Subgroups — C₃×C₁₃×#6898 #23745026

Order 9477.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6898	C₃	1	27	yes	maximal, direct product factor
2	C₃×C₁₃×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	4	yes	maximal
4	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
7	C₃²×C₉×C₁₃	C₃²	1	8	yes	—
8	C₁₃×C₉⋊C₉	C₃²	1	72	yes	complemented
9	C₁₃×C₃²⋊C₉	C₃²	1	36	yes	—
10	C₉²×C₁₃	C₃²	1	9	yes	complemented
11	C₃×#6898	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	12	no	—
13	C₃³×C₁₃	C₃³	1	3	yes	—
14	C₃³×C₁₃	C₃³	1	1	yes	characteristic
15	C₃×C₉×C₁₃	—	3	12	no	—
16	C₃×C₉×C₁₃	—	3	24	no	—
17	C₃×C₉×C₁₃	C₃³	1	12	yes	—
18	C₃×C₉×C₁₃	C₃³	1	24	yes	—
19	#6898	C₃×C₁₃	1	27	yes	direct product factor
20	C₃×C₉⋊C₉	C₃×C₁₃	1	8	yes	complemented
21	C₃×C₃²⋊C₉	C₃×C₁₃	1	4	yes	—
22	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
23	C₃²×C₁₃	—	3	12	no	—
24	C₃²×C₁₃	—	9	9	no	—
25	C₃²×C₁₃	#737	1	12	yes	—
26	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
27	C₉×C₁₃	—	3	12	no	—
28	C₉×C₁₃	—	3	24	no	—
29	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
30	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
31	C₃²×C₉	C₃²×C₁₃	1	8	yes	—
32	C₉⋊C₉	C₃²×C₁₃	1	72	yes	complemented
33	C₃²⋊C₉	C₃²×C₁₃	1	36	yes	—
34	C₉²	C₃²×C₁₃	1	9	yes	complemented
35	C₃×C₁₃	—	9	3	no	—
36	C₃×C₁₃	#6898	1	9	yes	direct product factor
37	C₃×C₁₃	C₃×#737	1	4	yes	—
38	C₃³	—	3	12	no	—
39	C₃³	C₃³×C₁₃	1	3	yes	—
40	C₃³	C₃³×C₁₃	1	1	yes	characteristic
41	C₃×C₉	—	3	12	no	—
42	C₃×C₉	—	3	24	no	—
43	C₃×C₉	C₃³×C₁₃	1	12	yes	—
44	C₃×C₉	C₃³×C₁₃	1	24	yes	—
45	C₁₃	C₃×#6898	1	1	yes	characteristic, direct product factor, Sylow
46	C₃²	—	3	12	no	—
47	C₃²	—	9	9	no	—
48	C₃²	C₁₃×#737	1	12	yes	—
49	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
50	C₉	—	3	12	no	—
51	C₉	—	3	24	no	—
52	C₃	—	9	3	no	—
53	C₃	C₁₃×#6898	1	9	yes	direct product factor
54	C₃	C₃×C₁₃×#737	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
1. C₁₃×#6898	C₃	direct (N × H)
2. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
4. C₃×C₉²×C₁₃	C₃	semidirect
8. C₁₃×C₉⋊C₉	C₃²	semidirect
10. C₉²×C₁₃	C₃²	semidirect
11. C₃×#6898	C₁₃	direct (N × H)
19. #6898	C₃×C₁₃	direct (N × H)
20. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
22. C₃×C₉²	C₃×C₁₃	semidirect
32. C₉⋊C₉	C₃²×C₁₃	semidirect
34. C₉²	C₃²×C₁₃	semidirect
36. C₃×C₁₃	#6898	direct (N × H)
45. C₁₃	C₃×#6898	direct (N × H)
53. C₃	C₁₃×#6898	direct (N × H)

Subgroups — C3×C13×#6898 #23745026

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6898 #23745026