Group #23744709 — subgroups

Subgroups — C₁₃×#10624558 #23744709

Order 9477.

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

normal subgroups only

This group has 608 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	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
4	C₁₃×#6855	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	6	no	—
8	C₃×C₁₃×3₋¹⁺²	C₉	1	9	yes	complemented
9	C₃²×C₉×C₁₃	—	3	3	no	—
10	C₃²×C₉×C₁₃	—	3	9	no	—
11	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
13	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
14	C₁₃×C₃²⋊C₉	—	3	6	no	—
15	#10624558	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	3	3	no	—
17	C₃³×C₁₃	—	3	6	no	—
18	C₃³×C₁₃	C₃×C₉	1	3	yes	—
19	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
20	C₃³×C₁₃	3₋¹⁺²	1	6	yes	—
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	3	27	no	—
23	C₃×C₉×C₁₃	—	3	27	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	—	3	3	no	—
26	C₃×C₉×C₁₃	—	3	6	no	—
27	C₃×C₉×C₁₃	—	3	6	no	—
28	C₃×C₉×C₁₃	—	3	6	no	—
29	C₃×C₉×C₁₃	—	3	18	no	—
30	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	complemented
31	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
32	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
33	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
34	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
35	#6855	C₃×C₁₃	1	9	yes	complemented
36	C₃²×C₁₃	—	3	9	no	—
37	C₃²×C₁₃	—	3	3	no	—
38	C₃²×C₁₃	—	3	6	no	—
39	C₃²×C₁₃	—	3	18	no	—
40	C₃²×C₁₃	C₃²⋊C₉	1	9	yes	—
41	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
42	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₃²×C₁₃	C₃×3₋¹⁺²	1	2	yes	—
44	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
45	C₃²×C₁₃	#737	1	6	yes	—
46	C₉×C₁₃	—	3	9	no	—
47	C₉×C₁₃	—	3	9	no	—
48	C₉×C₁₃	—	9	6	no	—
49	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	3	3	no	—
51	C₃×3₋¹⁺²	—	3	6	no	—
52	C₃×3₋¹⁺²	C₉×C₁₃	1	9	yes	complemented
53	C₃²×C₉	—	3	3	no	—
54	C₃²×C₉	—	3	9	no	—
55	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
56	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
57	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
58	C₃²⋊C₉	—	3	6	no	—
59	C₃×C₁₃	—	3	9	no	—
60	C₃×C₁₃	C₃×C₃²⋊C₉	1	1	yes	characteristic
61	C₃×C₁₃	C₉×3₋¹⁺²	1	3	yes	—
62	C₃×C₁₃	#6891	1	1	yes	characteristic
63	C₃×C₁₃	#6893	1	2	yes	—
64	C₃×C₁₃	#6894	1	6	yes	—
65	C₃³	—	3	3	no	—
66	C₃³	—	3	6	no	—
67	C₃³	C₃×C₉×C₁₃	1	3	yes	—
68	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
69	C₃³	C₁₃×3₋¹⁺²	1	6	yes	—
70	C₃³	C₃³×C₁₃	1	1	yes	characteristic
71	3₋¹⁺²	—	3	27	no	—
72	C₃×C₉	—	3	27	no	—
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	6	no	—
78	C₃×C₉	—	3	18	no	—
79	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	complemented
80	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
81	C₁₃	#10624558	1	1	yes	characteristic, direct product factor, Sylow
82	C₃²	—	3	9	no	—
83	C₃²	—	3	3	no	—
84	C₃²	—	3	6	no	—
85	C₃²	—	3	18	no	—
86	C₃²	C₁₃×C₃²⋊C₉	1	9	yes	—
87	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
88	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
89	C₃²	C₃×C₁₃×3₋¹⁺²	1	2	yes	—
90	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
91	C₃²	C₁₃×#737	1	6	yes	—
92	C₉	—	3	9	no	—
93	C₉	—	3	9	no	—
94	C₉	—	9	6	no	—
95	C₃	—	3	9	no	—
96	C₃	C₃×C₁₃×C₃²⋊C₉	1	1	yes	characteristic
97	C₃	C₉×C₁₃×3₋¹⁺²	1	3	yes	—
98	C₃	C₁₃×#6891	1	1	yes	characteristic
99	C₃	C₁₃×#6893	1	2	yes	—
100	C₃	C₁₃×#6894	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₁₃×3₋¹⁺²

