Group #23745004 — subgroups

Subgroups — C₁₃×#10624853 #23745004

Order 9477.

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

normal subgroups only

This group has 190 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×#6899	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	C₃²	1	1	yes	characteristic
10	C₃×C₁₃×H(3,𝔽₃)	—	3	1	no	—
11	C₁₃×#733	C₃²	1	4	yes	complemented
12	C₁₃×#732	—	3	2	no	—
13	C₁₃×#732	C₃²	1	2	yes	—
14	C₁₃×#732	C₃²	1	1	yes	characteristic
15	C₁₃×#732	C₃²	1	2	yes	complemented
16	C₁₃×#731	—	3	2	no	—
17	C₁₃×AΣL(1,𝔽₂₇)	—	3	2	no	—
18	C₁₃×C₉⋊C₉	—	3	2	no	—
19	C₁₃×C₉⋊C₉	C₃²	1	2	yes	complemented
20	C₁₃×C₃²⋊C₉	—	3	1	no	—
21	C₉²×C₁₃	C₃²	1	1	yes	characteristic, complemented
22	#10624853	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	4	no	—
28	C₁₃×H(3,𝔽₃)	—	3	2	no	—
29	C₁₃×H(3,𝔽₃)	—	3	2	no	—
30	C₁₃×H(3,𝔽₃)	—	3	1	no	—
31	C₁₃×H(3,𝔽₃)	—	9	2	no	—
32	C₃×C₉×C₁₃	—	3	1	no	—
33	C₃×C₉×C₁₃	—	3	2	no	—
34	C₃×C₉×C₁₃	—	9	2	no	—
35	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
36	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
37	#6913	C₃×C₁₃	1	2	yes	complemented
38	#6911	C₃×C₁₃	1	1	yes	characteristic, complemented
39	#6899	C₃×C₁₃	1	1	yes	characteristic, complemented
40	#6883	C₃×C₁₃	1	2	yes	complemented
41	#6881	C₃×C₁₃	1	4	yes	complemented
42	#6879	C₃×C₁₃	1	1	yes	characteristic, complemented
43	#6878	C₃×C₁₃	1	2	yes	complemented
44	C₃²×C₁₃	—	3	1	no	—
45	C₃²×C₁₃	—	9	1	no	—
46	C₃²×C₁₃	—	9	2	no	—
47	C₃²×C₁₃	—	9	2	no	—
48	C₃²×C₁₃	—	9	1	no	—
49	C₃²×C₁₃	—	27	3	no	—
50	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₉×C₁₃	—	3	2	no	—
52	C₉×C₁₃	—	3	1	no	—
53	C₉×C₁₃	—	9	1	no	—
54	C₉×C₁₃	—	9	2	no	—
55	C₉×C₁₃	—	9	4	no	—
56	#737	—	3	2	no	—
57	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
58	C₃×H(3,𝔽₃)	—	3	1	no	—
59	#733	C₃²×C₁₃	1	4	yes	complemented
60	#732	—	3	2	no	—
61	#732	C₃²×C₁₃	1	2	yes	—
62	#732	C₃²×C₁₃	1	1	yes	characteristic
63	#732	C₃²×C₁₃	1	2	yes	complemented
64	#731	—	3	2	no	—
65	AΣL(1,𝔽₂₇)	—	3	2	no	—
66	C₉⋊C₉	—	3	2	no	—
67	C₉⋊C₉	C₃²×C₁₃	1	2	yes	complemented
68	C₃²⋊C₉	—	3	1	no	—
69	C₉²	C₃²×C₁₃	1	1	yes	characteristic, complemented
70	C₃×C₁₃	—	3	1	no	—
71	C₃×C₁₃	—	9	1	no	—
72	C₃×C₁₃	—	27	2	no	—
73	C₃×C₁₃	—	27	2	no	—
74	C₃×C₁₃	—	27	1	no	—
75	C₃×C₁₃	#6911	1	1	yes	characteristic
76	C₃³	—	9	1	no	—
77	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	3₋¹⁺²	—	3	4	no	—
79	3₋¹⁺²	—	9	1	no	—
80	3₋¹⁺²	—	9	4	no	—
81	H(3,𝔽₃)	—	3	2	no	—
82	H(3,𝔽₃)	—	3	2	no	—
83	H(3,𝔽₃)	—	3	1	no	—
84	H(3,𝔽₃)	—	9	2	no	—
85	C₃×C₉	—	3	1	no	—
86	C₃×C₉	—	3	2	no	—
87	C₃×C₉	—	9	2	no	—
88	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
89	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
90	C₁₃	#10624853	1	1	yes	characteristic, direct product factor, Sylow
91	C₃²	—	3	1	no	—
92	C₃²	—	9	1	no	—
93	C₃²	—	9	2	no	—
94	C₃²	—	9	2	no	—
95	C₃²	—	9	1	no	—
96	C₃²	—	27	3	no	—
97	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
98	C₉	—	3	2	no	—
99	C₉	—	3	1	no	—
100	C₉	—	9	1	no	—
101	C₉	—	9	2	no	—
102	C₉	—	9	4	no	—
103	C₃	—	3	1	no	—
104	C₃	—	9	1	no	—
105	C₃	—	27	2	no	—
106	C₃	—	27	1	no	—
107	C₃	—	27	2	no	—
108	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×#6899

