Subgroups — C₁₃×#10624806 #23744957

Order 9477.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6891	C₃	1	2	yes	maximal
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#6868	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
7	C₃²×C₉×C₁₃	—	3	1	no	—
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₁₃×C₃²⋊C₉	—	3	2	no	—
10	C₁₃×C₃²⋊C₉	—	3	1	no	—
11	C₁₃×C₃²⋊C₉	—	3	2	no	—
12	C₁₃×C₃²⋊C₉	—	3	4	no	—
13	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
15	#10624806	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₃	—	3	3	no	—
17	C₃³×C₁₃	—	3	3	no	—
18	C₃³×C₁₃	—	9	2	no	—
19	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
20	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	9	6	no	—
23	C₃×C₉×C₁₃	—	3	3	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	9	no	—
27	C₃×C₉×C₁₃	—	9	3	no	—
28	#6891	C₃×C₁₃	1	2	yes	—
29	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
30	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
31	#6868	C₃×C₁₃	1	9	yes	complemented
32	C₃²×C₁₃	—	3	2	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	—	3	1	no	—
35	C₃²×C₁₃	—	3	1	no	—
36	C₃²×C₁₃	—	3	4	no	—
37	C₃²×C₁₃	—	3	2	no	—
38	C₃²×C₁₃	—	3	2	no	—
39	C₃²×C₁₃	—	9	9	no	—
40	C₃²×C₁₃	#732	1	3	yes	—
41	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃²×C₁₃	#737	1	3	yes	—
43	C₉×C₁₃	—	9	3	no	—
44	C₉×C₁₃	—	9	3	no	—
45	C₉×C₁₃	—	9	6	no	—
46	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
47	C₃×3₋¹⁺²	—	3	2	no	—
48	C₃²×C₉	—	3	1	no	—
49	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
50	C₃²⋊C₉	—	3	2	no	—
51	C₃²⋊C₉	—	3	1	no	—
52	C₃²⋊C₉	—	3	2	no	—
53	C₃²⋊C₉	—	3	4	no	—
54	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
55	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
56	C₃×C₁₃	—	3	3	no	—
57	C₃×C₁₃	—	3	3	no	—
58	C₃×C₁₃	—	9	2	no	—
59	C₃×C₁₃	#6893	1	1	yes	characteristic
60	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
61	C₃×C₁₃	#6912	1	2	yes	—
62	C₃³	—	3	3	no	—
63	C₃³	—	3	3	no	—
64	C₃³	—	9	2	no	—
65	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
66	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
67	C₃³	C₃³×C₁₃	1	1	yes	characteristic
68	3₋¹⁺²	—	9	6	no	—
69	C₃×C₉	—	3	3	no	—
70	C₃×C₉	—	3	3	no	—
71	C₃×C₉	—	3	6	no	—
72	C₃×C₉	—	3	9	no	—
73	C₃×C₉	—	9	3	no	—
74	C₁₃	#10624806	1	1	yes	characteristic, direct product factor, Sylow
75	C₃²	—	3	1	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	4	no	—
82	C₃²	—	9	9	no	—
83	C₃²	C₁₃×#732	1	3	yes	—
84	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
85	C₃²	C₁₃×#737	1	3	yes	—
86	C₉	—	9	3	no	—
87	C₉	—	9	3	no	—
88	C₉	—	9	6	no	—
89	C₃	—	3	3	no	—
90	C₃	—	3	3	no	—
91	C₃	—	9	2	no	—
92	C₃	C₁₃×#6893	1	1	yes	characteristic
93	C₃	C₃×C₁₃×#732	1	1	yes	characteristic
94	C₃	C₁₃×#6912	1	2	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
4. C₁₃×#6868	C₃	semidirect
15. #10624806	C₁₃	direct (N × H)
31. #6868	C₃×C₁₃	semidirect
74. C₁₃	#10624806	direct (N × H)

Subgroups — C13×#10624806 #23744957

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624806 #23744957