Subgroups — C₃×C₉×C₃³⋊C₁₃ #23748628

Order 9477.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₃³⋊C₁₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₃³⋊C₁₃	C₉	1	3	yes	direct product factor
4	C₃×C₃³⋊C₁₃	C₃²	1	1	yes	characteristic
5	C₃⁴×C₉	C₁₃	1	1	yes	maximal, characteristic, complemented, Sylow
6	C₃³⋊C₁₃	C₃×C₉	1	1	yes	characteristic, direct product factor
7	C₃×C₉×C₁₃	—	27	1	no	maximal
8	C₃⁵	C₃×C₁₃	1	1	yes	characteristic
9	C₃³×C₉	—	13	1	no	—
10	C₃³×C₉	—	13	6	no	—
11	C₃³×C₉	—	13	2	no	—
12	C₃³×C₉	C₃×C₁₃	1	3	yes	complemented
13	C₃²×C₁₃	—	27	1	no	—
14	C₉×C₁₃	—	27	3	no	—
15	C₃⁴	—	13	2	no	—
16	C₃⁴	—	13	6	no	—
17	C₃⁴	—	13	1	no	—
18	C₃⁴	C₉×C₁₃	1	3	yes	complemented
19	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
20	C₃²×C₉	—	13	12	no	—
21	C₃²×C₉	—	13	36	no	—
22	C₃²×C₉	—	13	1	no	—
23	C₃²×C₉	—	13	6	no	—
24	C₃²×C₉	—	13	18	no	—
25	C₃²×C₉	—	13	2	no	—
26	C₃²×C₉	—	13	6	no	—
27	C₃²×C₉	—	13	3	no	—
28	C₃²×C₉	—	13	6	no	—
29	C₃×C₁₃	—	27	3	no	—
30	C₃×C₁₃	—	27	1	no	—
31	C₃³	—	13	6	no	—
32	C₃³	—	13	2	no	—
33	C₃³	—	13	1	no	—
34	C₃³	—	13	3	no	—
35	C₃³	—	13	2	no	—
36	C₃³	—	13	6	no	—
37	C₃³	—	13	6	no	—
38	C₃³	—	13	18	no	—
39	C₃³	—	13	36	no	—
40	C₃³	—	13	12	no	—
41	C₃³	—	13	1	no	—
42	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic, complemented
43	C₃×C₉	—	13	12	no	—
44	C₃×C₉	—	13	36	no	—
45	C₃×C₉	—	13	2	no	—
46	C₃×C₉	—	13	6	no	—
47	C₃×C₉	—	13	3	no	—
48	C₃×C₉	—	13	18	no	—
49	C₃×C₉	—	13	6	no	—
50	C₃×C₉	C₃³⋊C₁₃	1	1	yes	characteristic, direct product factor
51	C₁₃	—	27	1	no	Sylow
52	C₃²	—	13	1	no	—
53	C₃²	—	13	6	no	—
54	C₃²	—	13	2	no	—
55	C₃²	—	13	18	no	—
56	C₃²	—	13	6	no	—
57	C₃²	—	13	12	no	—
58	C₃²	—	13	36	no	—
59	C₃²	—	13	6	no	—
60	C₃²	—	13	3	no	—
61	C₃²	—	13	2	no	—
62	C₃²	—	13	1	no	—
63	C₃²	C₃×C₃³⋊C₁₃	1	1	yes	characteristic
64	C₉	—	13	6	no	—
65	C₉	C₃×C₃³⋊C₁₃	1	3	yes	direct product factor
66	C₃	—	13	2	no	—
67	C₃	—	13	6	no	—
68	C₃	—	13	1	no	—
69	C₃	C₉×C₃³⋊C₁₃	1	3	yes	direct product factor
70	C₃	C₃²×C₃³⋊C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₉	C₃³⋊C₁₃
commutator, hypocenter	C₃³	C₃×C₉×C₁₃
Frattini	C₃	C₃²×C₃³⋊C₁₃
Fitting	C₃⁴×C₉	C₁₃
socle	C₃⁵	C₃×C₁₃
prime radical	C₃²×C₃³⋊C₁₃	C₃
cosocle	C₃⁴	C₃²×C₁₃
LCS	G ▷ C₃³
UCS	C₁ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
2. C₉×C₃³⋊C₁₃	C₃	direct (N × H)
3. C₃×C₃³⋊C₁₃	C₉	direct (N × H)
5. C₃⁴×C₉	C₁₃	semidirect
6. C₃³⋊C₁₃	C₃×C₉	direct (N × H)
12. C₃³×C₉	C₃×C₁₃	semidirect
18. C₃⁴	C₉×C₁₃	semidirect
42. C₃³	C₃×C₉×C₁₃	semidirect
50. C₃×C₉	C₃³⋊C₁₃	direct (N × H)
65. C₉	C₃×C₃³⋊C₁₃	direct (N × H)
69. C₃	C₉×C₃³⋊C₁₃	direct (N × H)

Subgroups — C3×C9×C33⋊C13 #23748628

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₉×C₃³⋊C₁₃ #23748628