Group #23745003 — subgroups

Subgroups — C₁₃×#10624852 #23745003

Order 9477.

188 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 68 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×#6913	C₃	1	2	yes	maximal, complemented
2	C₁₃×#6912	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6900	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6883	C₃	1	2	yes	maximal, complemented
5	C₁₃×#6882	C₃	1	2	yes	maximal, complemented
6	C₁₃×#6882	C₃	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#6881	C₃	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#6880	C₃	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#6878	C₃	1	2	yes	maximal, complemented
10	C₁₃×#737	—	3	2	no	—
11	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
12	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
13	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
14	C₁₃×#733	—	3	2	no	—
15	C₁₃×#733	C₃²	1	2	yes	—
16	C₁₃×#733	C₃²	1	2	yes	—
17	C₁₃×#733	C₃²	1	1	yes	characteristic
18	C₁₃×#733	C₃²	1	2	yes	—
19	C₁₃×#732	C₃²	1	2	yes	—
20	C₁₃×#731	—	3	2	no	—
21	C₁₃×AΣL(1,𝔽₂₇)	—	3	2	no	—
22	C₁₃×C₉⋊C₉	—	3	2	no	—
23	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
24	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
25	C₉²×C₁₃	C₃²	1	1	yes	characteristic
26	#10624852	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
28	C₁₃×3₋¹⁺²	—	3	2	no	—
29	C₁₃×3₋¹⁺²	—	3	2	no	—
30	C₁₃×3₋¹⁺²	—	3	2	no	—
31	C₁₃×3₋¹⁺²	—	3	1	no	—
32	C₁₃×3₋¹⁺²	—	9	1	no	—
33	C₁₃×3₋¹⁺²	—	9	3	no	—
34	C₁₃×3₋¹⁺²	—	9	4	no	—
35	C₁₃×3₋¹⁺²	—	9	2	no	—
36	C₁₃×H(3,𝔽₃)	—	3	2	no	—
37	C₃×C₉×C₁₃	—	3	1	no	—
38	C₃×C₉×C₁₃	—	3	1	no	—
39	C₃×C₉×C₁₃	—	3	1	no	—
40	C₃×C₉×C₁₃	—	9	2	no	—
41	C₃×C₉×C₁₃	—	9	1	no	—
42	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
43	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
44	#6913	C₃×C₁₃	1	2	yes	complemented
45	#6912	C₃×C₁₃	1	1	yes	characteristic, complemented
46	#6900	C₃×C₁₃	1	1	yes	characteristic, complemented
47	#6883	C₃×C₁₃	1	2	yes	complemented
48	#6882	C₃×C₁₃	1	2	yes	complemented
