Group #23744776 — subgroups

Subgroups — C₁₃×#10624625 #23744776

Order 9477.

200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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×#6895	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, 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	—	3	1	no	—
11	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
12	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
14	C₁₃×C₉⋊C₉	—	3	2	no	—
15	C₁₃×C₉⋊C₉	—	3	2	no	—
16	C₁₃×C₉⋊C₉	—	3	2	no	—
17	C₁₃×C₉⋊C₉	—	3	1	no	—
18	C₁₃×C₃²⋊C₉	—	3	2	no	—
19	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
20	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
21	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
22	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
23	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
24	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
25	C₉²×C₁₃	—	3	2	no	—
26	#10624625	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₃³×C₁₃	—	3	1	no	—
28	C₃³×C₁₃	C₃³	1	1	yes	characteristic
29	C₁₃×3₋¹⁺²	—	3	6	no	—
30	C₁₃×3₋¹⁺²	—	9	3	no	—
31	C₁₃×H(3,𝔽₃)	—	9	1	no	—
32	C₃×C₉×C₁₃	—	3	2	no	—
33	C₃×C₉×C₁₃	—	3	2	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	—	9	1	no	—
40	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
41	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
42	#6895	C₃×C₁₃	1	1	yes	characteristic, complemented
43	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
44	C₉×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
45	#6862	C₃×C₁₃	1	1	yes	characteristic, complemented
46	#6861	C₃×C₁₃	1	1	yes	characteristic, complemented
47	#6859	C₃×C₁₃	1	2	yes	—
48	#6858	C₃×C₁₃	1	2	yes	complemented
49	#6858	C₃×C₁₃	1	2	yes	complemented
50	#6857	C₃×C₁₃	1	1	yes	characteristic
51	C₃²×C₁₃	—	3	1	no	—
52	C₃²×C₁₃	—	3	2	no	—
53	C₃²×C₁₃	—	3	1	no	—
54	C₃²×C₁₃	—	9	1	no	—
55	C₃²×C₁₃	—	9	2	no	—
56	C₃²×C₁₃	—	9	1	no	—
57	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
58	C₉×C₁₃	—	3	6	no	—
59	C₉×C₁₃	—	3	2	no	—
60	C₉×C₁₃	—	3	1	no	—
61	C₉×C₁₃	—	9	2	no	—
62	C₉×C₁₃	—	9	1	no	—
63	C₉×C₁₃	—	9	2	no	—
64	C₉×C₁₃	—	9	2	no	—
65	C₉×C₁₃	—	9	1	no	—
66	C₉×C₁₃	—	9	1	no	—
67	C₃×3₋¹⁺²	—	3	1	no	—
68	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
69	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
70	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
71	C₉⋊C₉	—	3	2	no	—
72	C₉⋊C₉	—	3	2	no	—
73	C₉⋊C₉	—	3	2	no	—
74	C₉⋊C₉	—	3	1	no	—
75	C₃²⋊C₉	—	3	2	no	—
76	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
77	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
78	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
79	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
80	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
81	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
82	C₉²	—	3	2	no	—
83	C₃×C₁₃	—	9	1	no	—
84	C₃×C₁₃	—	27	1	no	—
85	C₃×C₁₃	#6908	1	2	yes	—
86	C₃×C₁₃	#6910	1	1	yes	characteristic
87	C₃×C₁₃	#6913	1	1	yes	characteristic
88	C₃³	—	3	1	no	—
89	C₃³	C₃³×C₁₃	1	1	yes	characteristic
90	3₋¹⁺²	—	3	6	no	—
91	3₋¹⁺²	—	9	3	no	—
92	H(3,𝔽₃)	—	9	1	no	—
93	C₃×C₉	—	3	2	no	—
94	C₃×C₉	—	3	2	no	—
95	C₃×C₉	—	3	2	no	—
96	C₃×C₉	—	3	1	no	—
97	C₃×C₉	—	3	1	no	—
98	C₃×C₉	—	3	2	no	—
99	C₃×C₉	—	3	1	no	—
100	C₃×C₉	—	9	1	no	—
101	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
102	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
103	C₁₃	#10624625	1	1	yes	characteristic, direct product factor, Sylow
104	C₃²	—	3	2	no	—
105	C₃²	—	3	1	no	—
106	C₃²	—	3	1	no	—
107	C₃²	—	9	2	no	—
108	C₃²	—	9	1	no	—
109	C₃²	—	9	1	no	—
110	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
111	C₉	—	3	6	no	—
112	C₉	—	3	1	no	—
113	C₉	—	3	2	no	—
114	C₉	—	9	2	no	—
115	C₉	—	9	2	no	—
116	C₉	—	9	1	no	—
117	C₉	—	9	1	no	—
118	C₉	—	9	2	no	—
119	C₉	—	9	1	no	—
120	C₃	—	9	1	no	—
121	C₃	—	27	1	no	—
122	C₃	C₁₃×#6908	1	2	yes	—
123	C₃	C₁₃×#6910	1	1	yes	characteristic
124	C₃	C₁₃×#6913	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6895

