Group #23745002 — subgroups

Subgroups — C₁₃×#10624851 #23745002

Order 9477.

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

normal subgroups only

This group has 200 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×#6911	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×#6881	C₃	1	4	yes	maximal, complemented
6	C₁₃×#6879	C₃	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#6878	C₃	1	2	yes	maximal, complemented
8	C₁₃×#737	—	3	2	no	—
9	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
10	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
11	C₃×C₁₃×H(3,𝔽₃)	—	3	1	no	—
12	C₁₃×#733	C₃²	1	4	yes	complemented
13	C₁₃×#732	—	3	2	no	—
14	C₁₃×#732	C₃²	1	2	yes	—
15	C₁₃×#732	C₃²	1	1	yes	characteristic
16	C₁₃×#732	C₃²	1	2	yes	complemented
17	C₁₃×#731	—	3	2	no	—
18	C₁₃×AΣL(1,𝔽₂₇)	—	3	2	no	—
19	C₁₃×C₉⋊C₉	—	3	2	no	—
20	C₁₃×C₉⋊C₉	C₃²	1	2	yes	complemented
21	C₉²×C₁₃	C₃²	1	1	yes	characteristic, complemented
22	#10624851	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₃³×C₁₃	—	9	1	no	—
24	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
25	C₁₃×3₋¹⁺²	—	3	4	no	—
26	C₁₃×3₋¹⁺²	—	9	1	no	—
27	C₁₃×3₋¹⁺²	—	9	3	no	—
28	C₁₃×3₋¹⁺²	—	9	4	no	—
29	C₁₃×H(3,𝔽₃)	—	3	2	no	—
30	C₁₃×H(3,𝔽₃)	—	3	2	no	—
31	C₁₃×H(3,𝔽₃)	—	3	1	no	—
32	C₁₃×H(3,𝔽₃)	—	9	2	no	—
33	C₃×C₉×C₁₃	—	3	1	no	—
34	C₃×C₉×C₁₃	—	3	2	no	—
35	C₃×C₉×C₁₃	—	9	2	no	—
36	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
37	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
38	#6913	C₃×C₁₃	1	2	yes	complemented
39	#6911	C₃×C₁₃	1	1	yes	characteristic, complemented
40	#6900	C₃×C₁₃	1	1	yes	characteristic, complemented
41	#6883	C₃×C₁₃	1	2	yes	complemented
42	#6881	C₃×C₁₃	1	4	yes	complemented
43	#6879	C₃×C₁₃	1	1	yes	characteristic, complemented
44	#6878	C₃×C₁₃	1	2	yes	complemented
45	C₃²×C₁₃	—	3	1	no	—
46	C₃²×C₁₃	—	9	1	no	—
47	C₃²×C₁₃	—	9	2	no	—
48	C₃²×C₁₃	—	9	2	no	—
49	C₃²×C₁₃	—	9	1	no	—
50	C₃²×C₁₃	—	27	3	no	—
51	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
52	C₉×C₁₃	—	3	3	no	—
53	C₉×C₁₃	—	3	2	no	—
54	C₉×C₁₃	—	3	1	no	—
55	C₉×C₁₃	—	9	2	no	—
56	C₉×C₁₃	—	9	4	no	—
57	#737	—	3	2	no	—
58	C₃×3₋¹⁺²	—	3	1	no	—
59	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
60	C₃×H(3,𝔽₃)	—	3	1	no	—
61	#733	C₃²×C₁₃	1	4	yes	complemented
62	#732	—	3	2	no	—
63	#732	C₃²×C₁₃	1	2	yes	—
64	#732	C₃²×C₁₃	1	1	yes	characteristic
65	#732	C₃²×C₁₃	1	2	yes	complemented
66	#731	—	3	2	no	—
67	AΣL(1,𝔽₂₇)	—	3	2	no	—
68	C₉⋊C₉	—	3	2	no	—
69	C₉⋊C₉	C₃²×C₁₃	1	2	yes	complemented
70	C₉²	C₃²×C₁₃	1	1	yes	characteristic, complemented
71	C₃×C₁₃	—	3	1	no	—
72	C₃×C₁₃	—	9	1	no	—
73	C₃×C₁₃	—	27	2	no	—
74	C₃×C₁₃	—	27	2	no	—
75	C₃×C₁₃	—	27	1	no	—
76	C₃×C₁₃	#6911	1	1	yes	characteristic
77	C₃³	—	9	1	no	—
78	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
79	3₋¹⁺²	—	3	4	no	—
80	3₋¹⁺²	—	9	1	no	—
81	3₋¹⁺²	—	9	3	no	—
82	3₋¹⁺²	—	9	4	no	—
83	H(3,𝔽₃)	—	3	2	no	—
84	H(3,𝔽₃)	—	3	2	no	—
85	H(3,𝔽₃)	—	3	1	no	—
86	H(3,𝔽₃)	—	9	2	no	—
87	C₃×C₉	—	3	1	no	—
88	C₃×C₉	—	3	2	no	—
89	C₃×C₉	—	9	2	no	—
90	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
91	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
92	C₁₃	#10624851	1	1	yes	characteristic, direct product factor, Sylow
93	C₃²	—	3	1	no	—
94	C₃²	—	9	1	no	—
95	C₃²	—	9	2	no	—
96	C₃²	—	9	2	no	—
97	C₃²	—	9	1	no	—
98	C₃²	—	27	3	no	—
99	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
100	C₉	—	3	3	no	—
101	C₉	—	3	2	no	—
102	C₉	—	3	1	no	—
103	C₉	—	9	2	no	—
104	C₉	—	9	4	no	—
105	C₃	—	3	1	no	—
106	C₃	—	9	1	no	—
107	C₃	—	27	2	no	—
108	C₃	—	27	1	no	—
109	C₃	—	27	2	no	—
110	C₃	C₁₃×#6911	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6913