49	#6882	C₃×C₁₃	1	1	yes	characteristic, complemented
50	#6881	C₃×C₁₃	1	1	yes	characteristic, complemented
51	#6880	C₃×C₁₃	1	1	yes	characteristic, complemented
52	#6878	C₃×C₁₃	1	2	yes	complemented
53	C₃²×C₁₃	—	3	1	no	—
54	C₃²×C₁₃	—	9	1	no	—
55	C₃²×C₁₃	—	9	2	no	—
56	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
57	C₉×C₁₃	—	3	3	no	—
58	C₉×C₁₃	—	3	2	no	—
59	C₉×C₁₃	—	3	1	no	—
60	C₉×C₁₃	—	9	1	no	—
61	C₉×C₁₃	—	9	1	no	—
62	C₉×C₁₃	—	9	2	no	—
63	C₉×C₁₃	—	9	2	no	—
64	C₉×C₁₃	—	9	2	no	—
65	C₉×C₁₃	—	9	1	no	—
66	#737	—	3	2	no	—
67	C₃×3₋¹⁺²	—	3	1	no	—
68	C₃×3₋¹⁺²	—	3	1	no	—
69	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
70	#733	—	3	2	no	—
71	#733	C₃²×C₁₃	1	2	yes	—
72	#733	C₃²×C₁₃	1	1	yes	characteristic
73	#733	C₃²×C₁₃	1	2	yes	—
74	#733	C₃²×C₁₃	1	2	yes	—
75	#732	C₃²×C₁₃	1	2	yes	—
76	#731	—	3	2	no	—
77	AΣL(1,𝔽₂₇)	—	3	2	no	—
78	C₉⋊C₉	—	3	2	no	—
79	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
80	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
81	C₉²	C₃²×C₁₃	1	1	yes	characteristic
82	C₃×C₁₃	—	3	1	no	—
83	C₃×C₁₃	—	9	1	no	—
84	C₃×C₁₃	—	27	2	no	—
85	C₃×C₁₃	#6911	1	1	yes	characteristic
86	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
87	3₋¹⁺²	—	3	2	no	—
88	3₋¹⁺²	—	3	2	no	—
89	3₋¹⁺²	—	3	2	no	—
90	3₋¹⁺²	—	3	1	no	—
91	3₋¹⁺²	—	9	1	no	—
92	3₋¹⁺²	—	9	3	no	—
93	3₋¹⁺²	—	9	4	no	—
94	3₋¹⁺²	—	9	2	no	—
95	H(3,𝔽₃)	—	3	2	no	—
96	C₃×C₉	—	3	1	no	—
97	C₃×C₉	—	3	1	no	—
98	C₃×C₉	—	3	1	no	—
99	C₃×C₉	—	9	2	no	—
100	C₃×C₉	—	9	1	no	—
101	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
102	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
103	C₁₃	#10624852	1	1	yes	characteristic, direct product factor, Sylow
104	C₃²	—	3	1	no	—
105	C₃²	—	9	1	no	—
106	C₃²	—	9	2	no	—
107	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
108	C₉	—	3	3	no	—
109	C₉	—	3	2	no	—
110	C₉	—	3	1	no	—
111	C₉	—	9	1	no	—
112	C₉	—	9	1	no	—
113	C₉	—	9	2	no	—
114	C₉	—	9	2	no	—
115	C₉	—	9	2	no	—
116	C₉	—	9	1	no	—
117	C₃	—	3	1	no	—
118	C₃	—	9	1	no	—
119	C₃	—	27	2	no	—
120	C₃	C₁₃×#6911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6913

