Subgroups — C₃³×C₃²⋊(C₁₉⋊C₃) #28356650

Order 13851.

11744 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₁₉⋊C₃	C₃	1	3	yes	maximal, complemented
2	C₃²×C₃²⋊(C₁₉⋊C₃)	C₃	1	117	yes	maximal, direct product factor
3	C₃⁵×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₁₉⋊C₃	—	3	81	no	—
5	C₃³×C₁₉⋊C₃	C₃²	1	117	yes	complemented
6	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	1053	yes	direct product factor
7	C₃⁴×C₁₉	—	3	27	no	—
8	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
9	C₃⁴×C₁₉	C₃²	1	39	yes	complemented
10	C₃³×H(3,𝔽₃)	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	—	3	351	no	—
12	C₃³×C₁₉	H(3,𝔽₃)	1	27	yes	complemented
13	C₃³×C₁₉	C₃³	1	13	yes	—
14	C₃³×C₁₉	C₃³	1	117	yes	complemented
15	C₃²×C₁₉⋊C₃	—	3	1053	no	—
16	C₃²×C₁₉⋊C₃	C₃³	1	351	yes	complemented
17	C₃²⋊(C₁₉⋊C₃)	C₃³	1	729	yes	direct product factor
18	C₃⁵	—	19	3	no	—
19	C₃⁵	C₁₉⋊C₃	1	1	yes	characteristic, complemented
20	C₃²×H(3,𝔽₃)	—	19	117	no	—
21	C₃²×C₁₉	—	3	351	no	—
22	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	117	yes	complemented
23	C₃²×C₁₉	C₃⁴	1	13	yes	—
24	C₃²×C₁₉	C₃⁴	1	27	yes	complemented
25	C₃×C₁₉⋊C₃	—	3	1053	no	—
26	C₃×C₁₉⋊C₃	C₃⁴	1	81	yes	complemented
27	C₃⁴	—	3	27	no	—
28	C₃⁴	—	19	117	no	—
29	C₃⁴	—	57	81	no	—
30	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
31	C₃⁴	C₃×C₁₉⋊C₃	1	39	yes	complemented
32	C₃×H(3,𝔽₃)	—	19	1053	no	—
33	C₃×C₁₉	—	3	27	no	—
34	C₃×C₁₉	C₃²×H(3,𝔽₃)	1	39	yes	complemented
35	C₃×C₁₉	C₃⁵	1	1	yes	characteristic
36	C₁₉⋊C₃	—	3	81	no	—
37	C₃³	—	3	351	no	—
38	C₃³	—	19	351	no	—
39	C₃³	—	57	1053	no	—
40	C₃³	C₃²⋊(C₁₉⋊C₃)	1	27	yes	direct product factor
41	C₃³	C₃²×C₁₉⋊C₃	1	13	yes	—
42	C₃³	C₃²×C₁₉⋊C₃	1	117	yes	complemented
43	H(3,𝔽₃)	—	19	729	no	—
44	C₁₉	C₃³×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
45	C₃²	—	3	351	no	—
46	C₃²	—	19	81	no	—
47	C₃²	—	57	1053	no	—
48	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	117	yes	direct product factor
49	C₃²	C₃³×C₁₉⋊C₃	1	13	yes	—
50	C₃²	C₃³×C₁₉⋊C₃	1	27	yes	complemented
51	C₃	—	3	27	no	—
52	C₃	—	57	81	no	—
53	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)	1	39	yes	direct product factor
54	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	C₃⁵×C₁₉	C₃
socle	C₃⁴×C₁₉	C₃²
hypercenter	C₃⁵	C₁₉⋊C₃
hypocenter	C₁₉	C₃³×H(3,𝔽₃)
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. C₃⁴×C₁₉⋊C₃	C₃	semidirect
2. C₃²×C₃²⋊(C₁₉⋊C₃)	C₃	direct (N × H)
3. C₃⁵×C₁₉	C₃	semidirect
5. C₃³×C₁₉⋊C₃	C₃²	semidirect
6. C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	direct (N × H)
9. C₃⁴×C₁₉	C₃²	semidirect
12. C₃³×C₁₉	H(3,𝔽₃)	semidirect
14. C₃³×C₁₉	C₃³	semidirect
16. C₃²×C₁₉⋊C₃	C₃³	semidirect
17. C₃²⋊(C₁₉⋊C₃)	C₃³	direct (N × H)
19. C₃⁵	C₁₉⋊C₃	semidirect
22. C₃²×C₁₉	C₃×H(3,𝔽₃)	semidirect
24. C₃²×C₁₉	C₃⁴	semidirect
26. C₃×C₁₉⋊C₃	C₃⁴	semidirect
31. C₃⁴	C₃×C₁₉⋊C₃	semidirect
34. C₃×C₁₉	C₃²×H(3,𝔽₃)	semidirect
40. C₃³	C₃²⋊(C₁₉⋊C₃)	direct (N × H)
42. C₃³	C₃²×C₁₉⋊C₃	semidirect
44. C₁₉	C₃³×H(3,𝔽₃)	semidirect
48. C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	direct (N × H)
50. C₃²	C₃³×C₁₉⋊C₃	semidirect
53. C₃	C₃²×C₃²⋊(C₁₉⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₁₉⋊C₃	3
C₃²×C₃²⋊(C₁₉⋊C₃)	3
C₃⁵×C₁₉	3
C₃³×H(3,𝔽₃)	19

Subgroups — C33×C32⋊(C19⋊C3) #28356650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₃²⋊(C₁₉⋊C₃) #28356650