Subgroups — C₃×C₁₁×C₂²⋊(C₁₃⋊C₃) #19104240

Order 5148.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₂²⋊(C₁₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₁×C₁₃⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₁×C₁₃	—	3	1	no	—
5	C₂²×C₁₁×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₂²⋊(C₁₃⋊C₃)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁×C₁₃	A₄	1	1	yes	characteristic, complemented
8	C₁₁×C₁₃⋊C₃	—	4	3	no	—
9	C₃×C₁₁×A₄	—	13	1	no	maximal, Hall
10	C₂×C₁₁×C₁₃	—	3	1	no	—
11	C₂²×C₃×C₁₃	C₃×C₁₁	1	1	yes	characteristic, complemented
12	C₂²⋊(C₁₃⋊C₃)	C₃×C₁₁	1	3	yes	direct product factor
13	C₁₁×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₃×C₁₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₁×A₄	—	13	3	no	—
16	C₃×C₁₃⋊C₃	—	4	1	no	Hall
17	C₃²×C₁₁	—	52	1	no	Hall
18	C₂×C₃×C₁₃	—	3	1	no	—
19	C₂×C₃×C₁₁	—	3	1	no	—
20	C₂²×C₁₃	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₁	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₃×C₁₃	C₁₁×A₄	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	4	3	no	—
24	C₃×A₄	—	13	1	no	Hall
25	C₃×C₁₁	—	52	3	no	—
26	C₃×C₁₁	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
27	C₂×C₁₃	—	3	1	no	—
28	C₂×C₁₁	—	3	1	no	—
29	C₁₃	C₃×C₁₁×A₄	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	A₄	—	13	3	no	—
32	C₁₁	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
33	C₃²	—	52	1	no	Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	52	3	no	—
37	C₃	C₁₁×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁	C₂²⋊(C₁₃⋊C₃)
commutator, hypocenter	C₂²×C₁₃	C₃²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₁×C₁₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₁₁×C₁₃	C₃	semidirect
2. C₁₁×C₂²⋊(C₁₃⋊C₃)	C₃	direct (N × H)
5. C₂²×C₁₁×C₁₃	C₃²	semidirect
6. C₃×C₂²⋊(C₁₃⋊C₃)	C₁₁	direct (N × H)
7. C₃×C₁₁×C₁₃	A₄	semidirect
11. C₂²×C₃×C₁₃	C₃×C₁₁	semidirect
12. C₂²⋊(C₁₃⋊C₃)	C₃×C₁₁	direct (N × H)
13. C₁₁×C₁₃	C₃×A₄	semidirect
14. C₂²×C₃×C₁₁	C₁₃⋊C₃	semidirect
20. C₂²×C₁₃	C₃²×C₁₁	semidirect
21. C₂²×C₁₁	C₃×C₁₃⋊C₃	semidirect
22. C₃×C₁₃	C₁₁×A₄	semidirect
26. C₃×C₁₁	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
29. C₁₃	C₃×C₁₁×A₄	semidirect
30. C₂²×C₃	C₁₁×C₁₃⋊C₃	semidirect
32. C₁₁	C₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
35. C₂²	C₃×C₁₁×C₁₃⋊C₃	semidirect
37. C₃	C₁₁×C₂²⋊(C₁₃⋊C₃)	direct (N × H)

Subgroups — C3×C11×C22⋊(C13⋊C3) #19104240

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₁×C₂²⋊(C₁₃⋊C₃) #19104240