₃³	1	3	yes	—
32	C₃³×C₁₃	C₃³	1	1	yes	characteristic
33	C₁₃×3₋¹⁺²	—	3	6	no	—
34	C₁₃×3₋¹⁺²	—	3	9	no	—
35	C₁₃×3₋¹⁺²	—	3	9	no	—
36	C₁₃×3₋¹⁺²	—	3	27	no	—
37	C₁₃×H(3,𝔽₃)	—	3	3	no	—
38	C₃×C₉×C₁₃	—	3	9	no	—
39	C₃×C₉×C₁₃	—	3	9	no	—
40	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
41	C₃×C₉×C₁₃	C₃³	1	6	yes	—
42	C₃×C₉×C₁₃	C₃³	1	18	yes	—
43	C₃×C₉×C₁₃	C₃³	1	6	yes	—
44	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
45	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
46	C₃×C₉×C₁₃	C₃³	1	3	yes	—
47	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
48	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
49	#6900	C₃×C₁₃	1	3	yes	complemented
50	#6899	C₃×C₁₃	1	6	yes	complemented
51	#6896	C₃×C₁₃	1	9	yes	complemented
52	#6894	C₃×C₁₃	1	6	yes	complemented
53	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	3	yes	—
54	C₉×3₋¹⁺²	C₃×C₁₃	1	9	yes	complemented
55	#6887	C₃×C₁₃	1	2	yes	complemented
56	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
57	C₃²×C₁₃	—	3	3	no	—
58	C₃²×C₁₃	—	3	3	no	—
59	C₃²×C₁₃	—	3	9	no	—
60	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
61	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
62	C₉×C₁₃	—	3	6	no	—
63	C₉×C₁₃	—	3	6	no	—
64	C₉×C₁₃	—	3	18	no	—
65	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
66	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
67	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
68	C₉×C₁₃	#737	1	9	yes	complemented
69	#737	—	3	9	no	—
70	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
71	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
72	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
73	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
74	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
75	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
76	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
77	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
78	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
79	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
80	C₉⋊C₉	C₃²×C₁₃	1	36	yes	—
81	C₉⋊C₉	C₃²×C₁₃	1	18	yes	—
82	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
83	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
84	C₉²	C₃²×C₁₃	1	3	yes	—
85	C₉²	C₃²×C₁₃	1	3	yes	—
86	C₉²	C₃²×C₁₃	1	2	yes	—
87	C₉²	C₃²×C₁₃	1	1	yes	characteristic
88	C₉²	C₃²×C₁₃	1	6	yes	—
89	C₃×C₁₃	—	3	3	no	—
90	C₃×C₁₃	—	9	3	no	—
91	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
92	C₃×C₁₃	C₃×#737	1	3	yes	—
93	C₃³	C₃³×C₁₃	1	3	yes	—
94	C₃³	C₃³×C₁₃	1	1	yes	characteristic
95	3₋¹⁺²	—	3	6	no	—
96	3₋¹⁺²	—	3	9	no	—
97	3₋¹⁺²	—	3	9	no	—
98	3₋¹⁺²	—	3	27	no	—
99	H(3,𝔽₃)	—	3	3	no	—
100	C₃×C₉	—	3	9	no	—
101	C₃×C₉	—	3	9	no	—
102	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
103	C₃×C₉	C₃³×C₁₃	1	6	yes	—
104	C₃×C₉	C₃³×C₁₃	1	18	yes	—
105	C₃×C₉	C₃³×C₁₃	1	6	yes	—
106	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
107	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
108	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
109	C₃×C₉	C₃³×C₁₃	1	3	yes	—
110	C₁₃	#10624879	1	1	yes	characteristic, direct product factor, Sylow
111	C₃²	—	3	3	no	—
112	C₃²	—	3	3	no	—
113	C₃²	—	3	9	no	—
114	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
115	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
116	C₉	—	3	6	no	—
117	C₉	—	3	6	no	—
118	C₉	—	3	18	no	—
119	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
120	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
121	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
122	C₉	C₁₃×#737	1	9	yes	complemented
123	C₃	—	3	3	no	—
124	C₃	—	9	3	no	—
125	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
126	C₃	C₃×C₁₃×#737	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₁₃×#737

C₃

yes

maximal, characteristic

C₁₃×#6900

C₃

yes

maximal, complemented

C₁₃×#6899

C₃

yes

maximal, complemented

C₁₃×#6896

C₃

yes

maximal, complemented

C₁₃×#6894

C₃

yes

maximal, complemented

C₁₃×C₉⋊H(3,𝔽₃)

C₃

yes

maximal

C₉×C₁₃×3₋¹⁺²

C₃

yes

maximal, complemented

C₁₃×#6887

C₃

yes

maximal, complemented

C₃×C₉²×C₁₃

C₃

yes

maximal, characteristic, complemented

C₁₃×#737

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×H(3,𝔽₃)

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

C₃²

yes

—

C₁₃×C₉⋊C₉

C₃²

yes

—

C₁₃×C₉⋊C₉

C₃²

yes

—

C₁₃×C₉⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₃

C₃²

yes

—

C₉²×C₁₃

C₃²

yes

—

C₉²×C₁₃

C₃²

yes

characteristic

C₉²×C₁₃

C₃²

yes

—

C₉²×C₁₃

C₃²

yes

—

#10624879

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

C₃³

yes

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×H(3,𝔽₃)

