Group #23744895 — subgroups

Subgroups — C₁₃×#10624744 #23744895

Order 9477.

458 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 104 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	C₃×C₁₃×#733	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	2	yes	maximal
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₃	—	3	1	no	—
11	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
12	C₁₃×#733	—	3	27	no	—
13	C₁₃×C₃²⋊C₉	—	3	2	no	—
14	C₁₃×C₃²⋊C₉	—	3	1	no	—
15	C₁₃×C₃²⋊C₉	—	3	4	no	—
16	C₁₃×C₃²⋊C₉	—	3	2	no	—
17	#10624744	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	—	3	3	no	—
19	C₃³×C₁₃	—	3	3	no	—
20	C₃³×C₁₃	—	9	2	no	—
21	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
22	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃³×C₁₃	C₃³	1	1	yes	characteristic
24	C₁₃×3₋¹⁺²	—	3	18	no	—
25	C₁₃×3₋¹⁺²	—	3	6	no	—
26	C₁₃×3₋¹⁺²	—	3	18	no	—
27	C₁₃×3₋¹⁺²	H(3,𝔽₃)	1	9	yes	—
28	C₃×C₉×C₁₃	—	3	9	no	—
29	C₃×C₉×C₁₃	—	3	3	no	—
30	C₃×C₉×C₁₃	—	3	9	no	—
31	C₃×C₉×C₁₃	—	3	3	no	—
32	C₃×C₉×C₁₃	—	3	6	no	—
33	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
34	C₃×#733	C₃×C₁₃	1	9	yes	complemented
35	#6891	C₃×C₁₃	1	2	yes	—
36	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
37	C₃²×C₁₃	—	3	2	no	—
38	C₃²×C₁₃	—	3	2	no	—
39	C₃²×C₁₃	—	3	1	no	—
40	C₃²×C₁₃	—	3	1	no	—
41	C₃²×C₁₃	—	3	4	no	—
42	C₃²×C₁₃	—	3	2	no	—
43	C₃²×C₁₃	—	3	2	no	—
44	C₃²×C₁₃	—	9	9	no	—
45	C₃²×C₁₃	#733	1	3	yes	complemented
46	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
47	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
48	C₉×C₁₃	—	3	9	no	—
49	C₉×C₁₃	—	9	3	no	—
50	C₉×C₁₃	—	9	6	no	—
51	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
52	C₃×3₋¹⁺²	—	3	2	no	—
53	C₃×3₋¹⁺²	—	3	9	no	—
54	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
55	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
56	C₃²×C₉	—	3	1	no	—
57	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
58	#733	—	3	27	no	—
59	C₃²⋊C₉	—	3	2	no	—
60	C₃²⋊C₉	—	3	1	no	—
61	C₃²⋊C₉	—	3	4	no	—
62	C₃²⋊C₉	—	3	2	no	—
63	C₃×C₁₃	—	3	3	no	—
64	C₃×C₁₃	—	3	3	no	—
65	C₃×C₁₃	—	9	2	no	—
66	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
67	C₃×C₁₃	C₃×#733	1	1	yes	characteristic
68	C₃×C₁₃	#6912	1	2	yes	—
69	C₃³	—	3	3	no	—
70	C₃³	—	3	3	no	—
71	C₃³	—	9	2	no	—
72	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
73	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
74	C₃³	C₃³×C₁₃	1	1	yes	characteristic
75	3₋¹⁺²	—	3	18	no	—
76	3₋¹⁺²	—	3	6	no	—
77	3₋¹⁺²	—	3	18	no	—
78	3₋¹⁺²	C₁₃×H(3,𝔽₃)	1	9	yes	—
79	C₃×C₉	—	3	9	no	—
80	C₃×C₉	—	3	3	no	—
81	C₃×C₉	—	3	3	no	—
82	C₃×C₉	—	3	6	no	—
83	C₃×C₉	—	3	9	no	—
84	C₁₃	#10624744	1	1	yes	characteristic, direct product factor, Sylow
85	C₃²	—	3	1	no	—
86	C₃²	—	3	1	no	—
87	C₃²	—	3	2	no	—
88	C₃²	—	3	2	no	—
89	C₃²	—	3	2	no	—
90	C₃²	—	3	2	no	—
91	C₃²	—	3	4	no	—
92	C₃²	—	9	9	no	—
93	C₃²	C₁₃×#733	1	3	yes	complemented
94	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
95	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
96	C₉	—	3	9	no	—
97	C₉	—	9	3	no	—
98	C₉	—	9	6	no	—
99	C₃	—	3	3	no	—
100	C₃	—	3	3	no	—
101	C₃	—	9	2	no	—
102	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
103	C₃	C₃×C₁₃×#733	1	1	yes	characteristic
104	C₃	C₁₃×#6912	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃×C₁₃×#733

C₃

yes

maximal, complemented

C₁₃×#6891

C₃

yes

maximal

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₁₃×#733

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

#10624744

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

H(3,𝔽₃)

yes

—

C₃³×C₁₃

H(3,𝔽₃)

yes

characteristic

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

C₃×#733

C₃×C₁₃

yes

complemented

#6891

C₃×C₁₃

yes

—

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

#733

yes

complemented

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

—

#733

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

C₃²⋊H(3,𝔽₃)

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₁₃×H(3,𝔽₃)

yes

—

C₃³

C₁₃×H(3,𝔽₃)

yes

characteristic

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

C₁₃×H(3,𝔽₃)

yes

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₁₃

#10624744

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₁₃×#733

yes

complemented

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

—

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

C₉

—

C₉

—

C₉

—

C₃

—

100

C₃

—

101

C₃

—

102

C₃

C₁₃×C₃²⋊H(3,𝔽₃)

yes

characteristic

103

C₃

C₃×C₁₃×#733

yes

characteristic

104

C₃

C₁₃×#6912

yes

—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃²×C₁₃

C₃×H(3,𝔽₃)

commutator, Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₃×C₁₃×#733	C₃	semidirect
17. #10624744	C₁₃	direct (N × H)
34. C₃×#733	C₃×C₁₃	semidirect
45. C₃²×C₁₃	#733	semidirect
84. C₁₃	#10624744	direct (N × H)
93. C₃²	C₁₃×#733	semidirect

H ≅ G/N

type

2. C₃×C₁₃×#733

C₃

semidirect

17. #10624744

C₁₃

direct (N × H)

34. C₃×#733

C₃×C₁₃

semidirect

45. C₃²×C₁₃

#733

semidirect

84. C₁₃

#10624744

direct (N × H)

93. C₃²

C₁₃×#733

semidirect

Subgroups — C₁₃×#10624744 #23744895

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624744 #23744895

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624744 #23744895