C₃

yes

maximal, characteristic, complemented

C₁₃×C₉⋊H(3,𝔽₃)

C₃

yes

maximal, characteristic

C₉×C₁₃×3₋¹⁺²

C₃

yes

maximal, 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

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×H(3,𝔽₃)

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊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

—

#10624625

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

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

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

characteristic

#6895

C₃×C₁₃

yes

characteristic, complemented

C₉⋊H(3,𝔽₃)

C₃×C₁₃

yes

characteristic

C₉×3₋¹⁺²

C₃×C₁₃

yes

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

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×H(3,𝔽₃)

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊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

#6908

yes

—

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃³

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

H(3,𝔽₃)

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

—

101

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

102

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

103

C₁₃

#10624625

yes

characteristic, direct product factor, Sylow

104

C₃²

—

105

C₃²

—

106

C₃²

—

107

C₃²

—

108

C₃²

—

109

C₃²

—

110

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

111

C₉

—

112

C₉

—

113

C₉

—

114

C₉

—

115

C₉

—

116

C₉

—

117

C₉

—

118

C₉

—

119

C₉

—

120

C₃

—

121

C₃

—

122

C₃

C₁₃×#6908

yes

—

123

C₃

C₁₃×#6910

yes

characteristic

124

C₃

C₁₃×#6913

yes

characteristic

	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×#6895	C₃	semidirect
3. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
4. C₁₃×#6862	C₃	semidirect
5. C₁₃×#6861	C₃	semidirect
7. C₁₃×#6858	C₃	semidirect
8. C₁₃×#6858	C₃	semidirect
26. #10624625	C₁₃	direct (N × H)
42. #6895	C₃×C₁₃	semidirect
44. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
45. #6862	C₃×C₁₃	semidirect
46. #6861	C₃×C₁₃	semidirect
48. #6858	C₃×C₁₃	semidirect
49. #6858	C₃×C₁₃	semidirect
103. C₁₃	#10624625	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6895

C₃

semidirect

3. C₉×C₁₃×3₋¹⁺²

C₃

semidirect

4. C₁₃×#6862

C₃

semidirect

5. C₁₃×#6861

C₃

semidirect

7. C₁₃×#6858

C₃

semidirect

8. C₁₃×#6858

C₃

semidirect

26. #10624625

C₁₃

direct (N × H)

42. #6895

C₃×C₁₃

semidirect

44. C₉×3₋¹⁺²

C₃×C₁₃

semidirect

45. #6862

C₃×C₁₃

semidirect

46. #6861

C₃×C₁₃

semidirect

48. #6858

C₃×C₁₃

semidirect

49. #6858

C₃×C₁₃

semidirect

103. C₁₃

#10624625

direct (N × H)

Subgroups — C₁₃×#10624625 #23744776

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624625 #23744776

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624625 #23744776