Group #23744950 — subgroups

Subgroups — C₁₃×#10624799 #23744950

Order 9477.

222 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 92 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	C₃×C₁₃×#733	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6894	C₃	1	2	yes	maximal
3	C₉×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₁₃×3₋¹⁺²⋊C₉	C₃	1	4	yes	maximal
6	C₁₃×3₋¹⁺²⋊C₉	C₃	1	2	yes	maximal
7	C₁₃×#6868	C₃	1	2	yes	maximal
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₁₃×#733	—	3	3	no	—
14	C₁₃×C₉⋊C₉	—	3	2	no	—
15	C₁₃×C₉⋊C₉	—	3	1	no	—
16	C₁₃×C₉⋊C₉	—	3	2	no	—
17	C₁₃×C₉⋊C₉	—	3	4	no	—
18	C₁₃×C₉⋊C₉	—	3	2	no	—
19	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
20	C₁₃×C₃²⋊C₉	C₃²	1	4	yes	—
21	C₉²×C₁₃	—	3	1	no	—
22	#10624799	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₃³×C₁₃	C₃³	1	1	yes	characteristic
24	C₁₃×3₋¹⁺²	—	3	2	no	—
25	C₁₃×3₋¹⁺²	—	3	2	no	—
26	C₁₃×3₋¹⁺²	—	3	4	no	—
27	C₁₃×3₋¹⁺²	3₋¹⁺²	1	3	yes	—
28	C₃×C₉×C₁₃	—	3	1	no	—
29	C₃×C₉×C₁₃	—	3	3	no	—
30	C₃×C₉×C₁₃	—	3	2	no	—
31	C₃×C₉×C₁₃	—	3	4	no	—
32	C₃×C₉×C₁₃	—	3	2	no	—
33	C₃×C₉×C₁₃	—	3	1	no	—
34	C₃×C₉×C₁₃	—	3	2	no	—
35	C₃×C₉×C₁₃	—	3	1	no	—
36	C₃×C₉×C₁₃	—	3	2	no	—
37	C₃×C₉×C₁₃	—	9	2	no	—
38	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
39	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
40	C₃×#733	C₃×C₁₃	1	1	yes	characteristic
41	#6894	C₃×C₁₃	1	2	yes	—
42	C₉×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
43	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
44	3₋¹⁺²⋊C₉	C₃×C₁₃	1	4	yes	—
45	3₋¹⁺²⋊C₉	C₃×C₁₃	1	2	yes	—
46	#6868	C₃×C₁₃	1	2	yes	—
47	C₃²×C₁₃	—	3	2	no	—
48	C₃²×C₁₃	—	3	1	no	—
49	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
50	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
51	C₃²×C₁₃	#737	1	2	yes	—
52	C₉×C₁₃	—	3	3	no	—
53	C₉×C₁₃	—	3	2	no	—
54	C₉×C₁₃	—	9	2	no	—
55	C₉×C₁₃	—	9	4	no	—
56	C₉×C₁₃	—	9	2	no	—
57	C₉×C₁₃	—	9	1	no	—
58	C₉×C₁₃	—	9	2	no	—
59	C₉×C₁₃	#733	1	3	yes	complemented
60	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
61	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
62	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
63	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
64	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
65	#733	—	3	3	no	—
66	C₉⋊C₉	—	3	2	no	—
67	C₉⋊C₉	—	3	1	no	—
68	C₉⋊C₉	—	3	2	no	—
69	C₉⋊C₉	—	3	4	no	—
70	C₉⋊C₉	—	3	2	no	—
71	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
72	C₃²⋊C₉	C₃²×C₁₃	1	4	yes	—
73	C₉²	—	3	1	no	—
74	C₃×C₁₃	—	3	1	no	—
75	C₃×C₁₃	—	3	2	no	—
76	C₃×C₁₃	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
77	C₃×C₁₃	C₃×#733	1	1	yes	characteristic
78	C₃×C₁₃	#6913	1	2	yes	—
79	C₃³	C₃³×C₁₃	1	1	yes	characteristic
80	3₋¹⁺²	—	3	2	no	—
81	3₋¹⁺²	—	3	2	no	—
82	3₋¹⁺²	—	3	4	no	—
83	3₋¹⁺²	C₁₃×3₋¹⁺²	1	3	yes	—
84	C₃×C₉	—	3	1	no	—
85	C₃×C₉	—	3	3	no	—
86	C₃×C₉	—	3	2	no	—
87	C₃×C₉	—	3	4	no	—
88	C₃×C₉	—	3	1	no	—
89	C₃×C₉	—	3	2	no	—
90	C₃×C₉	—	3	2	no	—
91	C₃×C₉	—	3	1	no	—
92	C₃×C₉	—	3	2	no	—
93	C₃×C₉	—	9	2	no	—
94	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
95	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
96	C₁₃	#10624799	1	1	yes	characteristic, direct product factor, Sylow
97	C₃²	—	3	1	no	—
98	C₃²	—	3	2	no	—
99	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
100	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
101	C₃²	C₁₃×#737	1	2	yes	—
102	C₉	—	3	3	no	—
103	C₉	—	3	2	no	—
104	C₉	—	9	1	no	—
105	C₉	—	9	2	no	—
106	C₉	—	9	2	no	—
107	C₉	—	9	2	no	—
108	C₉	—	9	4	no	—
109	C₉	C₁₃×#733	1	3	yes	complemented
110	C₃	—	3	1	no	—
111	C₃	—	3	2	no	—
112	C₃	C₁₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
113	C₃	C₃×C₁₃×#733	1	1	yes	characteristic
114	C₃	C₁₃×#6913	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₁₃×#733

