Group #23744925 — subgroups

Subgroups — C₁₃×#10624774 #23744925

Order 9477.

326 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₁₃×#6895	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6868	C₃	1	3	yes	maximal, complemented
4	C₁₃×#6867	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6866	C₃	1	3	yes	maximal
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
9	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
10	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
11	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
14	C₁₃×C₉⋊C₉	—	3	9	no	—
15	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
16	#10624774	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	3	1	no	—
18	C₃³×C₁₃	—	3	1	no	—
19	C₃³×C₁₃	—	3	1	no	—
20	C₃³×C₁₃	—	9	3	no	—
21	C₃³×C₁₃	3₋¹⁺²	1	3	yes	—
22	C₃³×C₁₃	C₃³	1	1	yes	characteristic
23	C₁₃×3₋¹⁺²	—	3	27	no	—
24	C₃×C₉×C₁₃	—	3	1	no	—
25	C₃×C₉×C₁₃	—	3	1	no	—
26	C₃×C₉×C₁₃	—	3	1	no	—
27	C₃×C₉×C₁₃	—	3	1	no	—
28	C₃×C₉×C₁₃	—	3	1	no	—
29	C₃×C₉×C₁₃	—	3	1	no	—
30	C₃×C₉×C₁₃	—	3	1	no	—
31	C₃×C₉×C₁₃	—	3	1	no	—
32	C₃×C₉×C₁₃	—	3	1	no	—
33	C₃×C₉×C₁₃	—	3	9	no	—
34	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
35	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
36	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
37	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
38	#6895	C₃×C₁₃	1	3	yes	complemented
39	#6868	C₃×C₁₃	1	3	yes	complemented
40	#6867	C₃×C₁₃	1	3	yes	complemented
41	#6866	C₃×C₁₃	1	3	yes	—
42	C₃²×C₁₃	—	3	3	no	—
43	C₃²×C₁₃	—	3	3	no	—
44	C₃²×C₁₃	—	9	3	no	—
45	C₃²×C₁₃	—	9	3	no	—
46	C₃²×C₁₃	—	9	3	no	—
47	C₃²×C₁₃	—	9	3	no	—
48	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
50	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
51	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
52	C₉×C₁₃	—	3	3	no	—
53	C₉×C₁₃	—	3	3	no	—
54	C₉×C₁₃	—	3	3	no	—
55	C₉×C₁₃	—	9	9	no	—
56	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
57	C₃×3₋¹⁺²	—	3	3	no	—
58	C₃×3₋¹⁺²	—	3	3	no	—
59	C₃×3₋¹⁺²	—	3	3	no	—
60	C₃×3₋¹⁺²	—	3	3	no	—
61	C₃²×C₉	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	C₉⋊C₉	—	3	9	no	—
65	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
66	C₃×C₁₃	—	3	1	no	—
67	C₃×C₁₃	—	3	1	no	—
68	C₃×C₁₃	—	3	1	no	—
69	C₃×C₁₃	—	9	3	no	—
70	C₃×C₁₃	#6891	1	1	yes	characteristic
71	C₃×C₁₃	#6913	1	3	yes	—
72	C₃³	—	3	1	no	—
73	C₃³	—	3	1	no	—
74	C₃³	—	3	1	no	—
75	C₃³	—	9	3	no	—
76	C₃³	C₁₃×3₋¹⁺²	1	3	yes	—
77	C₃³	C₃³×C₁₃	1	1	yes	characteristic
78	3₋¹⁺²	—	3	27	no	—
79	C₃×C₉	—	3	1	no	—
80	C₃×C₉	—	3	1	no	—
81	C₃×C₉	—	3	1	no	—
82	C₃×C₉	—	3	1	no	—
83	C₃×C₉	—	3	1	no	—
84	C₃×C₉	—	3	1	no	—
85	C₃×C₉	—	3	1	no	—
86	C₃×C₉	—	3	1	no	—
87	C₃×C₉	—	3	1	no	—
88	C₃×C₉	—	3	9	no	—
89	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
90	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
91	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
92	C₁₃	#10624774	1	1	yes	characteristic, direct product factor, Sylow
93	C₃²	—	3	3	no	—
94	C₃²	—	3	3	no	—
95	C₃²	—	9	3	no	—
96	C₃²	—	9	3	no	—
97	C₃²	—	9	3	no	—
98	C₃²	—	9	3	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	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
102	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
103	C₉	—	3	3	no	—
104	C₉	—	3	3	no	—
105	C₉	—	3	3	no	—
106	C₉	—	9	9	no	—
107	C₃	—	3	1	no	—
108	C₃	—	3	1	no	—
109	C₃	—	3	1	no	—
110	C₃	—	9	3	no	—
111	C₃	C₁₃×#6891	1	1	yes	characteristic
112	C₃	C₁₃×#6913	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₁₃×#6895

C₃

yes

maximal, complemented

C₁₃×#6868

C₃

yes

maximal, complemented

C₁₃×#6867

C₃

yes

maximal, complemented

C₁₃×#6866

C₃

yes

maximal

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

#10624774

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

3₋¹⁺²

yes

—

C₃³×C₁₃

C₃³

yes

characteristic

C₁₃×3₋¹⁺²

—

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

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

#6895

C₃×C₁₃

yes

complemented

#6868

C₃×C₁₃

yes

complemented

#6867

C₃×C₁₃

yes

complemented

#6866

C₃×C₁₃

yes

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

characteristic

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

#6891

yes

characteristic

C₃×C₁₃

#6913

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₁₃×3₋¹⁺²

yes

—

C₃³

C₃³×C₁₃

yes

characteristic

3₋¹⁺²

—

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

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₁₃

#10624774

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

100

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

101

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

102

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

103

C₉

—

104

C₉

—

105

C₉

—

106

C₉

—

107

C₃

—

108

C₃

—

109

C₃

—

110

C₃

—

111

C₃

C₁₃×#6891

yes

characteristic

112

C₃

C₁₃×#6913

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 ◁ C₃²×C₉×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 ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₁₃×#6895	C₃	semidirect
3. C₁₃×#6868	C₃	semidirect
4. C₁₃×#6867	C₃	semidirect
16. #10624774	C₁₃	direct (N × H)
38. #6895	C₃×C₁₃	semidirect
39. #6868	C₃×C₁₃	semidirect
40. #6867	C₃×C₁₃	semidirect
92. C₁₃	#10624774	direct (N × H)

H ≅ G/N

type

2. C₁₃×#6895

C₃

semidirect

3. C₁₃×#6868

C₃

semidirect

4. C₁₃×#6867

C₃

semidirect

16. #10624774

C₁₃

direct (N × H)

38. #6895

C₃×C₁₃

semidirect

39. #6868

C₃×C₁₃

semidirect

40. #6867

C₃×C₁₃

semidirect

92. C₁₃

#10624774

direct (N × H)

Subgroups — C₁₃×#10624774 #23744925

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624774 #23744925

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624774 #23744925