C₃

yes

maximal, complemented

C₁₃×#6912

C₃

yes

maximal, characteristic, complemented

C₁₃×#6900

C₃

yes

maximal, characteristic, complemented

C₁₃×#6883

C₃

yes

maximal, complemented

C₁₃×#6882

C₃

yes

maximal, complemented

C₁₃×#6882

C₃

yes

maximal, characteristic, complemented

C₁₃×#6881

C₃

yes

maximal, characteristic, complemented

C₁₃×#6880

C₃

yes

maximal, characteristic, complemented

C₁₃×#6878

C₃

yes

maximal, complemented

C₁₃×#737

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

characteristic

C₁₃×#733

—

C₁₃×#733

C₃²

yes

—

C₁₃×#733

C₃²

yes

—

C₁₃×#733

C₃²

yes

characteristic

C₁₃×#733

C₃²

yes

—

C₁₃×#732

C₃²

yes

—

C₁₃×#731

—

C₁₃×AΣL(1,𝔽₂₇)

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

C₃²

yes

characteristic

C₉²×C₁₃

C₃²

yes

characteristic

#10624852

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

H(3,𝔽₃)

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

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

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

C₃³

yes

characteristic

#6913

C₃×C₁₃

yes

complemented

#6912

C₃×C₁₃

yes

characteristic, complemented

#6900

C₃×C₁₃

yes

characteristic, complemented

#6883

C₃×C₁₃

yes

complemented

#6882

C₃×C₁₃

yes

complemented

#6882

C₃×C₁₃

yes

characteristic, complemented

#6881

C₃×C₁₃

yes

characteristic, complemented

#6880

C₃×C₁₃

yes

characteristic, complemented

#6878

C₃×C₁₃

yes

complemented

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

—

#737

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

characteristic

#733

—

#733

C₃²×C₁₃

yes

—

#733

C₃²×C₁₃

yes

characteristic

#733

C₃²×C₁₃

yes

—

#733

C₃²×C₁₃

yes

—

#732

C₃²×C₁₃

yes

—

#731

—

AΣL(1,𝔽₂₇)

—

C₉⋊C₉

—

C₉⋊C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

C₃²×C₁₃

yes

characteristic

C₉²

C₃²×C₁₃

yes

characteristic

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

#6911

yes

characteristic

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

H(3,𝔽₃)

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

—

101

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

102

C₃×C₉

C₃³×C₁₃

yes

characteristic

103

C₁₃

#10624852

yes

characteristic, direct product factor, Sylow

104

C₃²

—

105

C₃²

—

106

C₃²

—

107

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

108

C₉

—

109

C₉

—

110

C₉

—

111

C₉

—

112

C₉

—

113

C₉

—

114

C₉

—

115

C₉

—

116

C₉

—

117

C₃

—

118

C₃

—

119

C₃

—

120

C₃

C₁₃×#6911

yes

characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	#6911
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃²×C₁₃ ◁ C₃×C₁₃×3₋¹⁺² ◁ G

subgroup

G/H

center, socle

C₃×C₁₃

#6911

commutator, Frattini, cosocle

C₃×C₉

C₃³×C₁₃

LCS

G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃×C₁₃ ◁ C₃²×C₁₃ ◁ C₃×C₁₃×3₋¹⁺² ◁ G

N	H ≅ G/N	type
1. C₁₃×#6913	C₃	semidirect
2. C₁₃×#6912	C₃	semidirect
3. C₁₃×#6900	C₃	semidirect
4. C₁₃×#6883	C₃	semidirect
5. C₁₃×#6882	C₃	semidirect
6. C₁₃×#6882	C₃	semidirect
7. C₁₃×#6881	C₃	semidirect
8. C₁₃×#6880	C₃	semidirect
9. C₁₃×#6878	C₃	semidirect
26. #10624852	C₁₃	direct (N × H)
44. #6913	C₃×C₁₃	semidirect
45. #6912	C₃×C₁₃	semidirect
46. #6900	C₃×C₁₃	semidirect
47. #6883	C₃×C₁₃	semidirect
48. #6882	C₃×C₁₃	semidirect
49. #6882	C₃×C₁₃	semidirect
50. #6881	C₃×C₁₃	semidirect
51. #6880	C₃×C₁₃	semidirect
52. #6878	C₃×C₁₃	semidirect
103. C₁₃	#10624852	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6913

C₃

semidirect

2. C₁₃×#6912

C₃

semidirect

3. C₁₃×#6900

C₃

semidirect

4. C₁₃×#6883

C₃

semidirect

5. C₁₃×#6882

C₃

semidirect

6. C₁₃×#6882

C₃

semidirect

7. C₁₃×#6881

C₃

semidirect

8. C₁₃×#6880

C₃

semidirect

9. C₁₃×#6878

C₃

semidirect

26. #10624852

C₁₃

direct (N × H)

44. #6913

C₃×C₁₃

semidirect

45. #6912

C₃×C₁₃

semidirect

46. #6900

C₃×C₁₃

semidirect

47. #6883

C₃×C₁₃

semidirect

48. #6882

C₃×C₁₃

semidirect

49. #6882

C₃×C₁₃

semidirect

50. #6881

C₃×C₁₃

semidirect

51. #6880

C₃×C₁₃

semidirect

52. #6878

C₃×C₁₃

semidirect

103. C₁₃

#10624852

direct (N × H)

Subgroups — C₁₃×#10624852 #23745003

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624852 #23745003

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624852 #23745003