Subgroups — C₃×C₁₃×#6879 #23744986

Order 9477.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#732	C₃	1	3	yes	maximal, complemented
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6879	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₁₃×H(3,𝔽₃)	—	3	3	no	—
5	C₃²×C₉×C₁₃	—	3	1	no	—
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₁₃×#732	—	3	6	no	—
8	C₁₃×#732	C₃²	1	9	yes	complemented
9	C₉²×C₁₃	—	3	2	no	—
10	C₉²×C₁₃	C₃²	1	3	yes	complemented
11	C₃×#6879	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	9	3	no	—
13	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₁₃×H(3,𝔽₃)	—	3	9	no	—
15	C₁₃×H(3,𝔽₃)	—	9	6	no	—
16	C₃×C₉×C₁₃	—	3	9	no	—
17	C₃×C₉×C₁₃	—	3	2	no	—
18	C₃×C₉×C₁₃	—	3	1	no	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
21	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
22	C₃×#732	C₃×C₁₃	1	3	yes	complemented
23	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
24	#6879	C₃×C₁₃	1	9	yes	direct product factor
25	C₃²×C₁₃	—	3	3	no	—
26	C₃²×C₁₃	—	9	9	no	—
27	C₃²×C₁₃	—	27	9	no	—
28	C₃²×C₁₃	#732	1	2	yes	—
29	C₃²×C₁₃	#732	1	1	yes	characteristic
30	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₉×C₁₃	—	3	9	no	—
32	C₉×C₁₃	—	3	2	no	—
33	C₉×C₁₃	—	3	1	no	—
34	C₃×H(3,𝔽₃)	—	3	3	no	—
35	C₃²×C₉	—	3	1	no	—
36	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
37	#732	—	3	6	no	—
38	#732	C₃²×C₁₃	1	9	yes	complemented
39	C₉²	—	3	2	no	—
40	C₉²	C₃²×C₁₃	1	3	yes	complemented
41	C₃×C₁₃	—	3	1	no	—
42	C₃×C₁₃	—	3	2	no	—
43	C₃×C₁₃	—	27	9	no	—
44	C₃×C₁₃	#6879	1	3	yes	direct product factor
45	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
46	C₃³	—	9	3	no	—
47	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
48	H(3,𝔽₃)	—	3	9	no	—
49	H(3,𝔽₃)	—	9	6	no	—
50	C₃×C₉	—	3	9	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	3	1	no	—
53	C₃×C₉	—	3	3	no	—
54	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
55	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
56	C₁₃	C₃×#6879	1	1	yes	characteristic, direct product factor, Sylow
57	C₃²	—	3	3	no	—
58	C₃²	—	9	9	no	—
59	C₃²	—	27	9	no	—
60	C₃²	C₁₃×#732	1	2	yes	—
61	C₃²	C₁₃×#732	1	1	yes	characteristic
62	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
63	C₉	—	3	9	no	—
64	C₉	—	3	2	no	—
65	C₉	—	3	1	no	—
66	C₃	—	3	1	no	—
67	C₃	—	3	2	no	—
68	C₃	—	27	9	no	—
69	C₃	C₁₃×#6879	1	3	yes	direct product factor
70	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₁₃	#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
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
1. C₃×C₁₃×#732	C₃	semidirect
2. C₃×C₉²×C₁₃	C₃	semidirect
3. C₁₃×#6879	C₃	direct (N × H)
8. C₁₃×#732	C₃²	semidirect
10. C₉²×C₁₃	C₃²	semidirect
11. C₃×#6879	C₁₃	direct (N × H)
22. C₃×#732	C₃×C₁₃	semidirect
23. C₃×C₉²	C₃×C₁₃	semidirect
24. #6879	C₃×C₁₃	direct (N × H)
38. #732	C₃²×C₁₃	semidirect
40. C₉²	C₃²×C₁₃	semidirect
44. C₃×C₁₃	#6879	direct (N × H)
56. C₁₃	C₃×#6879	direct (N × H)
69. C₃	C₁₃×#6879	direct (N × H)

Subgroups — C3×C13×#6879 #23744986

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6879 #23744986