Subgroups — C₃×C₁₃×#6860 #23744733

Order 9477.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
3	C₁₃×#6860	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	4	no	—
6	C₃×C₁₃×3₋¹⁺²	—	3	18	no	—
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
8	C₃²×C₉×C₁₃	—	3	2	no	—
9	C₃²×C₉×C₁₃	—	3	2	no	—
10	C₁₃×C₃²⋊C₉	—	3	4	no	—
11	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₃×#6860	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	6	no	—
14	C₃³×C₁₃	—	3	6	no	—
15	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
16	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₁₃×3₋¹⁺²	—	3	36	no	—
19	C₁₃×3₋¹⁺²	—	3	18	no	—
20	C₃×C₉×C₁₃	—	3	18	no	—
21	C₃×C₉×C₁₃	—	3	6	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	9	6	no	—
24	C₃²×3₋¹⁺²	C₃×C₁₃	1	2	yes	—
25	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
26	#6860	C₃×C₁₃	1	9	yes	direct product factor
27	C₃²×C₁₃	—	3	4	no	—
28	C₃²×C₁₃	—	3	2	no	—
29	C₃²×C₁₃	—	3	4	no	—
30	C₃²×C₁₃	—	3	2	no	—
31	C₃²×C₁₃	—	9	9	no	—
32	C₃²×C₁₃	AΣL(1,𝔽₂₇)	1	6	yes	—
33	C₃²×C₁₃	#733	1	6	yes	—
34	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₉×C₁₃	—	3	18	no	—
36	C₉×C₁₃	—	9	6	no	—
37	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
38	C₃×3₋¹⁺²	—	3	4	no	—
39	C₃×3₋¹⁺²	—	3	18	no	—
40	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
41	C₃²×C₉	—	3	2	no	—
42	C₃²×C₉	—	3	2	no	—
43	C₃²⋊C₉	—	3	4	no	—
44	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
45	C₃×C₁₃	—	9	2	no	—
46	C₃×C₁₃	—	9	1	no	—
47	C₃×C₁₃	#6860	1	9	yes	direct product factor
48	C₃×C₁₃	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
49	C₃×C₁₃	C₃×#733	1	2	yes	—
50	C₃³	—	3	6	no	—
51	C₃³	—	3	6	no	—
52	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
53	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃³	C₃³×C₁₃	1	1	yes	characteristic
55	3₋¹⁺²	—	3	36	no	—
56	3₋¹⁺²	—	3	18	no	—
57	C₃×C₉	—	3	18	no	—
58	C₃×C₉	—	3	6	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	9	6	no	—
61	C₁₃	C₃×#6860	1	1	yes	characteristic, direct product factor, Sylow
62	C₃²	—	3	4	no	—
63	C₃²	—	3	2	no	—
64	C₃²	—	3	4	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	9	9	no	—
67	C₃²	C₁₃×AΣL(1,𝔽₂₇)	1	6	yes	—
68	C₃²	C₁₃×#733	1	6	yes	—
69	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
70	C₉	—	3	18	no	—
71	C₉	—	9	6	no	—
72	C₃	—	9	2	no	—
73	C₃	—	9	1	no	—
74	C₃	C₁₃×#6860	1	9	yes	direct product factor
75	C₃	C₃×C₁₃×AΣL(1,𝔽₂₇)	1	2	yes	—
76	C₃	C₃×C₁₃×#733	1	2	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6860	C₃	direct (N × H)
12. C₃×#6860	C₁₃	direct (N × H)
26. #6860	C₃×C₁₃	direct (N × H)
47. C₃×C₁₃	#6860	direct (N × H)
61. C₁₃	C₃×#6860	direct (N × H)
74. C₃	C₁₃×#6860	direct (N × H)

Subgroups — C3×C13×#6860 #23744733

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6860 #23744733