Subgroups — C₃×C₁₃×#6896 #23745024

Order 9477.

884 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal
2	C₁₃×#6896	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₁₃×C₉⋊C₉	C₃	1	4	yes	maximal, complemented
4	C₃×C₁₃×C₉⋊C₉	C₃	1	4	yes	maximal, complemented
5	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
6	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×3₋¹⁺²	—	3	18	no	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	18	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
13	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
14	C₁₃×C₉⋊C₉	C₃²	1	36	yes	complemented
15	C₁₃×C₉⋊C₉	C₃²	1	36	yes	complemented
16	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
17	C₉²×C₁₃	C₃²	1	9	yes	complemented
18	C₃×#6896	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃³×C₁₃	—	3	6	no	—
20	C₃³×C₁₃	—	3	6	no	—
21	C₃³×C₁₃	C₃³	1	3	yes	—
22	C₃³×C₁₃	C₃³	1	1	yes	characteristic
23	C₁₃×3₋¹⁺²	—	3	54	no	—
24	C₃×C₉×C₁₃	—	3	12	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	12	no	—
27	C₃×C₉×C₁₃	3₋¹⁺²	1	18	yes	complemented
28	C₃×C₉×C₁₃	C₃³	1	6	yes	—
29	C₃×C₉×C₁₃	C₃³	1	12	yes	—
30	C₃×C₉×C₁₃	C₃³	1	12	yes	—
31	C₃×C₉×C₁₃	C₃³	1	6	yes	—
32	C₃²×3₋¹⁺²	C₃×C₁₃	1	2	yes	—
33	#6896	C₃×C₁₃	1	27	yes	direct product factor
34	C₃×C₉⋊C₉	C₃×C₁₃	1	4	yes	complemented
35	C₃×C₉⋊C₉	C₃×C₁₃	1	4	yes	complemented
36	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
37	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
38	C₃²×C₁₃	—	3	6	no	—
39	C₃²×C₁₃	—	3	6	no	—
40	C₃²×C₁₃	—	9	9	no	—
41	C₃²×C₁₃	C₃×3₋¹⁺²	1	6	yes	—
42	C₃²×C₁₃	#737	1	6	yes	—
43	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
44	C₉×C₁₃	—	3	12	no	—
45	C₉×C₁₃	—	3	6	no	—
46	C₉×C₁₃	—	3	12	no	—
47	C₉×C₁₃	C₃×3₋¹⁺²	1	18	yes	complemented
48	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
49	C₃×3₋¹⁺²	—	3	18	no	—
50	C₃×3₋¹⁺²	C₃²×C₁₃	1	18	yes	—
51	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
52	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
53	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
54	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
55	C₉⋊C₉	C₃²×C₁₃	1	36	yes	complemented
56	C₉⋊C₉	C₃²×C₁₃	1	36	yes	complemented
57	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
58	C₉²	C₃²×C₁₃	1	9	yes	complemented
59	C₃×C₁₃	—	9	3	no	—
60	C₃×C₁₃	#6896	1	9	yes	direct product factor
61	C₃×C₁₃	C₃²×3₋¹⁺²	1	2	yes	—
62	C₃×C₁₃	C₃×#737	1	2	yes	—
63	C₃³	—	3	6	no	—
64	C₃³	—	3	6	no	—
65	C₃³	C₃³×C₁₃	1	3	yes	—
66	C₃³	C₃³×C₁₃	1	1	yes	characteristic
67	3₋¹⁺²	—	3	54	no	—
68	C₃×C₉	—	3	12	no	—
69	C₃×C₉	—	3	6	no	—
70	C₃×C₉	—	3	12	no	—
71	C₃×C₉	C₁₃×3₋¹⁺²	1	18	yes	complemented
72	C₃×C₉	C₃³×C₁₃	1	6	yes	—
73	C₃×C₉	C₃³×C₁₃	1	12	yes	—
74	C₃×C₉	C₃³×C₁₃	1	12	yes	—
75	C₃×C₉	C₃³×C₁₃	1	6	yes	—
76	C₁₃	C₃×#6896	1	1	yes	characteristic, direct product factor, Sylow
77	C₃²	—	3	6	no	—
78	C₃²	—	3	6	no	—
79	C₃²	—	9	9	no	—
80	C₃²	C₃×C₁₃×3₋¹⁺²	1	6	yes	—
81	C₃²	C₁₃×#737	1	6	yes	—
82	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
83	C₉	—	3	12	no	—
84	C₉	—	3	6	no	—
85	C₉	—	3	12	no	—
86	C₉	C₃×C₁₃×3₋¹⁺²	1	18	yes	complemented
87	C₃	—	9	3	no	—
88	C₃	C₁₃×#6896	1	9	yes	direct product factor
89	C₃	C₃²×C₁₃×3₋¹⁺²	1	2	yes	—
90	C₃	C₃×C₁₃×#737	1	2	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×#6896	C₃	direct (N × H)
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
4. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
6. C₃×C₉²×C₁₃	C₃	semidirect
14. C₁₃×C₉⋊C₉	C₃²	semidirect
15. C₁₃×C₉⋊C₉	C₃²	semidirect
17. C₉²×C₁₃	C₃²	semidirect
18. C₃×#6896	C₁₃	direct (N × H)
27. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
33. #6896	C₃×C₁₃	direct (N × H)
34. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
35. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
37. C₃×C₉²	C₃×C₁₃	semidirect
47. C₉×C₁₃	C₃×3₋¹⁺²	semidirect
55. C₉⋊C₉	C₃²×C₁₃	semidirect
56. C₉⋊C₉	C₃²×C₁₃	semidirect
58. C₉²	C₃²×C₁₃	semidirect
60. C₃×C₁₃	#6896	direct (N × H)
71. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
76. C₁₃	C₃×#6896	direct (N × H)
86. C₉	C₃×C₁₃×3₋¹⁺²	semidirect
88. C₃	C₁₃×#6896	direct (N × H)

Subgroups — C3×C13×#6896 #23745024

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6896 #23745024