Subgroups — C₁₃×#10624910 #23745061

Order 9477.

740 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6893	C₃	1	9	yes	maximal, complemented
2	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	3	yes	maximal, complemented
4	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	18	yes	complemented
8	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
9	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	9	yes	complemented
11	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
12	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
13	C₁₃×C₃²⋊C₉	C₃²	1	54	yes	complemented
14	#10624910	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	9	1	no	—
16	C₃³×C₁₃	—	9	3	no	—
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₃³×C₁₃	C₃³	1	3	yes	—
19	C₃³×C₁₃	C₃³	1	9	yes	—
20	C₁₃×3₋¹⁺²	—	9	9	no	—
21	C₁₃×3₋¹⁺²	—	9	18	no	—
22	C₁₃×H(3,𝔽₃)	—	9	3	no	—
23	C₁₃×H(3,𝔽₃)	—	9	9	no	—
24	C₃×C₉×C₁₃	—	9	9	no	—
25	C₃×C₉×C₁₃	C₃³	1	27	yes	—
26	#6893	C₃×C₁₃	1	9	yes	complemented
27	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	27	yes	complemented
28	#6891	C₃×C₁₃	1	3	yes	complemented
29	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
30	C₃²×C₁₃	—	3	9	no	—
31	C₃²×C₁₃	—	3	1	no	—
32	C₃²×C₁₃	—	3	3	no	—
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	3	27	no	—
35	C₃²×C₁₃	—	3	3	no	—
36	C₃²×C₁₃	—	3	6	no	—
37	C₃²×C₁₃	—	9	9	no	—
38	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
39	C₉×C₁₃	—	3	27	no	—
40	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
41	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
42	C₃×3₋¹⁺²	C₃²×C₁₃	1	18	yes	complemented
43	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	9	yes	—
44	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
45	C₃²×C₉	C₃²×C₁₃	1	9	yes	complemented
46	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
47	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
48	C₃²⋊C₉	C₃²×C₁₃	1	54	yes	complemented
49	C₃×C₁₃	—	9	9	no	—
50	C₃×C₁₃	—	9	1	no	—
51	C₃×C₁₃	—	9	3	no	—
52	C₃×C₁₃	H(5,𝔽₃)	1	1	yes	characteristic
53	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	—
54	C₃³	—	9	1	no	—
55	C₃³	—	9	3	no	—
56	C₃³	C₃³×C₁₃	1	1	yes	characteristic
57	C₃³	C₃³×C₁₃	1	3	yes	—
58	C₃³	C₃³×C₁₃	1	9	yes	—
59	3₋¹⁺²	—	9	9	no	—
60	3₋¹⁺²	—	9	18	no	—
61	H(3,𝔽₃)	—	9	3	no	—
62	H(3,𝔽₃)	—	9	9	no	—
63	C₃×C₉	—	9	9	no	—
64	C₃×C₉	C₃³×C₁₃	1	27	yes	—
65	C₁₃	#10624910	1	1	yes	characteristic, direct product factor, Sylow
66	C₃²	—	3	9	no	—
67	C₃²	—	3	1	no	—
68	C₃²	—	3	3	no	—
69	C₃²	—	3	3	no	—
70	C₃²	—	3	27	no	—
71	C₃²	—	3	3	no	—
72	C₃²	—	3	6	no	—
73	C₃²	—	9	9	no	—
74	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
75	C₉	—	3	27	no	—
76	C₃	—	9	1	no	—
77	C₃	—	9	3	no	—
78	C₃	—	9	9	no	—
79	C₃	C₁₃×H(5,𝔽₃)	1	1	yes	characteristic
80	C₃	C₁₃×3₋¹⁺⁴	1	3	yes	—

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

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#6893	C₃	semidirect
2. C₁₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
3. C₁₃×#6891	C₃	semidirect
7. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
10. C₃²×C₉×C₁₃	C₃²	semidirect
13. C₁₃×C₃²⋊C₉	C₃²	semidirect
14. #10624910	C₁₃	direct (N × H)
26. #6893	C₃×C₁₃	semidirect
27. C₉⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
28. #6891	C₃×C₁₃	semidirect
42. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
45. C₃²×C₉	C₃²×C₁₃	semidirect
48. C₃²⋊C₉	C₃²×C₁₃	semidirect
65. C₁₃	#10624910	direct (N × H)

Subgroups — C13×#10624910 #23745061

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624910 #23745061