Subgroups — C₁₃×#10624589 #23744740

Order 9477.

668 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	2	yes	maximal, complemented
2	C₁₃×#6891	C₃	1	2	yes	maximal, complemented
3	C₁₃×#6856	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	—	3	2	no	—
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
7	C₃×C₁₃×H(3,𝔽₃)	—	3	2	no	—
8	C₃×C₁₃×H(3,𝔽₃)	—	3	2	no	—
9	C₃×C₁₃×H(3,𝔽₃)	—	3	18	no	—
10	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	6	yes	complemented
11	C₁₃×C₃²⋊C₉	—	3	4	no	—
12	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	complemented
13	#10624589	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	3	18	no	—
15	C₃³×C₁₃	—	3	6	no	—
16	C₃³×C₁₃	—	3	6	no	—
17	C₃³×C₁₃	—	9	2	no	—
18	C₃³×C₁₃	—	9	12	no	—
19	C₃³×C₁₃	—	9	6	no	—
20	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
22	C₃³×C₁₃	C₃³	1	1	yes	characteristic
23	C₁₃×3₋¹⁺²	—	9	6	no	—
24	C₁₃×H(3,𝔽₃)	—	3	18	no	—
25	C₁₃×H(3,𝔽₃)	—	3	18	no	—
26	C₁₃×H(3,𝔽₃)	—	3	18	no	—
27	C₃×C₉×C₁₃	—	3	6	no	—
28	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	2	yes	complemented
29	#6891	C₃×C₁₃	1	2	yes	complemented
30	#6856	C₃×C₁₃	1	9	yes	complemented
31	C₃²×C₁₃	—	3	2	no	—
32	C₃²×C₁₃	—	3	4	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	—	3	18	no	—
36	C₃²×C₁₃	—	3	2	no	—
37	C₃²×C₁₃	—	3	2	no	—
38	C₃²×C₁₃	—	9	9	no	—
39	C₃²×C₁₃	—	9	54	no	—
40	C₃²×C₁₃	—	9	6	no	—
41	C₃²×C₁₃	—	9	12	no	—
42	C₃²×C₁₃	AΣL(1,𝔽₂₇)	1	6	yes	—
43	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
44	C₉×C₁₃	—	9	6	no	—
45	C₃⁴	—	3	2	no	—
46	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
47	C₃×3₋¹⁺²	—	3	2	no	—
48	C₃×H(3,𝔽₃)	—	3	2	no	—
49	C₃×H(3,𝔽₃)	—	3	2	no	—
50	C₃×H(3,𝔽₃)	—	3	18	no	—
51	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	6	yes	complemented
52	C₃²⋊C₉	—	3	4	no	—
53	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	complemented
54	C₃×C₁₃	—	3	6	no	—
55	C₃×C₁₃	—	9	1	no	—
56	C₃×C₁₃	—	9	1	no	—
57	C₃×C₁₃	—	9	18	no	—
58	C₃×C₁₃	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
59	C₃×C₁₃	#6911	1	2	yes	—
60	C₃³	—	3	18	no	—
61	C₃³	—	3	6	no	—
62	C₃³	—	3	6	no	—
63	C₃³	—	9	2	no	—
64	C₃³	—	9	12	no	—
65	C₃³	—	9	6	no	—
66	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
67	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
68	C₃³	C₃³×C₁₃	1	1	yes	characteristic
69	3₋¹⁺²	—	9	6	no	—
70	H(3,𝔽₃)	—	3	18	no	—
71	H(3,𝔽₃)	—	3	18	no	—
72	H(3,𝔽₃)	—	3	18	no	—
73	C₃×C₉	—	3	6	no	—
74	C₁₃	#10624589	1	1	yes	characteristic, direct product factor, Sylow
75	C₃²	—	3	2	no	—
76	C₃²	—	3	4	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	18	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	9	9	no	—
83	C₃²	—	9	54	no	—
84	C₃²	—	9	6	no	—
85	C₃²	—	9	12	no	—
86	C₃²	C₁₃×AΣL(1,𝔽₂₇)	1	6	yes	—
87	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
88	C₉	—	9	6	no	—
89	C₃	—	3	6	no	—
90	C₃	—	9	1	no	—
91	C₃	—	9	1	no	—
92	C₃	—	9	18	no	—
93	C₃	C₃×C₁₃×AΣL(1,𝔽₂₇)	1	2	yes	—
94	C₃	C₁₃×#6911	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×H(3,𝔽₃)	C₃	semidirect
2. C₁₃×#6891	C₃	semidirect
3. C₁₃×#6856	C₃	semidirect
10. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
12. C₁₃×C₃²⋊C₉	C₃²	semidirect
13. #10624589	C₁₃	direct (N × H)
28. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
29. #6891	C₃×C₁₃	semidirect
30. #6856	C₃×C₁₃	semidirect
51. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
53. C₃²⋊C₉	C₃²×C₁₃	semidirect
74. C₁₃	#10624589	direct (N × H)

Subgroups — C13×#10624589 #23744740

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624589 #23744740