Subgroups — C₁₃×#10624906 #23745057

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×#6897	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6894	C₃	1	12	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	2	yes	maximal
5	C₉×C₁₃×3₋¹⁺²	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	6	yes	—
17	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
19	C₉²×C₁₃	C₃²	1	9	yes	complemented
20	#10624906	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃³×C₁₃	—	3	6	no	—
22	C₃³×C₁₃	—	9	2	no	—
23	C₃³×C₁₃	C₃³	1	1	yes	characteristic
24	C₃³×C₁₃	C₃³	1	1	yes	characteristic
25	C₃³×C₁₃	C₃³	1	2	yes	—
26	C₁₃×3₋¹⁺²	—	3	18	no	—
27	C₃×C₉×C₁₃	—	9	6	no	—
28	C₃×C₉×C₁₃	C₃³	1	6	yes	—
29	C₃×C₉×C₁₃	C₃³	1	18	yes	—
30	C₃×C₉×C₁₃	C₃³	1	12	yes	—
31	#6898	C₃×C₁₃	1	9	yes	complemented
32	#6897	C₃×C₁₃	1	9	yes	complemented
33	#6894	C₃×C₁₃	1	12	yes	complemented
34	#6891	C₃×C₁₃	1	2	yes	—
35	C₉×3₋¹⁺²	C₃×C₁₃	1	6	yes	complemented
36	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
37	C₃²×C₁₃	—	3	2	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	—	3	2	no	—
43	C₃²×C₁₃	—	3	2	no	—
44	C₃²×C₁₃	—	9	9	no	—
45	C₃²×C₁₃	#737	1	6	yes	—
46	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
47	C₉×C₁₃	—	3	18	no	—
48	C₉×C₁₃	—	3	6	no	—
49	C₉×C₁₃	—	3	12	no	—
50	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
51	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
52	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
53	C₉⋊C₉	C₃²×C₁₃	1	36	yes	complemented
54	C₉⋊C₉	C₃²×C₁₃	1	36	yes	complemented
55	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
56	C₃²⋊C₉	C₃²×C₁₃	1	4	yes	—
57	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
58	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
59	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
60	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
61	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
62	C₉²	C₃²×C₁₃	1	9	yes	complemented
63	C₃×C₁₃	—	3	6	no	—
64	C₃×C₁₃	—	9	1	no	—
65	C₃×C₁₃	—	9	1	no	—
66	C₃×C₁₃	C₃×#737	1	2	yes	—
67	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
68	C₃³	—	3	6	no	—
69	C₃³	—	9	2	no	—
70	C₃³	C₃³×C₁₃	1	1	yes	characteristic
71	C₃³	C₃³×C₁₃	1	1	yes	characteristic
72	C₃³	C₃³×C₁₃	1	2	yes	—
73	3₋¹⁺²	—	3	18	no	—
74	C₃×C₉	—	9	6	no	—
75	C₃×C₉	C₃³×C₁₃	1	6	yes	—
76	C₃×C₉	C₃³×C₁₃	1	18	yes	—
77	C₃×C₉	C₃³×C₁₃	1	12	yes	—
78	C₁₃	#10624906	1	1	yes	characteristic, direct product factor, Sylow
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	3	2	no	—
83	C₃²	—	3	2	no	—
84	C₃²	—	3	2	no	—
85	C₃²	—	3	2	no	—
86	C₃²	—	9	9	no	—
87	C₃²	C₁₃×#737	1	6	yes	—
88	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
89	C₉	—	3	18	no	—
90	C₉	—	3	6	no	—
91	C₉	—	3	12	no	—
92	C₃	—	3	6	no	—
93	C₃	—	9	1	no	—
94	C₃	—	9	1	no	—
95	C₃	C₃×C₁₃×#737	1	2	yes	—
96	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×#6897	C₃	semidirect
3. C₁₃×#6894	C₃	semidirect
5. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
10. C₁₃×C₉⋊C₉	C₃²	semidirect
11. C₁₃×C₉⋊C₉	C₃²	semidirect
19. C₉²×C₁₃	C₃²	semidirect
20. #10624906	C₁₃	direct (N × H)
31. #6898	C₃×C₁₃	semidirect
32. #6897	C₃×C₁₃	semidirect
33. #6894	C₃×C₁₃	semidirect
35. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
53. C₉⋊C₉	C₃²×C₁₃	semidirect
54. C₉⋊C₉	C₃²×C₁₃	semidirect
62. C₉²	C₃²×C₁₃	semidirect
78. C₁₃	#10624906	direct (N × H)

Subgroups — C13×#10624906 #23745057

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624906 #23745057