Group #23744714 — subgroups

Subgroups — C₁₃×#10624563 #23744714

Order 9477.

758 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 152 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, complemented
2	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃⁴×C₁₃	C₃²	1	3	yes	—
7	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
9	C₃×C₁₃×H(3,𝔽₃)	—	3	3	no	—
10	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
11	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
13	C₁₃×C₃²⋊C₉	—	3	6	no	—
14	C₁₃×C₃²⋊C₉	—	3	27	no	—
15	#10624563	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	3	9	no	—
17	C₃³×C₁₃	—	3	3	no	—
18	C₃³×C₁₃	—	3	3	no	—
19	C₃³×C₁₃	—	3	3	no	—
20	C₃³×C₁₃	—	3	6	no	—
21	C₃³×C₁₃	—	3	18	no	—
22	C₃³×C₁₃	—	3	6	no	—
23	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
24	C₃³×C₁₃	3₋¹⁺²	1	9	yes	complemented
25	C₃³×C₁₃	C₃³	1	1	yes	characteristic
26	C₁₃×3₋¹⁺²	—	3	27	no	—
27	C₁₃×H(3,𝔽₃)	—	3	27	no	—
28	C₃×C₉×C₁₃	—	3	3	no	—
29	C₃×C₉×C₁₃	—	3	6	no	—
30	C₃×C₉×C₁₃	—	3	6	no	—
31	C₃×C₉×C₁₃	—	3	18	no	—
32	C₃×C₉×C₁₃	H(3,𝔽₃)	1	9	yes	complemented
33	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic, complemented
34	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
35	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	complemented
36	C₃×C₃²⋊C₉	C₃×C₁₃	1	9	yes	complemented
37	C₃²×C₁₃	—	3	3	no	—
38	C₃²×C₁₃	—	3	3	no	—
39	C₃²×C₁₃	—	3	9	no	—
40	C₃²×C₁₃	—	3	27	no	—
41	C₃²×C₁₃	—	3	6	no	—
42	C₃²×C₁₃	—	9	3	no	—
43	C₃²×C₁₃	—	9	18	no	—
44	C₃²×C₁₃	—	9	9	no	—
45	C₃²×C₁₃	—	9	6	no	—
46	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
47	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
48	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
49	C₃²×C₁₃	#737	1	6	yes	—
50	C₉×C₁₃	—	3	9	no	—
51	C₉×C₁₃	—	9	6	no	—
52	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
53	C₃⁴	C₃²×C₁₃	1	3	yes	—
54	C₃×3₋¹⁺²	—	3	3	no	—
55	C₃×3₋¹⁺²	—	3	9	no	—
56	C₃×H(3,𝔽₃)	—	3	3	no	—
57	C₃×H(3,𝔽₃)	—	3	9	no	—
58	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
59	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
60	C₃²⋊C₉	—	3	6	no	—
61	C₃²⋊C₉	—	3	27	no	—
62	C₃×C₁₃	—	9	3	no	—
63	C₃×C₁₃	—	9	9	no	—
64	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
65	C₃×C₁₃	#6891	1	1	yes	characteristic
66	C₃×C₁₃	C₉⋊H(3,𝔽₃)	1	9	yes	—
67	C₃×C₁₃	#6893	1	2	yes	—
68	C₃³	—	3	9	no	—
69	C₃³	—	3	3	no	—
70	C₃³	—	3	3	no	—
71	C₃³	—	3	3	no	—
72	C₃³	—	3	6	no	—
73	C₃³	—	3	18	no	—
74	C₃³	—	3	6	no	—
75	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
76	C₃³	C₁₃×3₋¹⁺²	1	9	yes	complemented
77	C₃³	C₃³×C₁₃	1	1	yes	characteristic
78	3₋¹⁺²	—	3	27	no	—
79	H(3,𝔽₃)	—	3	27	no	—
80	C₃×C₉	—	3	3	no	—
81	C₃×C₉	—	3	6	no	—
82	C₃×C₉	—	3	6	no	—
83	C₃×C₉	—	3	18	no	—
84	C₃×C₉	C₁₃×H(3,𝔽₃)	1	9	yes	complemented
85	C₁₃	#10624563	1	1	yes	characteristic, direct product factor, Sylow
86	C₃²	—	3	3	no	—
87	C₃²	—	3	3	no	—
88	C₃²	—	3	9	no	—
89	C₃²	—	3	27	no	—
90	C₃²	—	3	6	no	—
91	C₃²	—	9	3	no	—
92	C₃²	—	9	18	no	—
93	C₃²	—	9	9	no	—
94	C₃²	—	9	6	no	—
95	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
96	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
97	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
98	C₃²	C₁₃×#737	1	6	yes	—
99	C₉	—	3	9	no	—
100	C₉	—	9	6	no	—
101	C₃	—	9	3	no	—
102	C₃	—	9	9	no	—
103	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
104	C₃	C₁₃×#6891	1	1	yes	characteristic
105	C₃	C₁₃×C₉⋊H(3,𝔽₃)	1	9	yes	—
106	C₃	C₁₃×#6893	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic, complemented

