Subgroups — C₃×C₁₃×#6880 #23744987

Order 9477.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#733	C₃	1	3	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6880	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
5	C₃²×C₉×C₁₃	—	3	1	no	—
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₁₃×#733	—	3	6	no	—
8	C₁₃×#733	C₃²	1	9	yes	—
9	C₉²×C₁₃	—	3	2	no	—
10	C₉²×C₁₃	C₃²	1	3	yes	—
11	C₃×#6880	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₁₃×3₋¹⁺²	—	3	9	no	—
14	C₁₃×3₋¹⁺²	—	9	6	no	—
15	C₃×C₉×C₁₃	—	3	9	no	—
16	C₃×C₉×C₁₃	—	3	2	no	—
17	C₃×C₉×C₁₃	—	3	1	no	—
18	C₃×C₉×C₁₃	—	3	3	no	—
19	C₃×C₉×C₁₃	—	9	3	no	—
20	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
21	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
22	C₃×#733	C₃×C₁₃	1	3	yes	—
23	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
24	#6880	C₃×C₁₃	1	9	yes	direct product factor
25	C₃²×C₁₃	—	3	3	no	—
26	C₃²×C₁₃	#732	1	2	yes	—
27	C₃²×C₁₃	#732	1	1	yes	characteristic
28	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₉×C₁₃	—	3	9	no	—
30	C₉×C₁₃	—	3	2	no	—
31	C₉×C₁₃	—	3	1	no	—
32	C₉×C₁₃	—	9	9	no	—
33	C₃×3₋¹⁺²	—	3	3	no	—
34	C₃²×C₉	—	3	1	no	—
35	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
36	#733	—	3	6	no	—
37	#733	C₃²×C₁₃	1	9	yes	—
38	C₉²	—	3	2	no	—
39	C₉²	C₃²×C₁₃	1	3	yes	—
40	C₃×C₁₃	—	3	1	no	—
41	C₃×C₁₃	—	3	2	no	—
42	C₃×C₁₃	#6880	1	3	yes	direct product factor
43	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
44	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
45	3₋¹⁺²	—	3	9	no	—
46	3₋¹⁺²	—	9	6	no	—
47	C₃×C₉	—	3	9	no	—
48	C₃×C₉	—	3	2	no	—
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	3	3	no	—
51	C₃×C₉	—	9	3	no	—
52	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
53	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
54	C₁₃	C₃×#6880	1	1	yes	characteristic, direct product factor, Sylow
55	C₃²	—	3	3	no	—
56	C₃²	C₁₃×#732	1	2	yes	—
57	C₃²	C₁₃×#732	1	1	yes	characteristic
58	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
59	C₉	—	3	9	no	—
60	C₉	—	3	2	no	—
61	C₉	—	3	1	no	—
62	C₉	—	9	9	no	—
63	C₃	—	3	1	no	—
64	C₃	—	3	2	no	—
65	C₃	C₁₃×#6880	1	3	yes	direct product factor
66	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₁₃	#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
prime radical	C₃³×C₁₃	H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃³×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6880	C₃	direct (N × H)
11. C₃×#6880	C₁₃	direct (N × H)
24. #6880	C₃×C₁₃	direct (N × H)
42. C₃×C₁₃	#6880	direct (N × H)
54. C₁₃	C₃×#6880	direct (N × H)
65. C₃	C₁₃×#6880	direct (N × H)

Subgroups — C3×C13×#6880 #23744987

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6880 #23744987