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

complemented

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

characteristic

C₃×C₉×C₁₃

C₃³

yes

characteristic

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

characteristic

C₃×#737

C₃×C₁₃

yes

characteristic

#6900

C₃×C₁₃

yes

complemented

#6899

C₃×C₁₃

yes

complemented

#6896

C₃×C₁₃

yes

complemented

#6894

C₃×C₁₃

yes

complemented

C₉⋊H(3,𝔽₃)

C₃×C₁₃

yes

—

C₉×3₋¹⁺²

C₃×C₁₃

yes

complemented

#6887

C₃×C₁₃

yes

complemented

C₃×C₉²

C₃×C₁₃

yes

characteristic, complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

C₃⁴

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₃×3₋¹⁺²

yes

—

C₉×C₁₃

C₃×3₋¹⁺²

yes

—

C₉×C₁₃

C₃×3₋¹⁺²

yes

—

C₉×C₁₃

#737

yes

complemented

#737

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×H(3,𝔽₃)

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

C₃²×C₁₃

yes

—

C₉⋊C₉

C₃²×C₁₃

yes

—

C₉⋊C₉

C₃²×C₁₃

yes

—

C₉⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₉²

C₃²×C₁₃

yes

—

C₉²

C₃²×C₁₃

yes

—

C₉²

C₃²×C₁₃

yes

—

C₉²

C₃²×C₁₃

yes

characteristic

C₉²

C₃²×C₁₃

yes

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₃

C₃×#737

yes

—

C₃³

C₃³×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

H(3,𝔽₃)

—

100

C₃×C₉

—

101

C₃×C₉

—

102

C₃×C₉

C₁₃×3₋¹⁺²

yes

complemented

103

C₃×C₉

C₃³×C₁₃

yes

—

104

C₃×C₉

C₃³×C₁₃

yes

—

105

C₃×C₉

C₃³×C₁₃

yes

—

106

C₃×C₉

C₃³×C₁₃

yes

characteristic

107

C₃×C₉

C₃³×C₁₃

yes

characteristic

108

C₃×C₉

C₃³×C₁₃

yes

characteristic

109

C₃×C₉

C₃³×C₁₃

yes

—

110

C₁₃

#10624879

yes

characteristic, direct product factor, Sylow

111

C₃²

—

112

C₃²

—

113

C₃²

—

114

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

115

C₃²

C₃⁴×C₁₃

yes

characteristic

116

C₉

—

117

C₉

—

118

C₉

—

119

C₉

C₃×C₁₃×3₋¹⁺²

yes

—

120

C₉

C₃×C₁₃×3₋¹⁺²

yes

—

121

C₉

C₃×C₁₃×3₋¹⁺²

yes

—

122

C₉

C₁₃×#737

yes

complemented

123

C₃

—

124

C₃

—

125

C₃

C₃²×C₁₃×3₋¹⁺²

yes

characteristic

126

C₃

C₃×C₁₃×#737

yes

—

	subgroup	G/H
center	C₃×C₉×C₁₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
socle	C₃²×C₁₃	C₃⁴
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₃ ◁ G

subgroup

G/H

center

C₃×C₉×C₁₃

C₃³

commutator, Frattini, cosocle

C₃²

C₃⁴×C₁₃

socle

C₃²×C₁₃

C₃⁴

prime radical

C₃×C₁₃×H(3,𝔽₃)

C₃²

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₁₃×#6900	C₃	semidirect
3. C₁₃×#6899	C₃	semidirect
4. C₁₃×#6896	C₃	semidirect
5. C₁₃×#6894	C₃	semidirect
7. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
8. C₁₃×#6887	C₃	semidirect
9. C₃×C₉²×C₁₃	C₃	semidirect
30. #10624879	C₁₃	direct (N × H)
40. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
49. #6900	C₃×C₁₃	semidirect
50. #6899	C₃×C₁₃	semidirect
51. #6896	C₃×C₁₃	semidirect
52. #6894	C₃×C₁₃	semidirect
54. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
55. #6887	C₃×C₁₃	semidirect
56. C₃×C₉²	C₃×C₁₃	semidirect
68. C₉×C₁₃	#737	semidirect
102. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
110. C₁₃	#10624879	direct (N × H)
122. C₉	C₁₃×#737	semidirect

H ≅ G/N

type

2. C₁₃×#6900

C₃

semidirect

3. C₁₃×#6899

C₃

semidirect

4. C₁₃×#6896

C₃

semidirect

5. C₁₃×#6894

C₃

semidirect

7. C₉×C₁₃×3₋¹⁺²

C₃

semidirect

8. C₁₃×#6887

C₃

semidirect

9. C₃×C₉²×C₁₃

C₃

semidirect

30. #10624879

C₁₃

direct (N × H)

40. C₃×C₉×C₁₃

3₋¹⁺²

semidirect

49. #6900

C₃×C₁₃

semidirect

50. #6899

C₃×C₁₃

semidirect

51. #6896

C₃×C₁₃

semidirect

52. #6894

C₃×C₁₃

semidirect

54. C₉×3₋¹⁺²

C₃×C₁₃

semidirect

55. #6887

C₃×C₁₃

semidirect

56. C₃×C₉²

C₃×C₁₃

semidirect

68. C₉×C₁₃

#737

semidirect

102. C₃×C₉

C₁₃×3₋¹⁺²

semidirect

110. C₁₃

#10624879

direct (N × H)

122. C₉

C₁₃×#737

semidirect

Subgroups — C₁₃×#10624879 #23745030

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624879 #23745030

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624879 #23745030