Subgroups — C₃²×C₉²×C₁₃ #23745006

Order 9477.

2132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	4	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	36	yes	maximal, direct product factor
3	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
4	C₃²×C₉×C₁₃	C₉	1	108	yes	direct product factor
5	C₃²×C₉×C₁₃	C₃²	1	48	yes	—
6	C₉²×C₁₃	C₃²	1	81	yes	direct product factor
7	C₃²×C₉²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₃	C₃×C₉	1	36	yes	—
9	C₃³×C₁₃	C₃³	1	4	yes	—
10	C₃×C₉×C₁₃	C₃×C₉	1	432	yes	direct product factor
11	C₃×C₉×C₁₃	C₃³	1	36	yes	—
12	C₃³×C₉	C₃×C₁₃	1	4	yes	—
13	C₃×C₉²	C₃×C₁₃	1	36	yes	direct product factor
14	C₃²×C₁₃	C₉²	1	81	yes	direct product factor
15	C₃²×C₁₃	C₃²×C₉	1	48	yes	—
16	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
17	C₉×C₁₃	C₃²×C₉	1	108	yes	direct product factor
18	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
19	C₃²×C₉	C₉×C₁₃	1	108	yes	direct product factor
20	C₃²×C₉	C₃²×C₁₃	1	48	yes	—
21	C₉²	C₃²×C₁₃	1	81	yes	direct product factor
22	C₃×C₁₃	C₃×C₉²	1	36	yes	direct product factor
23	C₃×C₁₃	C₃³×C₉	1	4	yes	—
24	C₃³	C₃×C₉×C₁₃	1	36	yes	—
25	C₃³	C₃³×C₁₃	1	4	yes	—
26	C₃×C₉	C₃×C₉×C₁₃	1	432	yes	direct product factor
27	C₃×C₉	C₃³×C₁₃	1	36	yes	—
28	C₁₃	C₃²×C₉²	1	1	yes	characteristic, direct product factor, Sylow
29	C₃²	C₉²×C₁₃	1	81	yes	direct product factor
30	C₃²	C₃²×C₉×C₁₃	1	48	yes	—
31	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
32	C₉	C₃²×C₉×C₁₃	1	108	yes	direct product factor
33	C₃	C₃×C₉²×C₁₃	1	36	yes	direct product factor
34	C₃	C₃³×C₉×C₁₃	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₉²×C₁₃	C₃	direct (N × H)
4. C₃²×C₉×C₁₃	C₉	direct (N × H)
6. C₉²×C₁₃	C₃²	direct (N × H)
7. C₃²×C₉²	C₁₃	direct (N × H)
10. C₃×C₉×C₁₃	C₃×C₉	direct (N × H)
13. C₃×C₉²	C₃×C₁₃	direct (N × H)
14. C₃²×C₁₃	C₉²	direct (N × H)
17. C₉×C₁₃	C₃²×C₉	direct (N × H)
19. C₃²×C₉	C₉×C₁₃	direct (N × H)
21. C₉²	C₃²×C₁₃	direct (N × H)
22. C₃×C₁₃	C₃×C₉²	direct (N × H)
26. C₃×C₉	C₃×C₉×C₁₃	direct (N × H)
28. C₁₃	C₃²×C₉²	direct (N × H)
29. C₃²	C₉²×C₁₃	direct (N × H)
32. C₉	C₃²×C₉×C₁₃	direct (N × H)
33. C₃	C₃×C₉²×C₁₃	direct (N × H)

Subgroups — C32×C92×C13 #23745006

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₉²×C₁₃ #23745006