C₃

yes

maximal, characteristic

C₃³×C₉×C₁₃

C₃

yes

maximal, characteristic

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal

C₁₃×#6855

C₃

yes

maximal, complemented

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

—

C₃×C₁₃×3₋¹⁺²

C₉

yes

complemented

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₃²×C₉×C₁₃

C₃²

yes

—

C₁₃×C₃²⋊C₉

—

#10624558

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃×C₉

yes

—

C₃³×C₁₃

H(3,𝔽₃)

yes

—

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

yes

complemented

C₃×C₉×C₁₃

3₋¹⁺²

yes

complemented

C₃²×3₋¹⁺²

C₃×C₁₃

yes

characteristic

C₃³×C₉

C₃×C₁₃

yes

characteristic

C₃×C₃²⋊C₉

C₃×C₁₃

yes

—

#6855

C₃×C₁₃

yes

complemented

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃²⋊C₉

yes

—

C₃²×C₁₃

C₃²×C₉

yes

characteristic

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

C₃×3₋¹⁺²

yes

—

C₃²×C₁₃

#737

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₉×C₁₃

yes

complemented

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²×C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

—

C₃×C₁₃

—

C₃×C₁₃

C₃×C₃²⋊C₉

yes

characteristic

C₃×C₁₃

C₉×3₋¹⁺²

yes

—

C₃×C₁₃

#6891

yes

characteristic

C₃×C₁₃

#6893

yes

—

C₃×C₁₃

#6894

yes

—

C₃³

—

C₃³

—

C₃³

C₃×C₉×C₁₃

yes

—

C₃³

C₁₃×H(3,𝔽₃)

yes

—

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×C₁₃

yes

complemented

C₃×C₉

C₁₃×3₋¹⁺²

yes

complemented

C₁₃

#10624558

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

C₁₃×C₃²⋊C₉

yes

—

C₃²

C₃²×C₉×C₁₃

yes

characteristic

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₃×C₁₃×3₋¹⁺²

yes

—

C₃²

C₁₃×#737

yes

—

C₉

—

C₉

—

C₉

—

C₃

—

C₃

C₃×C₁₃×C₃²⋊C₉

yes

characteristic

C₃

C₉×C₁₃×3₋¹⁺²

yes

—

C₃

C₁₃×#6891

yes

characteristic

C₃

C₁₃×#6893

yes

—

100

C₃

C₁₃×#6894

yes

—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃³×C₁₃

C₃³

commutator

C₃²

C₃²×C₉×C₁₃

Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃³×C₁₃ ◁ G

N	H ≅ G/N	type
4. C₁₃×#6855	C₃	semidirect
8. C₃×C₁₃×3₋¹⁺²	C₉	semidirect
15. #10624558	C₁₃	direct (N × H)
30. C₃×C₉×C₁₃	C₃×C₉	semidirect
31. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
35. #6855	C₃×C₁₃	semidirect
52. C₃×3₋¹⁺²	C₉×C₁₃	semidirect
79. C₃×C₉	C₃×C₉×C₁₃	semidirect
80. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
81. C₁₃	#10624558	direct (N × H)

H ≅ G/N

type

4. C₁₃×#6855

C₃

semidirect

8. C₃×C₁₃×3₋¹⁺²

C₉

semidirect

15. #10624558

C₁₃

direct (N × H)

30. C₃×C₉×C₁₃

C₃×C₉

semidirect

31. C₃×C₉×C₁₃

3₋¹⁺²

semidirect

35. #6855

C₃×C₁₃

semidirect

52. C₃×3₋¹⁺²

C₉×C₁₃

semidirect

79. C₃×C₉

C₃×C₉×C₁₃

semidirect

80. C₃×C₉

C₁₃×3₋¹⁺²

semidirect

81. C₁₃

#10624558

direct (N × H)

Subgroups — C₁₃×#10624558 #23744709

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624558 #23744709

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624558 #23744709