Subgroups — C₃×C₁₃×#6895 #23745022

Order 9477.

836 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×#6895	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₁₃×C₉⋊C₉	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃²×C₉×C₁₃	—	3	9	no	—
7	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₁₃×C₉⋊C₉	C₃²	1	81	yes	complemented
11	C₁₃×C₃²⋊C₉	C₃²	1	27	yes	—
12	C₃×#6895	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	9	no	—
14	C₃³×C₁₃	3₋¹⁺²	1	9	yes	—
15	C₃³×C₁₃	C₃³	1	3	yes	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₁₃	—	3	27	no	—
18	C₃×C₉×C₁₃	—	3	9	no	—
19	C₃×C₉×C₁₃	—	3	27	no	—
20	C₃×C₉×C₁₃	C₃³	1	27	yes	—
21	C₃×C₉×C₁₃	C₃³	1	9	yes	—
22	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
23	#6895	C₃×C₁₃	1	27	yes	direct product factor
24	C₃×C₉⋊C₉	C₃×C₁₃	1	9	yes	complemented
25	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
26	C₃²×C₁₃	—	3	9	no	—
27	C₃²×C₁₃	—	3	27	no	—
28	C₃²×C₁₃	C₃×3₋¹⁺²	1	9	yes	—
29	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
30	C₃²×C₁₃	#737	1	9	yes	—
31	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
32	C₉×C₁₃	—	3	9	no	—
33	C₉×C₁₃	—	3	27	no	—
34	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
35	C₃²×C₉	—	3	9	no	—
36	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
37	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
38	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
39	C₉⋊C₉	C₃²×C₁₃	1	81	yes	complemented
40	C₃²⋊C₉	C₃²×C₁₃	1	27	yes	—
41	C₃×C₁₃	—	3	9	no	—
42	C₃×C₁₃	#6895	1	9	yes	direct product factor
43	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
44	C₃×C₁₃	C₃×#737	1	3	yes	—
45	C₃³	—	3	9	no	—
46	C₃³	C₁₃×3₋¹⁺²	1	9	yes	—
47	C₃³	C₃³×C₁₃	1	3	yes	—
48	C₃³	C₃³×C₁₃	1	1	yes	characteristic
49	C₃×C₉	—	3	27	no	—
50	C₃×C₉	—	3	9	no	—
51	C₃×C₉	—	3	27	no	—
52	C₃×C₉	C₃³×C₁₃	1	27	yes	—
53	C₃×C₉	C₃³×C₁₃	1	9	yes	—
54	C₁₃	C₃×#6895	1	1	yes	characteristic, direct product factor, Sylow
55	C₃²	—	3	27	no	—
56	C₃²	—	3	9	no	—
57	C₃²	C₃×C₁₃×3₋¹⁺²	1	9	yes	—
58	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
59	C₃²	C₁₃×#737	1	9	yes	—
60	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
61	C₉	—	3	9	no	—
62	C₉	—	3	27	no	—
63	C₃	—	3	9	no	—
64	C₃	C₁₃×#6895	1	9	yes	direct product factor
65	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
66	C₃	C₃×C₁₃×#737	1	3	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×#6895	C₃	direct (N × H)
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
10. C₁₃×C₉⋊C₉	C₃²	semidirect
12. C₃×#6895	C₁₃	direct (N × H)
23. #6895	C₃×C₁₃	direct (N × H)
24. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
39. C₉⋊C₉	C₃²×C₁₃	semidirect
42. C₃×C₁₃	#6895	direct (N × H)
54. C₁₃	C₃×#6895	direct (N × H)
64. C₃	C₁₃×#6895	direct (N × H)

Subgroups — C3×C13×#6895 #23745022

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6895 #23745022