Subgroups — C₃×C₁₃×#6900 #23745029

Order 9477.

1076 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	4	yes	maximal
2	C₁₃×#6900	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₁₃×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
4	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	36	no	—
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	36	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	8	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
10	C₁₃×C₉⋊C₉	C₃²	1	72	yes	complemented
11	C₉²×C₁₃	C₃²	1	9	yes	complemented
12	C₃×#6900	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	12	no	—
14	C₃³×C₁₃	C₃³	1	3	yes	—
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×3₋¹⁺²	—	3	108	no	—
17	C₃×C₉×C₁₃	—	3	24	no	—
18	C₃×C₉×C₁₃	3₋¹⁺²	1	36	yes	complemented
19	C₃×C₉×C₁₃	C₃³	1	24	yes	—
20	C₃×C₉×C₁₃	C₃³	1	12	yes	—
21	C₃²×3₋¹⁺²	C₃×C₁₃	1	4	yes	—
22	#6900	C₃×C₁₃	1	27	yes	direct product factor
23	C₃×C₉⋊C₉	C₃×C₁₃	1	8	yes	complemented
24	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
25	C₃²×C₁₃	—	3	12	no	—
26	C₃²×C₁₃	—	9	9	no	—
27	C₃²×C₁₃	C₃×3₋¹⁺²	1	12	yes	—
28	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
29	C₉×C₁₃	—	3	24	no	—
30	C₉×C₁₃	C₃×3₋¹⁺²	1	36	yes	complemented
31	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
32	C₃×3₋¹⁺²	—	3	36	no	—
33	C₃×3₋¹⁺²	C₃²×C₁₃	1	36	yes	—
34	C₃²×C₉	C₃²×C₁₃	1	8	yes	—
35	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
36	C₉⋊C₉	C₃²×C₁₃	1	72	yes	complemented
37	C₉²	C₃²×C₁₃	1	9	yes	complemented
38	C₃×C₁₃	—	9	3	no	—
39	C₃×C₁₃	#6900	1	9	yes	direct product factor
40	C₃×C₁₃	C₃²×3₋¹⁺²	1	4	yes	—
41	C₃³	—	3	12	no	—
42	C₃³	C₃³×C₁₃	1	3	yes	—
43	C₃³	C₃³×C₁₃	1	1	yes	characteristic
44	3₋¹⁺²	—	3	108	no	—
45	C₃×C₉	—	3	24	no	—
46	C₃×C₉	C₁₃×3₋¹⁺²	1	36	yes	complemented
47	C₃×C₉	C₃³×C₁₃	1	24	yes	—
48	C₃×C₉	C₃³×C₁₃	1	12	yes	—
49	C₁₃	C₃×#6900	1	1	yes	characteristic, direct product factor, Sylow
50	C₃²	—	3	12	no	—
51	C₃²	—	9	9	no	—
52	C₃²	C₃×C₁₃×3₋¹⁺²	1	12	yes	—
53	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
54	C₉	—	3	24	no	—
55	C₉	C₃×C₁₃×3₋¹⁺²	1	36	yes	complemented
56	C₃	—	9	3	no	—
57	C₃	C₁₃×#6900	1	9	yes	direct product factor
58	C₃	C₃²×C₁₃×3₋¹⁺²	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6900	C₃	direct (N × H)
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
4. C₃×C₉²×C₁₃	C₃	semidirect
10. C₁₃×C₉⋊C₉	C₃²	semidirect
11. C₉²×C₁₃	C₃²	semidirect
12. C₃×#6900	C₁₃	direct (N × H)
18. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
22. #6900	C₃×C₁₃	direct (N × H)
23. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
24. C₃×C₉²	C₃×C₁₃	semidirect
30. C₉×C₁₃	C₃×3₋¹⁺²	semidirect
36. C₉⋊C₉	C₃²×C₁₃	semidirect
37. C₉²	C₃²×C₁₃	semidirect
39. C₃×C₁₃	#6900	direct (N × H)
46. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
49. C₁₃	C₃×#6900	direct (N × H)
55. C₉	C₃×C₁₃×3₋¹⁺²	semidirect
57. C₃	C₁₃×#6900	direct (N × H)

Subgroups — C3×C13×#6900 #23745029

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6900 #23745029