C₃

yes

maximal, characteristic

C₁₃×#6894

C₃

yes

maximal

C₉×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, characteristic

C₁₃×3₋¹⁺²⋊C₉

C₃

yes

maximal

C₁₃×3₋¹⁺²⋊C₉

C₃

yes

maximal

C₁₃×#6868

C₃

yes

maximal

C₃×C₁₃×3₋¹⁺²

C₃²

yes

—

C₃×C₁₃×3₋¹⁺²

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×#733

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₃

—

#10624799

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

—

C₁₃×3₋¹⁺²

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

characteristic

C₃×#733

C₃×C₁₃

yes

characteristic

#6894

C₃×C₁₃

yes

—

C₉×3₋¹⁺²

C₃×C₁₃

yes

characteristic

C₃×C₉⋊C₉

C₃×C₁₃

yes

characteristic

3₋¹⁺²⋊C₉

C₃×C₁₃

yes

—

3₋¹⁺²⋊C₉

C₃×C₁₃

yes

—

#6868

C₃×C₁₃

yes

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₃

#737

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

#733

yes

complemented

C₃×3₋¹⁺²

C₃²×C₁₃

yes

—

C₃×3₋¹⁺²

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

—

#733

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₉²

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

C₉⋊H(3,𝔽₃)

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

C₁₃

#10624799

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

100

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

101

C₃²

C₁₃×#737

yes

—

102

C₉

—

103

C₉

—

104

C₉

—

105

C₉

—

106

C₉

—

107

C₉

—

108

C₉

—

109

C₉

C₁₃×#733

yes

complemented

110

C₃

—

111

C₃

—

112

C₃

C₁₃×C₉⋊H(3,𝔽₃)

yes

characteristic

113

C₃

C₃×C₁₃×#733

yes

characteristic

114

C₃

C₁₃×#6913

yes

—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃³×C₁₃	C₃³
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃²×C₁₃

C₃×H(3,𝔽₃)

commutator, Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃³×C₁₃

C₃³

LCS

G ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
22. #10624799	C₁₃	direct (N × H)
59. C₉×C₁₃	#733	semidirect
96. C₁₃	#10624799	direct (N × H)
109. C₉	C₁₃×#733	semidirect

H ≅ G/N

type

22. #10624799

C₁₃

direct (N × H)

59. C₉×C₁₃

#733

semidirect

96. C₁₃

#10624799

direct (N × H)

109. C₉

C₁₃×#733

semidirect

Subgroups — C₁₃×#10624799 #23744950

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624799 #23744950

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624799 #23744950