Group #23744712 — subgroups

Subgroups — C₁₃×#10624561 #23744712

Order 9477.

374 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 206 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×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₉⋊C₉	C₃	1	3	yes	maximal
4	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
6	C₁₃×#6855	C₃	1	6	yes	maximal
7	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₁₃×C₉⋊C₉	—	3	9	no	—
14	C₁₃×C₉⋊C₉	—	3	3	no	—
15	C₁₃×C₉⋊C₉	—	3	3	no	—
16	C₁₃×C₉⋊C₉	C₉	1	9	yes	complemented
17	C₉²×C₁₃	—	3	3	no	—
18	#10624561	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃³×C₁₃	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₁₃	—	3	3	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	3	6	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	—	3	3	no	—
26	C₃×C₉×C₁₃	—	3	2	no	—
27	C₃×C₉×C₁₃	—	3	1	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	C₃×C₉	1	9	yes	—
32	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	—
33	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	—
34	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
35	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
36	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
37	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
38	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
39	C₃×C₉⋊C₉	C₃×C₁₃	1	3	yes	—
40	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
41	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
42	#6855	C₃×C₁₃	1	6	yes	—
43	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
44	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
45	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
46	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
47	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
48	C₃²×C₁₃	#737	1	6	yes	—
49	C₉×C₁₃	—	3	9	no	—
50	C₉×C₁₃	—	3	9	no	—
51	C₉×C₁₃	—	9	3	no	—
52	C₉×C₁₃	—	9	2	no	—
53	C₉×C₁₃	—	9	1	no	—
54	C₉×C₁₃	C₉⋊C₉	1	9	yes	complemented
55	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
56	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
57	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
58	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
59	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
60	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
61	C₉⋊C₉	—	3	9	no	—
62	C₉⋊C₉	—	3	3	no	—
63	C₉⋊C₉	—	3	3	no	—
64	C₉⋊C₉	C₉×C₁₃	1	9	yes	complemented
65	C₉²	—	3	3	no	—
66	C₃×C₁₃	C₃×C₉⋊C₉	1	1	yes	characteristic
67	C₃×C₁₃	C₉×3₋¹⁺²	1	3	yes	—
68	C₃×C₁₃	#6894	1	3	yes	—
69	C₃×C₁₃	#6896	1	3	yes	—
70	C₃×C₁₃	#6899	1	2	yes	—
71	C₃×C₁₃	#6900	1	1	yes	characteristic
72	C₃³	C₃³×C₁₃	1	1	yes	characteristic
73	C₃×C₉	—	3	3	no	—
74	C₃×C₉	—	3	3	no	—
75	C₃×C₉	—	3	6	no	—
76	C₃×C₉	—	3	6	no	—
77	C₃×C₉	—	3	3	no	—
78	C₃×C₉	—	3	3	no	—
79	C₃×C₉	—	3	2	no	—
80	C₃×C₉	—	3	1	no	—
81	C₃×C₉	—	3	3	no	—
82	C₃×C₉	—	3	6	no	—
83	C₃×C₉	—	3	6	no	—
84	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
85	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	—
86	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	—
87	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
88	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
89	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
90	C₁₃	#10624561	1	1	yes	characteristic, direct product factor, Sylow
91	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
92	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
93	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
94	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
95	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
96	C₃²	C₁₃×#737	1	6	yes	—
97	C₉	—	3	9	no	—
98	C₉	—	3	9	no	—
99	C₉	—	9	3	no	—
100	C₉	—	9	2	no	—
101	C₉	—	9	1	no	—
102	C₉	C₁₃×C₉⋊C₉	1	9	yes	complemented
103	C₃	C₃×C₁₃×C₉⋊C₉	1	1	yes	characteristic
104	C₃	C₉×C₁₃×3₋¹⁺²	1	3	yes	—
105	C₃	C₁₃×#6894	1	3	yes	—
106	C₃	C₁₃×#6896	1	3	yes	—
107	C₃	C₁₃×#6899	1	2	yes	—
108	C₃	C₁₃×#6900	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, characteristic

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, characteristic

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal

C₃×C₁₃×C₉⋊C₉

C₃

yes

maximal, characteristic

C₃×C₉²×C₁₃

C₃

yes

maximal, characteristic

C₁₃×#6855

C₃

yes

maximal

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

C₉

yes

complemented

C₉²×C₁₃

—

#10624561

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

C₃³

yes

characteristic

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

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

C₃×C₉

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃×C₉×C₁₃

3₋¹⁺²

yes

—

C₃×C₉⋊C₉

C₃×C₁₃

yes

characteristic

C₃×C₉⋊C₉

C₃×C₁₃

yes

characteristic

C₃×C₉⋊C₉

C₃×C₁₃

yes

—

C₃×C₉⋊C₉

C₃×C₁₃

yes

characteristic

C₃×C₉²

C₃×C₁₃

yes

characteristic

#6855

C₃×C₁₃

yes

—

C₃²×C₁₃

C₃²×C₉

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

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

#737

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

C₉⋊C₉

yes

complemented

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

C₉×C₁₃

yes

complemented

C₉²

—

C₃×C₁₃

C₃×C₉⋊C₉

yes

characteristic

C₃×C₁₃

C₉×3₋¹⁺²

yes

—

C₃×C₁₃

#6894

yes

—

C₃×C₁₃

#6896

yes

—

C₃×C₁₃

#6899

yes

—

C₃×C₁₃

#6900

yes

characteristic

C₃³

C₃³×C₁₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₃×C₉×C₁₃

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₃×C₉

C₁₃×3₋¹⁺²

yes

—

C₁₃

#10624561

yes

characteristic, direct product factor, Sylow

C₃²

C₃²×C₉×C₁₃

yes

characteristic

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

C₃²

C₃×C₁₃×3₋¹⁺²

yes

characteristic

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₁₃×#737

yes

—

C₉

—

C₉

—

C₉

—

100

C₉

—

101

C₉

—

102

C₉

C₁₃×C₉⋊C₉

yes

complemented

103

C₃

C₃×C₁₃×C₉⋊C₉

yes

characteristic

104

C₃

C₉×C₁₃×3₋¹⁺²

yes

—

105

C₃

C₁₃×#6894

yes

—

106

C₃

C₁₃×#6896

yes

—

107

C₃

C₁₃×#6899

yes

—

108

C₃

C₁₃×#6900

yes

characteristic

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

subgroup

G/H

center, socle, prime radical

C₃³×C₁₃

C₃³

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃³

C₃³×C₁₃

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃³×C₁₃ ◁ G

N	H ≅ G/N	type
16. C₁₃×C₉⋊C₉	C₉	semidirect
18. #10624561	C₁₃	direct (N × H)
54. C₉×C₁₃	C₉⋊C₉	semidirect
64. C₉⋊C₉	C₉×C₁₃	semidirect
90. C₁₃	#10624561	direct (N × H)
102. C₉	C₁₃×C₉⋊C₉	semidirect

H ≅ G/N

type

16. C₁₃×C₉⋊C₉

C₉

semidirect

18. #10624561

C₁₃

direct (N × H)

54. C₉×C₁₃

C₉⋊C₉

semidirect

64. C₉⋊C₉

C₉×C₁₃

semidirect

90. C₁₃

#10624561

direct (N × H)

102. C₉

C₁₃×C₉⋊C₉

semidirect

Subgroups — C₁₃×#10624561 #23744712

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624561 #23744712

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624561 #23744712