Subgroups — C₁₃×#10624771 #23744922

Order 9477.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6891	C₃	1	3	yes	maximal
3	C₁₃×#6867	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
6	C₃×C₁₃×3₋¹⁺²	—	3	1	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₁₃×C₃²⋊C₉	—	3	6	no	—
11	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
12	#10624771	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	3	no	—
14	C₃³×C₁₃	—	9	3	no	—
15	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
16	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₁₃×3₋¹⁺²	—	3	18	no	—
19	C₁₃×3₋¹⁺²	—	3	9	no	—
20	C₁₃×3₋¹⁺²	—	9	9	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	3	9	no	—
24	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
25	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
26	#6891	C₃×C₁₃	1	3	yes	—
27	#6867	C₃×C₁₃	1	9	yes	complemented
28	C₃²×C₁₃	—	3	3	no	—
29	C₃²×C₁₃	—	3	2	no	—
30	C₃²×C₁₃	—	3	1	no	—
31	C₃²×C₁₃	—	3	3	no	—
32	C₃²×C₁₃	—	3	6	no	—
33	C₃²×C₁₃	—	9	9	no	—
34	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
36	C₉×C₁₃	—	3	9	no	—
37	C₉×C₁₃	—	9	9	no	—
38	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
39	C₃×3₋¹⁺²	—	3	2	no	—
40	C₃×3₋¹⁺²	—	3	1	no	—
41	C₃×3₋¹⁺²	—	3	3	no	—
42	C₃×3₋¹⁺²	—	3	9	no	—
43	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
44	C₃²⋊C₉	—	3	6	no	—
45	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
46	C₃×C₁₃	—	3	3	no	—
47	C₃×C₁₃	—	9	1	no	—
48	C₃×C₁₃	—	9	2	no	—
49	C₃×C₁₃	#6891	1	1	yes	characteristic
50	C₃×C₁₃	#6910	1	3	yes	—
51	C₃³	—	3	3	no	—
52	C₃³	—	9	3	no	—
53	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
54	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
55	C₃³	C₃³×C₁₃	1	1	yes	characteristic
56	3₋¹⁺²	—	3	18	no	—
57	3₋¹⁺²	—	3	9	no	—
58	3₋¹⁺²	—	9	9	no	—
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	6	no	—
61	C₃×C₉	—	3	9	no	—
62	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
63	C₁₃	#10624771	1	1	yes	characteristic, direct product factor, Sylow
64	C₃²	—	3	3	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	3	1	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	6	no	—
69	C₃²	—	9	9	no	—
70	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
71	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
72	C₉	—	3	9	no	—
73	C₉	—	9	9	no	—
74	C₃	—	3	3	no	—
75	C₃	—	9	1	no	—
76	C₃	—	9	2	no	—
77	C₃	C₁₃×#6891	1	1	yes	characteristic
78	C₃	C₁₃×#6910	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6867	C₃	semidirect
12. #10624771	C₁₃	direct (N × H)
24. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
27. #6867	C₃×C₁₃	semidirect
62. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
63. C₁₃	#10624771	direct (N × H)

Subgroups — C13×#10624771 #23744922

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624771 #23744922