Subgroups — C₁₃×#10624722 #23744873

Order 9477.

304 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#732	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₃×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
3	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×H(3,𝔽₃)⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₁₃×#6868	C₃	1	2	yes	maximal, complemented
6	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
7	C₃²×C₉×C₁₃	—	3	3	no	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₁₃×#732	C₉	1	9	yes	complemented
12	C₁₃×C₉⋊C₉	—	3	3	no	—
13	C₁₃×C₃²⋊C₉	—	3	6	no	—
14	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
15	#10624722	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	3	3	no	—
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₁₃×H(3,𝔽₃)	—	3	6	no	—
19	C₁₃×H(3,𝔽₃)	C₃×C₉	1	9	yes	complemented
20	C₃×C₉×C₁₃	—	3	1	no	—
21	C₃×C₉×C₁₃	—	3	2	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	3	2	no	—
24	C₃×C₉×C₁₃	—	9	1	no	—
25	C₃×C₉×C₁₃	—	9	9	no	—
26	C₃×C₉×C₁₃	—	9	2	no	—
27	C₃×C₉×C₁₃	C₃×C₉	1	3	yes	complemented
28	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
29	C₃×#732	C₃×C₁₃	1	1	yes	characteristic
30	C₉×H(3,𝔽₃)	C₃×C₁₃	1	3	yes	complemented
31	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
32	H(3,𝔽₃)⋊C₉	C₃×C₁₃	1	6	yes	complemented
33	#6868	C₃×C₁₃	1	2	yes	complemented
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	—	3	1	no	—
36	C₃²×C₁₃	—	3	9	no	—
37	C₃²×C₁₃	—	9	6	no	—
38	C₃²×C₁₃	—	9	3	no	—
39	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	C₃²×C₁₃	#737	1	2	yes	—
42	C₉×C₁₃	—	3	3	no	—
43	C₉×C₁₃	—	3	3	no	—
44	C₉×C₁₃	—	9	2	no	—
45	C₉×C₁₃	—	9	6	no	—
46	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
47	C₃²×C₉	—	3	3	no	—
48	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
49	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
50	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
51	#732	C₉×C₁₃	1	9	yes	complemented
52	C₉⋊C₉	—	3	3	no	—
53	C₃²⋊C₉	—	3	6	no	—
54	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
55	C₃×C₁₃	—	3	1	no	—
56	C₃×C₁₃	—	3	2	no	—
57	C₃×C₁₃	—	9	9	no	—
58	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
59	C₃×C₁₃	#6911	1	1	yes	characteristic
60	C₃×C₁₃	#6913	1	2	yes	—
61	C₃³	—	3	3	no	—
62	C₃³	C₃³×C₁₃	1	1	yes	characteristic
63	H(3,𝔽₃)	—	3	6	no	—
64	H(3,𝔽₃)	C₃×C₉×C₁₃	1	9	yes	complemented
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	2	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	—	3	2	no	—
69	C₃×C₉	—	9	1	no	—
70	C₃×C₉	—	9	9	no	—
71	C₃×C₉	—	9	2	no	—
72	C₃×C₉	C₃×C₉×C₁₃	1	3	yes	complemented
73	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
74	C₁₃	#10624722	1	1	yes	characteristic, direct product factor, Sylow
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	9	3	no	—
79	C₃²	—	9	6	no	—
80	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
81	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
82	C₃²	C₁₃×#737	1	2	yes	—
83	C₉	—	3	3	no	—
84	C₉	—	3	3	no	—
85	C₉	—	9	6	no	—
86	C₉	—	9	2	no	—
87	C₃	—	3	1	no	—
88	C₃	—	3	2	no	—
89	C₃	—	9	9	no	—
90	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
91	C₃	C₁₃×#6911	1	1	yes	characteristic
92	C₃	C₁₃×#6913	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃×C₁₃×#732	C₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₃×H(3,𝔽₃)	C₃	semidirect
3. C₃×C₁₃×C₉⋊C₉	C₃	semidirect
4. C₁₃×H(3,𝔽₃)⋊C₉	C₃	semidirect
5. C₁₃×#6868	C₃	semidirect
11. C₁₃×#732	C₉	semidirect
15. #10624722	C₁₃	direct (N × H)
19. C₁₃×H(3,𝔽₃)	C₃×C₉	semidirect
27. C₃×C₉×C₁₃	C₃×C₉	semidirect
30. C₉×H(3,𝔽₃)	C₃×C₁₃	semidirect
31. C₃×C₉⋊C₉	C₃×C₁₃	semidirect
32. H(3,𝔽₃)⋊C₉	C₃×C₁₃	semidirect
33. #6868	C₃×C₁₃	semidirect
51. #732	C₉×C₁₃	semidirect
64. H(3,𝔽₃)	C₃×C₉×C₁₃	semidirect
72. C₃×C₉	C₃×C₉×C₁₃	semidirect
74. C₁₃	#10624722	direct (N × H)

Subgroups — C13×#10624722 #23744873

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624722 #23744873