Group #23745011 — subgroups

Subgroups — C₃×C₉×C₁₃×3₋¹⁺² #23745011

Order 9477.

1148 conjugacy classes of subgroups; only the 872 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 872 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	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×3₋¹⁺²	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₁₃×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
6	C₃×C₉²×C₁₃	C₃	1	3	yes	maximal, complemented
7	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×3₋¹⁺²	C₉	1	27	yes	direct product factor
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
10	C₃²×C₉×C₁₃	—	3	9	no	—
11	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
13	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
14	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
15	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
16	C₁₃×C₉⋊C₉	C₃²	1	54	yes	complemented
17	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
18	C₉²×C₁₃	C₃²	1	27	yes	complemented
19	C₃×C₉×3₋¹⁺²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃³×C₁₃	—	3	3	no	—
21	C₃³×C₁₃	—	3	6	no	—
22	C₃³×C₁₃	C₃×C₉	1	9	yes	—
23	C₃³×C₁₃	C₃³	1	3	yes	—
24	C₃³×C₁₃	C₃³	1	1	yes	characteristic
25	C₁₃×3₋¹⁺²	C₃×C₉	1	81	yes	direct product factor
26	C₃×C₉×C₁₃	—	3	6	no	—
27	C₃×C₉×C₁₃	—	3	18	no	—
28	C₃×C₉×C₁₃	—	3	27	no	—
29	C₃×C₉×C₁₃	C₃×C₉	1	27	yes	complemented
30	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	direct product factor
31	C₃×C₉×C₁₃	C₃³	1	18	yes	—
32	C₃×C₉×C₁₃	C₃³	1	6	yes	—
33	C₃×C₉×C₁₃	C₃³	1	9	yes	—
34	C₃×C₉×C₁₃	C₃³	1	3	yes	—
35	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
36	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
37	C₉×3₋¹⁺²	C₃×C₁₃	1	27	yes	direct product factor
38	C₃×C₉⋊C₉	C₃×C₁₃	1	6	yes	complemented
39	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
40	C₃×C₉²	C₃×C₁₃	1	3	yes	complemented
41	C₃²×C₁₃	—	3	3	no	—
42	C₃²×C₁₃	—	3	6	no	—
43	C₃²×C₁₃	—	3	27	no	—
44	C₃²×C₁₃	C₃²×C₉	1	9	yes	—
45	C₃²×C₁₃	C₃²×C₉	1	3	yes	—
46	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
47	C₃²×C₁₃	#737	1	6	yes	—
48	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
49	C₉×C₁₃	—	3	6	no	—
50	C₉×C₁₃	—	3	18	no	—
51	C₉×C₁₃	C₃²×C₉	1	27	yes	complemented
52	C₉×C₁₃	C₃×3₋¹⁺²	1	9	yes	direct product factor
53	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
54	C₃×3₋¹⁺²	C₉×C₁₃	1	27	yes	direct product factor
55	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
56	C₃²×C₉	—	3	9	no	—
57	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
58	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
59	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
60	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
61	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
62	C₉⋊C₉	C₃²×C₁₃	1	54	yes	complemented
63	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
64	C₉²	C₃²×C₁₃	1	27	yes	complemented
65	C₃×C₁₃	—	3	9	no	—
66	C₃×C₁₃	C₉×3₋¹⁺²	1	9	yes	direct product factor
67	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
68	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
69	C₃×C₁₃	C₃×#737	1	2	yes	—
70	C₃³	—	3	3	no	—
71	C₃³	—	3	6	no	—
72	C₃³	C₃×C₉×C₁₃	1	9	yes	—
73	C₃³	C₃³×C₁₃	1	3	yes	—
74	C₃³	C₃³×C₁₃	1	1	yes	characteristic
75	3₋¹⁺²	C₃×C₉×C₁₃	1	81	yes	direct product factor
76	C₃×C₉	—	3	6	no	—
77	C₃×C₉	—	3	18	no	—
78	C₃×C₉	—	3	27	no	—
79	C₃×C₉	C₃×C₉×C₁₃	1	27	yes	complemented
80	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	direct product factor
81	C₃×C₉	C₃³×C₁₃	1	18	yes	—
82	C₃×C₉	C₃³×C₁₃	1	6	yes	—
83	C₃×C₉	C₃³×C₁₃	1	9	yes	—
84	C₃×C₉	C₃³×C₁₃	1	3	yes	—
85	C₁₃	C₃×C₉×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
86	C₃²	—	3	27	no	—
87	C₃²	—	3	3	no	—
88	C₃²	—	3	6	no	—
89	C₃²	C₃²×C₉×C₁₃	1	9	yes	—
90	C₃²	C₃²×C₉×C₁₃	1	3	yes	—
91	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
92	C₃²	C₁₃×#737	1	6	yes	—
93	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
94	C₉	—	3	6	no	—
95	C₉	—	3	18	no	—
96	C₉	C₃²×C₉×C₁₃	1	27	yes	complemented
97	C₉	C₃×C₁₃×3₋¹⁺²	1	9	yes	direct product factor
98	C₃	—	3	9	no	—
99	C₃	C₉×C₁₃×3₋¹⁺²	1	9	yes	direct product factor
100	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic
101	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
102	C₃	C₃×C₁₃×#737	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃³×C₉×C₁₃

