Subgroups — C₁₃×#10624872 #23745023

Order 9477.

824 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	6	yes	maximal, complemented
3	C₁₃×#6894	C₃	1	18	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	3	yes	maximal
5	C₉×C₁₃×3₋¹⁺²	C₃	1	9	yes	maximal, complemented
6	C₁₃×#6887	C₃	1	3	yes	maximal, complemented
7	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
9	C₃²×C₉×C₁₃	—	3	9	no	—
10	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
13	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
14	C₁₃×C₉⋊C₉	C₃²	1	18	yes	complemented
15	C₁₃×C₉⋊C₉	C₃²	1	54	yes	complemented
16	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
17	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
18	C₉²×C₁₃	C₃²	1	9	yes	complemented
19	#10624872	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃³×C₁₃	—	3	3	no	—
21	C₃³×C₁₃	—	3	9	no	—
22	C₃³×C₁₃	C₃³	1	1	yes	characteristic
23	C₃³×C₁₃	C₃³	1	3	yes	—
24	C₁₃×3₋¹⁺²	—	3	27	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	18	no	—
27	C₃×C₉×C₁₃	—	3	9	no	—
28	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
29	C₃×C₉×C₁₃	C₃³	1	27	yes	—
30	C₃×C₉×C₁₃	C₃³	1	6	yes	—
31	C₃×C₉×C₁₃	C₃³	1	2	yes	—
32	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
33	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
34	#6895	C₃×C₁₃	1	6	yes	complemented
35	#6894	C₃×C₁₃	1	18	yes	complemented
36	#6891	C₃×C₁₃	1	3	yes	—
37	C₉×3₋¹⁺²	C₃×C₁₃	1	9	yes	complemented
38	#6887	C₃×C₁₃	1	3	yes	complemented
39	C₃²×C₁₃	—	3	27	no	—
40	C₃²×C₁₃	—	3	3	no	—
41	C₃²×C₁₃	—	3	3	no	—
42	C₃²×C₁₃	—	3	6	no	—
43	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
44	C₃²×C₁₃	#737	1	9	yes	—
45	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
46	C₉×C₁₃	—	3	6	no	—
47	C₉×C₁₃	—	3	27	no	—
48	C₉×C₁₃	C₃×3₋¹⁺²	1	6	yes	—
49	C₉×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
50	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
51	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
52	C₃²×C₉	—	3	9	no	—
53	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
54	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
55	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
56	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
57	C₉⋊C₉	C₃²×C₁₃	1	18	yes	complemented
58	C₉⋊C₉	C₃²×C₁₃	1	54	yes	complemented
59	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
60	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
61	C₉²	C₃²×C₁₃	1	9	yes	complemented
62	C₃×C₁₃	—	3	3	no	—
63	C₃×C₁₃	—	3	9	no	—
64	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
65	C₃×C₁₃	C₃×#737	1	3	yes	—
66	C₃³	—	3	3	no	—
67	C₃³	—	3	9	no	—
68	C₃³	C₃³×C₁₃	1	1	yes	characteristic
69	C₃³	C₃³×C₁₃	1	3	yes	—
70	3₋¹⁺²	—	3	27	no	—
71	C₃×C₉	—	3	6	no	—
72	C₃×C₉	—	3	9	no	—
73	C₃×C₉	—	3	18	no	—
74	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
75	C₃×C₉	C₃³×C₁₃	1	27	yes	—
76	C₃×C₉	C₃³×C₁₃	1	6	yes	—
77	C₃×C₉	C₃³×C₁₃	1	2	yes	—
78	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
79	C₁₃	#10624872	1	1	yes	characteristic, direct product factor, Sylow
80	C₃²	—	3	27	no	—
81	C₃²	—	3	3	no	—
82	C₃²	—	3	3	no	—
83	C₃²	—	3	6	no	—
84	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
85	C₃²	C₁₃×#737	1	9	yes	—
86	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
87	C₉	—	3	6	no	—
88	C₉	—	3	27	no	—
89	C₉	C₃×C₁₃×3₋¹⁺²	1	6	yes	—
90	C₉	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
91	C₃	—	3	3	no	—
92	C₃	—	3	9	no	—
93	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
94	C₃	C₃×C₁₃×#737	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6895	C₃	semidirect
3. C₁₃×#6894	C₃	semidirect
5. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
6. C₁₃×#6887	C₃	semidirect
14. C₁₃×C₉⋊C₉	C₃²	semidirect
15. C₁₃×C₉⋊C₉	C₃²	semidirect
18. C₉²×C₁₃	C₃²	semidirect
19. #10624872	C₁₃	direct (N × H)
28. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
34. #6895	C₃×C₁₃	semidirect
35. #6894	C₃×C₁₃	semidirect
37. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
38. #6887	C₃×C₁₃	semidirect
57. C₉⋊C₉	C₃²×C₁₃	semidirect
58. C₉⋊C₉	C₃²×C₁₃	semidirect
61. C₉²	C₃²×C₁₃	semidirect
74. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
79. C₁₃	#10624872	direct (N × H)

Subgroups — C13×#10624872 #23745023

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624872 #23745023