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

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

C₁₃×C₃²⋊C₉

—

C₉²×C₁₃

C₃²

yes

characteristic, complemented

#10624853

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×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

#6899

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

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

C₃²⋊C₉

—

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

—

—

—

—

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

C₃×C₉

C₃³×C₁₃

yes

characteristic

C₁₃

#10624853

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

C₉

—

C₉

—

100

C₉

—

101

C₉

—

102

C₉

—

103

C₃

—

104

C₃

—

105

C₃

—

106

C₃

—

107

C₃

—

108

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×#6899	C₃	semidirect
4. C₁₃×#6883	C₃	semidirect
5. C₁₃×#6881	C₃	semidirect
6. C₁₃×#6879	C₃	semidirect
7. C₁₃×#6878	C₃	semidirect
11. C₁₃×#733	C₃²	semidirect
15. C₁₃×#732	C₃²	semidirect
19. C₁₃×C₉⋊C₉	C₃²	semidirect
21. C₉²×C₁₃	C₃²	semidirect
22. #10624853	C₁₃	direct (N × H)
37. #6913	C₃×C₁₃	semidirect
38. #6911	C₃×C₁₃	semidirect
39. #6899	C₃×C₁₃	semidirect
40. #6883	C₃×C₁₃	semidirect
41. #6881	C₃×C₁₃	semidirect
42. #6879	C₃×C₁₃	semidirect
43. #6878	C₃×C₁₃	semidirect
59. #733	C₃²×C₁₃	semidirect
63. #732	C₃²×C₁₃	semidirect
67. C₉⋊C₉	C₃²×C₁₃	semidirect
69. C₉²	C₃²×C₁₃	semidirect
90. C₁₃	#10624853	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6913

C₃

semidirect

2. C₁₃×#6911

C₃

semidirect

3. C₁₃×#6899

C₃

semidirect

4. C₁₃×#6883

C₃

semidirect

5. C₁₃×#6881

C₃

semidirect

6. C₁₃×#6879

C₃

semidirect

7. C₁₃×#6878

C₃

semidirect

11. C₁₃×#733

C₃²

semidirect

15. C₁₃×#732

C₃²

semidirect

19. C₁₃×C₉⋊C₉

C₃²

semidirect

21. C₉²×C₁₃

C₃²

semidirect

22. #10624853

C₁₃

direct (N × H)

37. #6913

C₃×C₁₃

semidirect

38. #6911

C₃×C₁₃

semidirect

39. #6899

C₃×C₁₃

semidirect

40. #6883

C₃×C₁₃

semidirect

41. #6881

C₃×C₁₃

semidirect

42. #6879

C₃×C₁₃

semidirect

43. #6878

C₃×C₁₃

semidirect

59. #733

C₃²×C₁₃

semidirect

63. #732

C₃²×C₁₃

semidirect

67. C₉⋊C₉

C₃²×C₁₃

semidirect

69. C₉²

C₃²×C₁₃

semidirect

90. C₁₃

#10624853

direct (N × H)

Subgroups — C₁₃×#10624853 #23745004

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624853 #23745004

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624853 #23745004