C₃²×C₁₃×H(3,𝔽₃)

C₃

yes

maximal, characteristic

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, complemented

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃⁴×C₁₃

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×H(3,𝔽₃)

—

C₃×C₁₃×H(3,𝔽₃)

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

#10624563

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

H(3,𝔽₃)

yes

—

C₃³×C₁₃

3₋¹⁺²

yes

complemented

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×H(3,𝔽₃)

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

complemented

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic, complemented

C₃²×H(3,𝔽₃)

C₃×C₁₃

yes

characteristic

C₃×C₃²⋊C₉

C₃×C₁₃

yes

complemented

C₃×C₃²⋊C₉

C₃×C₁₃

yes

complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

#737

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃⁴

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×H(3,𝔽₃)

—

C₃×H(3,𝔽₃)

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

C₃²⋊H(3,𝔽₃)

yes

characteristic

C₃×C₁₃

#6891

yes

characteristic

C₃×C₁₃

C₉⋊H(3,𝔽₃)

yes

—

C₃×C₁₃

#6893

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₁₃×H(3,𝔽₃)

yes

—

C₃³

C₁₃×3₋¹⁺²

yes

complemented

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

H(3,𝔽₃)

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

complemented

C₁₃

#10624563

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

—

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₁₃×#737

yes

—

C₉

—

100

C₉

—

101

C₃

—

102

C₃

—

103

C₃

C₁₃×C₃²⋊H(3,𝔽₃)

yes

characteristic

104

C₃

C₁₃×#6891

yes

characteristic

105

C₃

C₁₃×C₉⋊H(3,𝔽₃)

yes

—

106

C₃

C₁₃×#6893

yes

—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃³×C₁₃

C₃³

commutator, Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃²×C₁₃×H(3,𝔽₃)

C₃

LCS

G ▷ C₃³ ▷ C₁

UCS

C₁ ◁ C₃³×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₃²×C₁₃×3₋¹⁺²	C₃	semidirect
3. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
4. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
15. #10624563	C₁₃	direct (N × H)
24. C₃³×C₁₃	3₋¹⁺²	semidirect
32. C₃×C₉×C₁₃	H(3,𝔽₃)	semidirect
33. C₃²×3₋¹⁺²	C₃×C₁₃	semidirect
35. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
36. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
76. C₃³	C₁₃×3₋¹⁺²	semidirect
84. C₃×C₉	C₁₃×H(3,𝔽₃)	semidirect
85. C₁₃	#10624563	direct (N × H)

H ≅ G/N

type

1. C₃²×C₁₃×3₋¹⁺²

C₃

semidirect

3. C₃×C₁₃×C₃²⋊C₉

C₃

semidirect

4. C₃×C₁₃×C₃²⋊C₉

C₃

semidirect

15. #10624563

C₁₃

direct (N × H)

24. C₃³×C₁₃

3₋¹⁺²

semidirect

32. C₃×C₉×C₁₃

H(3,𝔽₃)

semidirect

33. C₃²×3₋¹⁺²

C₃×C₁₃

semidirect

35. C₃×C₃²⋊C₉

C₃×C₁₃

semidirect

36. C₃×C₃²⋊C₉

C₃×C₁₃

semidirect

76. C₃³

C₁₃×3₋¹⁺²

semidirect

84. C₃×C₉

C₁₃×H(3,𝔽₃)

semidirect

85. C₁₃

#10624563

direct (N × H)

Subgroups — C₁₃×#10624563 #23744714

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624563 #23744714

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624563 #23744714