Subgroups — C₃×C₁₃×#6887 #23745009

Order 9477.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6887	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₁₃×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃×C₉²×C₁₃	C₃	1	3	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	C₉	1	27	yes	complemented
8	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
12	C₁₃×C₉⋊C₉	C₃²	1	54	yes	complemented
13	C₁₃×C₃²⋊C₉	C₃²	1	27	yes	—
14	C₉²×C₁₃	C₃²	1	27	yes	complemented
15	C₃×#6887	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	3	9	no	—
17	C₃³×C₁₃	C₃×C₉	1	9	yes	—
18	C₃³×C₁₃	C₃³	1	3	yes	—
19	C₃³×C₁₃	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₁₃	—	3	27	no	—
21	C₃×C₉×C₁₃	C₃×C₉	1	18	yes	—
22	C₃×C₉×C₁₃	C₃×C₉	1	9	yes	—
23	C₃×C₉×C₁₃	C₃×C₉	1	81	yes	complemented
24	C₃×C₉×C₁₃	C₃³	1	27	yes	—
25	C₃×C₉×C₁₃	C₃³	1	3	yes	—
26	C₃×C₉×C₁₃	C₃³	1	6	yes	—
27	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
28	#6887	C₃×C₁₃	1	27	yes	direct product factor
29	C₃×C₉⋊C₉	C₃×C₁₃	1	6	yes	complemented
30	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
31	C₃×C₉²	C₃×C₁₃	1	3	yes	complemented
32	C₃²×C₁₃	—	3	9	no	—
33	C₃²×C₁₃	—	3	27	no	—
34	C₃²×C₁₃	C₃²×C₉	1	9	yes	—
35	C₃²×C₁₃	C₃²×C₉	1	3	yes	—
36	C₃²×C₁₃	#737	1	9	yes	—
37	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
38	C₉×C₁₃	—	3	27	no	—
39	C₉×C₁₃	C₃²×C₉	1	18	yes	—
40	C₉×C₁₃	C₃²×C₉	1	9	yes	—
41	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
42	C₃²×C₉	C₉×C₁₃	1	27	yes	complemented
43	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
44	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
45	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
46	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
47	C₉⋊C₉	C₃²×C₁₃	1	54	yes	complemented
48	C₃²⋊C₉	C₃²×C₁₃	1	27	yes	—
49	C₉²	C₃²×C₁₃	1	27	yes	complemented
50	C₃×C₁₃	—	3	9	no	—
51	C₃×C₁₃	#6887	1	9	yes	direct product factor
52	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
53	C₃×C₁₃	C₃×#737	1	3	yes	—
54	C₃³	—	3	9	no	—
55	C₃³	C₃×C₉×C₁₃	1	9	yes	—
56	C₃³	C₃³×C₁₃	1	3	yes	—
57	C₃³	C₃³×C₁₃	1	1	yes	characteristic
58	C₃×C₉	—	3	27	no	—
59	C₃×C₉	C₃×C₉×C₁₃	1	18	yes	—
60	C₃×C₉	C₃×C₉×C₁₃	1	9	yes	—
61	C₃×C₉	C₃×C₉×C₁₃	1	81	yes	complemented
62	C₃×C₉	C₃³×C₁₃	1	27	yes	—
63	C₃×C₉	C₃³×C₁₃	1	3	yes	—
64	C₃×C₉	C₃³×C₁₃	1	6	yes	—
65	C₁₃	C₃×#6887	1	1	yes	characteristic, direct product factor, Sylow
66	C₃²	—	3	27	no	—
67	C₃²	—	3	9	no	—
68	C₃²	C₃²×C₉×C₁₃	1	9	yes	—
69	C₃²	C₃²×C₉×C₁₃	1	3	yes	—
70	C₃²	C₁₃×#737	1	9	yes	—
71	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
72	C₉	—	3	27	no	—
73	C₉	C₃²×C₉×C₁₃	1	9	yes	—
74	C₉	C₃²×C₉×C₁₃	1	18	yes	—
75	C₃	—	3	9	no	—
76	C₃	C₁₃×#6887	1	9	yes	direct product factor
77	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic
78	C₃	C₃×C₁₃×#737	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉×C₁₃	C₃²
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₃²	C₃⁴×C₁₃
socle	C₃³×C₁₃	C₃³
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6887	C₃	direct (N × H)
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
5. C₃×C₉²×C₁₃	C₃	semidirect
7. C₃²×C₉×C₁₃	C₉	semidirect
12. C₁₃×C₉⋊C₉	C₃²	semidirect
14. C₉²×C₁₃	C₃²	semidirect
15. C₃×#6887	C₁₃	direct (N × H)
23. C₃×C₉×C₁₃	C₃×C₉	semidirect
28. #6887	C₃×C₁₃	direct (N × H)
29. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
31. C₃×C₉²	C₃×C₁₃	semidirect
42. C₃²×C₉	C₉×C₁₃	semidirect
47. C₉⋊C₉	C₃²×C₁₃	semidirect
49. C₉²	C₃²×C₁₃	semidirect
51. C₃×C₁₃	#6887	direct (N × H)
61. C₃×C₉	C₃×C₉×C₁₃	semidirect
65. C₁₃	C₃×#6887	direct (N × H)
76. C₃	C₁₃×#6887	direct (N × H)

Subgroups — C3×C13×#6887 #23745009

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6887 #23745009