Subgroups — C₁₃×#10624902 #23745053

Order 9477.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6898	C₃	1	9	yes	maximal, complemented
2	C₁₃×#6896	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6895	C₃	1	12	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	2	yes	maximal
5	C₁₃×#6887	C₃	1	6	yes	maximal, complemented
6	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
7	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
10	C₁₃×C₉⋊C₉	C₃²	1	36	yes	complemented
11	C₁₃×C₉⋊C₉	C₃²	1	36	yes	complemented
12	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
13	C₁₃×C₃²⋊C₉	C₃²	1	4	yes	—
14	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
15	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
16	C₁₃×C₃²⋊C₉	C₃²	1	12	yes	—
17	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₉²×C₁₃	C₃²	1	9	yes	complemented
19	#10624902	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃³×C₁₃	—	3	6	no	—
21	C₃³×C₁₃	—	9	2	no	—
22	C₃³×C₁₃	C₃³	1	1	yes	characteristic
23	C₃³×C₁₃	C₃³	1	1	yes	characteristic
24	C₃³×C₁₃	C₃³	1	2	yes	—
25	C₁₃×3₋¹⁺²	—	9	6	no	—
26	C₃×C₉×C₁₃	—	3	18	no	—
27	C₃×C₉×C₁₃	C₃³	1	6	yes	—
28	C₃×C₉×C₁₃	C₃³	1	18	yes	—
29	C₃×C₉×C₁₃	C₃³	1	12	yes	—
30	#6898	C₃×C₁₃	1	9	yes	complemented
31	#6896	C₃×C₁₃	1	9	yes	complemented
32	#6895	C₃×C₁₃	1	12	yes	complemented
33	#6891	C₃×C₁₃	1	2	yes	—
34	#6887	C₃×C₁₃	1	6	yes	complemented
35	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
36	C₃²×C₁₃	—	3	2	no	—
37	C₃²×C₁₃	—	3	4	no	—
38	C₃²×C₁₃	—	3	2	no	—
39	C₃²×C₁₃	—	3	2	no	—
40	C₃²×C₁₃	—	3	2	no	—
41	C₃²×C₁₃	—	3	2	no	—
42	C₃²×C₁₃	—	9	9	no	—
43	C₃²×C₁₃	#737	1	6	yes	—
44	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
45	C₉×C₁₃	—	3	6	no	—
46	C₉×C₁₃	—	3	12	no	—
47	C₉×C₁₃	—	3	18	no	—
48	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
49	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
50	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
51	C₉⋊C₉	C₃²×C₁₃	1	36	yes	complemented
52	C₉⋊C₉	C₃²×C₁₃	1	36	yes	complemented
53	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
54	C₃²⋊C₉	C₃²×C₁₃	1	4	yes	—
55	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
56	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
57	C₃²⋊C₉	C₃²×C₁₃	1	12	yes	—
58	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
59	C₉²	C₃²×C₁₃	1	9	yes	complemented
60	C₃×C₁₃	—	3	6	no	—
61	C₃×C₁₃	—	9	1	no	—
62	C₃×C₁₃	—	9	1	no	—
63	C₃×C₁₃	C₃×#737	1	2	yes	—
64	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
65	C₃³	—	3	6	no	—
66	C₃³	—	9	2	no	—
67	C₃³	C₃³×C₁₃	1	1	yes	characteristic
68	C₃³	C₃³×C₁₃	1	1	yes	characteristic
69	C₃³	C₃³×C₁₃	1	2	yes	—
70	3₋¹⁺²	—	9	6	no	—
71	C₃×C₉	—	3	18	no	—
72	C₃×C₉	C₃³×C₁₃	1	6	yes	—
73	C₃×C₉	C₃³×C₁₃	1	18	yes	—
74	C₃×C₉	C₃³×C₁₃	1	12	yes	—
75	C₁₃	#10624902	1	1	yes	characteristic, direct product factor, Sylow
76	C₃²	—	3	2	no	—
77	C₃²	—	3	4	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	9	9	no	—
83	C₃²	C₁₃×#737	1	6	yes	—
84	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
85	C₉	—	3	6	no	—
86	C₉	—	3	12	no	—
87	C₉	—	3	18	no	—
88	C₃	—	3	6	no	—
89	C₃	—	9	1	no	—
90	C₃	—	9	1	no	—
91	C₃	C₃×C₁₃×#737	1	2	yes	—
92	C₃	C₁₃×3₋¹⁺⁴	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#6898	C₃	semidirect
2. C₁₃×#6896	C₃	semidirect
3. C₁₃×#6895	C₃	semidirect
5. C₁₃×#6887	C₃	semidirect
10. C₁₃×C₉⋊C₉	C₃²	semidirect
11. C₁₃×C₉⋊C₉	C₃²	semidirect
18. C₉²×C₁₃	C₃²	semidirect
19. #10624902	C₁₃	direct (N × H)
30. #6898	C₃×C₁₃	semidirect
31. #6896	C₃×C₁₃	semidirect
32. #6895	C₃×C₁₃	semidirect
34. #6887	C₃×C₁₃	semidirect
51. C₉⋊C₉	C₃²×C₁₃	semidirect
52. C₉⋊C₉	C₃²×C₁₃	semidirect
59. C₉²	C₃²×C₁₃	semidirect
75. C₁₃	#10624902	direct (N × H)

Subgroups — C13×#10624902 #23745053

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624902 #23745053