Subgroups — C₃×C₁₃×#6861 #23744735

Order 9477.

284 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal
3	C₁₃×#6861	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃²×C₉×C₁₃	—	3	1	no	—
6	C₃²×C₉×C₁₃	—	3	3	no	—
7	C₁₃×C₃²⋊C₉	—	3	2	no	—
8	C₁₃×C₃²⋊C₉	—	3	6	no	—
9	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
10	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
11	C₃×#6861	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	3	no	—
13	C₃³×C₁₃	—	3	3	no	—
14	C₃³×C₁₃	—	3	6	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	C₃×C₉×C₁₃	—	3	3	no	—
19	C₃×C₉×C₁₃	—	3	9	no	—
20	C₃×C₉×C₁₃	—	9	3	no	—
21	C₃×C₉×C₁₃	—	9	9	no	—
22	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
23	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
24	#6861	C₃×C₁₃	1	9	yes	direct product factor
25	C₃²×C₁₃	—	3	2	no	—
26	C₃²×C₁₃	—	3	1	no	—
27	C₃²×C₁₃	—	3	2	no	—
28	C₃²×C₁₃	—	3	1	no	—
29	C₃²×C₁₃	—	3	4	no	—
30	C₃²×C₁₃	—	3	2	no	—
31	C₃²×C₁₃	—	9	9	no	—
32	C₃²×C₁₃	#731	1	3	yes	—
33	C₃²×C₁₃	#732	1	3	yes	—
34	C₃²×C₁₃	#733	1	6	yes	—
35	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₉×C₁₃	—	9	3	no	—
37	C₉×C₁₃	—	9	9	no	—
38	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
39	C₃²×C₉	—	3	1	no	—
40	C₃²×C₉	—	3	3	no	—
41	C₃²⋊C₉	—	3	2	no	—
42	C₃²⋊C₉	—	3	6	no	—
43	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
44	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
45	C₃×C₁₃	—	9	2	no	—
46	C₃×C₁₃	—	9	1	no	—
47	C₃×C₁₃	#6861	1	9	yes	direct product factor
48	C₃×C₁₃	C₃×#731	1	1	yes	characteristic
49	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
50	C₃×C₁₃	C₃×#733	1	2	yes	—
51	C₃³	—	3	3	no	—
52	C₃³	—	3	3	no	—
53	C₃³	—	3	6	no	—
54	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
55	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
56	C₃³	C₃³×C₁₃	1	1	yes	characteristic
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	—	3	9	no	—
59	C₃×C₉	—	9	3	no	—
60	C₃×C₉	—	9	9	no	—
61	C₁₃	C₃×#6861	1	1	yes	characteristic, direct product factor, Sylow
62	C₃²	—	3	2	no	—
63	C₃²	—	3	1	no	—
64	C₃²	—	3	2	no	—
65	C₃²	—	3	1	no	—
66	C₃²	—	3	4	no	—
67	C₃²	—	3	2	no	—
68	C₃²	—	9	9	no	—
69	C₃²	C₁₃×#731	1	3	yes	—
70	C₃²	C₁₃×#732	1	3	yes	—
71	C₃²	C₁₃×#733	1	6	yes	—
72	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
73	C₉	—	9	3	no	—
74	C₉	—	9	9	no	—
75	C₃	—	9	2	no	—
76	C₃	—	9	1	no	—
77	C₃	C₁₃×#6861	1	9	yes	direct product factor
78	C₃	C₃×C₁₃×#731	1	1	yes	characteristic
79	C₃	C₃×C₁₃×#732	1	1	yes	characteristic
80	C₃	C₃×C₁₃×#733	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6861	C₃	direct (N × H)
11. C₃×#6861	C₁₃	direct (N × H)
24. #6861	C₃×C₁₃	direct (N × H)
47. C₃×C₁₃	#6861	direct (N × H)
61. C₁₃	C₃×#6861	direct (N × H)
77. C₃	C₁₃×#6861	direct (N × H)

Subgroups — C3×C13×#6861 #23744735

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6861 #23744735