C₃

yes

maximal, complemented

C₁₃×#6911

C₃

yes

maximal, characteristic, complemented

C₁₃×#6900

C₃

yes

maximal, characteristic, complemented

C₁₃×#6883

C₃

yes

maximal, complemented

C₁₃×#6881

C₃

yes

maximal, complemented

C₁₃×#6879

C₃

yes

maximal, characteristic, complemented

C₁₃×#6878

C₃

yes

maximal, complemented

C₁₃×#737

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

characteristic

C₃×C₁₃×H(3,𝔽₃)

—

C₁₃×#733

C₃²

yes

complemented

C₁₃×#732

—

C₁₃×#732

C₃²

yes

—

C₁₃×#732

C₃²

yes

characteristic

C₁₃×#732

C₃²

yes

complemented

C₁₃×#731

—

C₁₃×AΣL(1,𝔽₂₇)

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

C₃²

yes

complemented

C₉²×C₁₃

C₃²

yes

characteristic, complemented

#10624851

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

H(3,𝔽₃)

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×H(3,𝔽₃)

—

C₁₃×H(3,𝔽₃)

—

C₁₃×H(3,𝔽₃)

—

C₁₃×H(3,𝔽₃)

—

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

#6911

C₃×C₁₃

yes

characteristic, complemented

#6900

C₃×C₁₃

yes

characteristic, complemented

#6883

C₃×C₁₃

yes

complemented

#6881

C₃×C₁₃

yes

complemented

#6879

C₃×C₁₃

yes

characteristic, complemented

#6878

C₃×C₁₃

yes

complemented

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

—

#737

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

characteristic

C₃×H(3,𝔽₃)

—

#733

C₃²×C₁₃

yes

complemented

#732

—

#732

C₃²×C₁₃

yes

—

#732

C₃²×C₁₃

yes

characteristic

#732

C₃²×C₁₃

yes

complemented

#731

—

AΣL(1,𝔽₂₇)

—

C₉⋊C₉

—

C₉⋊C₉

C₃²×C₁₃

yes

complemented

C₉²

C₃²×C₁₃

yes

characteristic, complemented

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

#6911

yes

characteristic

C₃³

—

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

—

—

—

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

C₃×C₉

C₃³×C₁₃

yes

characteristic

C₁₃

#10624851

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

100

C₉

—

101

C₉

—

102

C₉

—

103

C₉

—

104

C₉

—

105

C₃

—

106

C₃

—

107

C₃

—

108

C₃

—

109

C₃

—

110

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×#6911	C₃	semidirect
3. C₁₃×#6900	C₃	semidirect
4. C₁₃×#6883	C₃	semidirect
5. C₁₃×#6881	C₃	semidirect
6. C₁₃×#6879	C₃	semidirect
7. C₁₃×#6878	C₃	semidirect
12. C₁₃×#733	C₃²	semidirect
16. C₁₃×#732	C₃²	semidirect
20. C₁₃×C₉⋊C₉	C₃²	semidirect
21. C₉²×C₁₃	C₃²	semidirect
22. #10624851	C₁₃	direct (N × H)
38. #6913	C₃×C₁₃	semidirect
39. #6911	C₃×C₁₃	semidirect
40. #6900	C₃×C₁₃	semidirect
41. #6883	C₃×C₁₃	semidirect
42. #6881	C₃×C₁₃	semidirect
43. #6879	C₃×C₁₃	semidirect
44. #6878	C₃×C₁₃	semidirect
61. #733	C₃²×C₁₃	semidirect
65. #732	C₃²×C₁₃	semidirect
69. C₉⋊C₉	C₃²×C₁₃	semidirect
70. C₉²	C₃²×C₁₃	semidirect
92. C₁₃	#10624851	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6913

C₃

semidirect

2. C₁₃×#6911

C₃

semidirect

3. C₁₃×#6900

C₃

semidirect

4. C₁₃×#6883

C₃

semidirect

5. C₁₃×#6881

C₃

semidirect

6. C₁₃×#6879

C₃

semidirect

7. C₁₃×#6878

C₃

semidirect

12. C₁₃×#733

C₃²

semidirect

16. C₁₃×#732

C₃²

semidirect

20. C₁₃×C₉⋊C₉

C₃²

semidirect

21. C₉²×C₁₃

C₃²

semidirect

22. #10624851

C₁₃

direct (N × H)

38. #6913

C₃×C₁₃

semidirect

39. #6911

C₃×C₁₃

semidirect

40. #6900

C₃×C₁₃

semidirect

41. #6883

C₃×C₁₃

semidirect

42. #6881

C₃×C₁₃

semidirect

43. #6879

C₃×C₁₃

semidirect

44. #6878

C₃×C₁₃

semidirect

61. #733

C₃²×C₁₃

semidirect

65. #732

C₃²×C₁₃

semidirect

69. C₉⋊C₉

C₃²×C₁₃

semidirect

70. C₉²

C₃²×C₁₃

semidirect

92. C₁₃

#10624851

direct (N × H)

Subgroups — C₁₃×#10624851 #23745002

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624851 #23745002

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624851 #23745002