C₃

yes

maximal, characteristic

C₉×C₁₃×3₋¹⁺²

C₃

yes

maximal, direct product factor

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, complemented

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal

C₃×C₉²×C₁₃

C₃

yes

maximal, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

C₉

yes

direct product factor

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

C₃²

yes

complemented

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₃

C₃²

yes

complemented

C₃×C₉×3₋¹⁺²

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃×C₉

yes

—

C₃³×C₁₃

C₃³

yes

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

C₃×C₉

yes

direct product factor

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

C₃×C₉

yes

complemented

C₃×C₉×C₁₃

3₋¹⁺²

yes

direct product factor

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃×C₉×C₁₃

C₃³

yes

—

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

C₃³×C₉

C₃×C₁₃

yes

characteristic

C₉×3₋¹⁺²

C₃×C₁₃

yes

direct product factor

C₃×C₉⋊C₉

C₃×C₁₃

yes

complemented

C₃×C₃²⋊C₉

C₃×C₁₃

yes

—

C₃×C₉²

C₃×C₁₃

yes

complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃²×C₉

yes

—

C₃²×C₁₃

C₃²×C₉

yes

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

#737

yes

—

C₃²×C₁₃

C₃⁴

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₃²×C₉

yes

complemented

C₉×C₁₃

C₃×3₋¹⁺²

yes

direct product factor

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

C₉×C₁₃

yes

direct product factor

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

C₃²×C₁₃

yes

complemented

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₉²

C₃²×C₁₃

yes

complemented

C₃×C₁₃

—

C₃×C₁₃

C₉×3₋¹⁺²

yes

direct product factor

C₃×C₁₃

C₃³×C₉

yes

characteristic

C₃×C₁₃

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₃

C₃×#737

yes

—

C₃³

—

C₃³

—

C₃³

C₃×C₉×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

C₃×C₉×C₁₃

yes

direct product factor

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₉×C₁₃

yes

complemented

C₃×C₉

C₁₃×3₋¹⁺²

yes

direct product factor

C₃×C₉

C₃³×C₁₃

yes

—

C₃×C₉

C₃³×C₁₃

yes

—

C₃×C₉

C₃³×C₁₃

yes

—

C₃×C₉

C₃³×C₁₃

yes

—

C₁₃

C₃×C₉×3₋¹⁺²

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃²×C₉×C₁₃

yes

—

C₃²

C₃²×C₉×C₁₃

yes

—

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₁₃×#737

yes

—

C₃²

C₃⁴×C₁₃

yes

characteristic

C₉

—

C₉

—

C₉

C₃²×C₉×C₁₃

yes

complemented

C₉

