Subgroups — C₃²×C₅×C₉⋊C₉ #16814366

Order 3645.

1484 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅×C₉	C₃	1	3	yes	maximal
2	C₃³×C₅×C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₅×C₉⋊C₉	C₃	1	36	yes	maximal, direct product factor
4	C₃²×C₉⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₅	C₃²	1	1	yes	characteristic
6	C₃²×C₅×C₉	—	3	27	no	—
7	C₃²×C₅×C₉	C₉	1	27	yes	complemented
8	C₃²×C₅×C₉	C₃²	1	36	yes	—
9	C₃²×C₅×C₉	C₃²	1	12	yes	—
10	C₅×C₉⋊C₉	C₃²	1	81	yes	direct product factor
11	C₃³×C₉	C₃×C₅	1	3	yes	—
12	C₃³×C₉	C₃×C₅	1	1	yes	characteristic
13	C₃×C₉⋊C₉	C₃×C₅	1	36	yes	direct product factor
14	C₃³×C₅	C₃×C₉	1	9	yes	—
15	C₃³×C₅	3₋¹⁺²	1	27	yes	—
16	C₃³×C₅	C₃³	1	4	yes	—
17	C₃×C₅×C₉	—	3	108	no	—
18	C₃×C₅×C₉	C₃×C₉	1	108	yes	complemented
19	C₃×C₅×C₉	C₃³	1	27	yes	—
20	C₃×C₅×C₉	C₃³	1	9	yes	—
21	C₃⁴	C₃²×C₅	1	1	yes	characteristic
22	C₃²×C₉	—	3	27	no	—
23	C₃²×C₉	C₅×C₉	1	27	yes	complemented
24	C₃²×C₉	C₃²×C₅	1	36	yes	—
25	C₃²×C₉	C₃²×C₅	1	12	yes	—
26	C₉⋊C₉	C₃²×C₅	1	81	yes	direct product factor
27	C₃²×C₅	C₉⋊C₉	1	81	yes	direct product factor
28	C₃²×C₅	C₃²×C₉	1	12	yes	—
29	C₃²×C₅	C₃×3₋¹⁺²	1	36	yes	—
30	C₃²×C₅	C₃⁴	1	1	yes	characteristic
31	C₅×C₉	—	3	27	no	—
32	C₅×C₉	C₃²×C₉	1	27	yes	complemented
33	C₃³	C₃×C₅×C₉	1	9	yes	—
34	C₃³	C₅×3₋¹⁺²	1	27	yes	—
35	C₃³	C₃³×C₅	1	4	yes	—
36	C₃×C₉	—	3	108	no	—
37	C₃×C₉	C₃×C₅×C₉	1	108	yes	complemented
38	C₃×C₉	C₃³×C₅	1	27	yes	—
39	C₃×C₉	C₃³×C₅	1	9	yes	—
40	C₃×C₅	C₃×C₉⋊C₉	1	36	yes	direct product factor
41	C₃×C₅	C₃³×C₉	1	1	yes	characteristic
42	C₃×C₅	C₃²×3₋¹⁺²	1	3	yes	—
43	C₃²	C₅×C₉⋊C₉	1	81	yes	direct product factor
44	C₃²	C₃²×C₅×C₉	1	12	yes	—
45	C₃²	C₃×C₅×3₋¹⁺²	1	36	yes	—
46	C₃²	C₃⁴×C₅	1	1	yes	characteristic
47	C₉	—	3	27	no	—
48	C₉	C₃²×C₅×C₉	1	27	yes	complemented
49	C₅	C₃²×C₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₃	C₃×C₅×C₉⋊C₉	1	36	yes	direct product factor
51	C₃	C₃³×C₅×C₉	1	1	yes	characteristic
52	C₃	C₃²×C₅×3₋¹⁺²	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₃⁴×C₅	C₃²
commutator	C₃	C₃³×C₅×C₉
Frattini, cosocle	C₃²	C₃⁴×C₅
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃⁴×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₉⋊C₉	C₃	direct (N × H)
4. C₃²×C₉⋊C₉	C₅	direct (N × H)
7. C₃²×C₅×C₉	C₉	semidirect
10. C₅×C₉⋊C₉	C₃²	direct (N × H)
13. C₃×C₉⋊C₉	C₃×C₅	direct (N × H)
18. C₃×C₅×C₉	C₃×C₉	semidirect
23. C₃²×C₉	C₅×C₉	semidirect
26. C₉⋊C₉	C₃²×C₅	direct (N × H)
27. C₃²×C₅	C₉⋊C₉	direct (N × H)
32. C₅×C₉	C₃²×C₉	semidirect
37. C₃×C₉	C₃×C₅×C₉	semidirect
40. C₃×C₅	C₃×C₉⋊C₉	direct (N × H)
43. C₃²	C₅×C₉⋊C₉	direct (N × H)
48. C₉	C₃²×C₅×C₉	semidirect
49. C₅	C₃²×C₉⋊C₉	direct (N × H)
50. C₃	C₃×C₅×C₉⋊C₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃³×C₅×C₉	3
C₃×C₅×C₉⋊C₉	3
C₃²×C₉⋊C₉	5

Subgroups — C32×C5×C9⋊C9 #16814366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₉⋊C₉ #16814366