Subgroups — C₃³×#10587025 #28356654

Order 13851.

7208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587025	C₃	1	117	yes	maximal, direct product factor
2	C₃³×#4294	C₃	1	3	yes	maximal, complemented
3	C₃⁵×C₁₉	C₃	1	1	yes	maximal, characteristic
4	C₃×#10587025	C₃²	1	1053	yes	direct product factor
5	C₃²×#4294	C₃²	1	117	yes	complemented
6	C₃⁴×C₁₉	—	3	27	no	—
7	C₃⁴×C₁₉	C₃²	1	39	yes	—
8	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
9	C₃³×3₋¹⁺²	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	—	3	351	no	—
11	C₃³×C₁₉	3₋¹⁺²	1	27	yes	complemented
12	C₃³×C₁₉	C₃³	1	117	yes	—
13	C₃³×C₁₉	C₃³	1	13	yes	—
14	#10587025	C₃³	1	729	yes	direct product factor
15	C₃×#4294	C₃³	1	351	yes	complemented
16	C₃⁵	C₁₉⋊C₃	1	1	yes	characteristic
17	C₃²×3₋¹⁺²	—	19	117	no	—
18	C₃³×C₉	—	19	3	no	—
19	C₃²×C₁₉	—	3	351	no	—
20	C₃²×C₁₉	C₃×3₋¹⁺²	1	117	yes	complemented
21	C₃²×C₁₉	C₃⁴	1	27	yes	—
22	C₃²×C₁₉	C₃⁴	1	13	yes	—
23	#4294	C₃⁴	1	81	yes	complemented
24	C₃⁴	—	3	27	no	—
25	C₃⁴	C₃×C₁₉⋊C₃	1	39	yes	—
26	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
27	C₃×3₋¹⁺²	—	19	1053	no	—
28	C₃²×C₉	—	19	117	no	—
29	C₃×C₁₉	—	3	27	no	—
30	C₃×C₁₉	C₃²×3₋¹⁺²	1	39	yes	complemented
31	C₃×C₁₉	C₃⁵	1	1	yes	characteristic
32	C₃³	—	3	351	no	—
33	C₃³	#10587025	1	27	yes	direct product factor
34	C₃³	C₃²×C₁₉⋊C₃	1	117	yes	—
35	C₃³	C₃²×C₁₉⋊C₃	1	13	yes	—
36	3₋¹⁺²	—	19	729	no	—
37	C₃×C₉	—	19	351	no	—
38	C₁₉	C₃³×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
39	C₃²	—	3	351	no	—
40	C₃²	C₃×#10587025	1	117	yes	direct product factor
41	C₃²	C₃³×C₁₉⋊C₃	1	27	yes	—
42	C₃²	C₃³×C₁₉⋊C₃	1	13	yes	—
43	C₉	—	19	81	no	—
44	C₃	—	3	27	no	—
45	C₃	C₃²×#10587025	1	39	yes	direct product factor
46	C₃	C₃⁴×C₁₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃⁴	C₃×C₁₉⋊C₃
commutator, cosocle	C₃×C₁₉	C₃⁵
Frattini	C₃	C₃⁴×C₁₉⋊C₃
Fitting, prime radical	C₃⁵×C₁₉	C₃
socle	C₃⁴×C₁₉	C₃²
hypercenter	C₃⁵	C₁₉⋊C₃
hypocenter	C₁₉	C₃³×3₋¹⁺²
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃⁴ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃²×#10587025	C₃	direct (N × H)
2. C₃³×#4294	C₃	semidirect
4. C₃×#10587025	C₃²	direct (N × H)
5. C₃²×#4294	C₃²	semidirect
11. C₃³×C₁₉	3₋¹⁺²	semidirect
14. #10587025	C₃³	direct (N × H)
15. C₃×#4294	C₃³	semidirect
20. C₃²×C₁₉	C₃×3₋¹⁺²	semidirect
23. #4294	C₃⁴	semidirect
30. C₃×C₁₉	C₃²×3₋¹⁺²	semidirect
33. C₃³	#10587025	direct (N × H)
38. C₁₉	C₃³×3₋¹⁺²	semidirect
40. C₃²	C₃×#10587025	direct (N × H)
45. C₃	C₃²×#10587025	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#10587025	3
C₃³×#4294	3
C₃⁵×C₁₉	3
C₃³×3₋¹⁺²	19

Subgroups — C33×#10587025 #28356654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×#10587025 #28356654