C₃×C₁₃×3₋¹⁺²

yes

direct product factor

C₃

—

C₃

C₉×C₁₃×3₋¹⁺²

yes

direct product factor

100

C₃

C₃³×C₉×C₁₃

yes

characteristic

101

C₃

C₃²×C₁₃×3₋¹⁺²

yes

characteristic

102

C₃

C₃×C₁₃×#737

yes

—

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

subgroup

G/H

center

C₃²×C₉×C₁₃

C₃²

commutator

C₃

C₃³×C₉×C₁₃

Frattini, cosocle

C₃²

C₃⁴×C₁₃

socle

C₃³×C₁₃

C₃³

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
3. C₉×C₁₃×3₋¹⁺²	C₃	direct (N × H)
4. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
6. C₃×C₉²×C₁₃	C₃	semidirect
8. C₃×C₁₃×3₋¹⁺²	C₉	direct (N × H)
16. C₁₃×C₉⋊C₉	C₃²	semidirect
18. C₉²×C₁₃	C₃²	semidirect
19. C₃×C₉×3₋¹⁺²	C₁₃	direct (N × H)
25. C₁₃×3₋¹⁺²	C₃×C₉	direct (N × H)
29. C₃×C₉×C₁₃	C₃×C₉	semidirect
30. C₃×C₉×C₁₃	3₋¹⁺²	direct (N × H)
37. C₉×3₋¹⁺²	C₃×C₁₃	direct (N × H)
38. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
40. C₃×C₉²	C₃×C₁₃	semidirect
51. C₉×C₁₃	C₃²×C₉	semidirect
52. C₉×C₁₃	C₃×3₋¹⁺²	direct (N × H)
54. C₃×3₋¹⁺²	C₉×C₁₃	direct (N × H)
62. C₉⋊C₉	C₃²×C₁₃	semidirect
64. C₉²	C₃²×C₁₃	semidirect
66. C₃×C₁₃	C₉×3₋¹⁺²	direct (N × H)
75. 3₋¹⁺²	C₃×C₉×C₁₃	direct (N × H)
79. C₃×C₉	C₃×C₉×C₁₃	semidirect
80. C₃×C₉	C₁₃×3₋¹⁺²	direct (N × H)
85. C₁₃	C₃×C₉×3₋¹⁺²	direct (N × H)
96. C₉	C₃²×C₉×C₁₃	semidirect
97. C₉	C₃×C₁₃×3₋¹⁺²	direct (N × H)
99. C₃	C₉×C₁₃×3₋¹⁺²	direct (N × H)

H ≅ G/N

type

3. C₉×C₁₃×3₋¹⁺²

C₃

direct (N × H)

4. C₃×C₁₃×C₉⋊C₉

C₃

semidirect

6. C₃×C₉²×C₁₃

C₃

semidirect

8. C₃×C₁₃×3₋¹⁺²

C₉

direct (N × H)

16. C₁₃×C₉⋊C₉

C₃²

semidirect

18. C₉²×C₁₃

C₃²

semidirect

19. C₃×C₉×3₋¹⁺²

C₁₃

direct (N × H)

25. C₁₃×3₋¹⁺²

C₃×C₉

direct (N × H)

29. C₃×C₉×C₁₃

C₃×C₉

semidirect

30. C₃×C₉×C₁₃

3₋¹⁺²

direct (N × H)

37. C₉×3₋¹⁺²

C₃×C₁₃

direct (N × H)

38. C₃×C₉⋊C₉

C₃×C₁₃

semidirect

40. C₃×C₉²

C₃×C₁₃

semidirect

51. C₉×C₁₃

C₃²×C₉

semidirect

52. C₉×C₁₃

C₃×3₋¹⁺²

direct (N × H)

54. C₃×3₋¹⁺²

C₉×C₁₃

direct (N × H)

62. C₉⋊C₉

C₃²×C₁₃

semidirect

64. C₉²

C₃²×C₁₃

semidirect

66. C₃×C₁₃

C₉×3₋¹⁺²

direct (N × H)

75. 3₋¹⁺²

C₃×C₉×C₁₃

direct (N × H)

79. C₃×C₉

C₃×C₉×C₁₃

semidirect

80. C₃×C₉

C₁₃×3₋¹⁺²

direct (N × H)

85. C₁₃

C₃×C₉×3₋¹⁺²

direct (N × H)

96. C₉

C₃²×C₉×C₁₃

semidirect

97. C₉

C₃×C₁₃×3₋¹⁺²

direct (N × H)

99. C₃

C₉×C₁₃×3₋¹⁺²

direct (N × H)

Subgroups — C₃×C₉×C₁₃×3₋¹⁺² #23745011

Conjugacy classes of subgroups

Complements

Subgroups — C3×C9×C13×3−1+2 #23745011

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₉×C₁₃×3₋¹⁺² #23745011