Subgroups — C₃×C₄×C₁₃×C₁₉⋊C₃ #22580219

Order 8892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₉⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	1	3	yes	—
7	C₄×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
9	C₁₃×C₁₉⋊C₃	C₃×C₄	1	3	yes	direct product factor
10	C₃×C₄×C₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic
12	C₃²×C₄×C₁₃	—	19	1	no	maximal, Hall
13	C₂×C₃×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic
14	C₁₃×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃²×C₁₃	—	19	1	no	—
16	C₃×C₄×C₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
17	C₄×C₁₉⋊C₃	C₃×C₁₃	1	3	yes	direct product factor
18	C₃×C₁₉⋊C₃	C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄×C₁₃	—	19	3	no	—
20	C₃×C₄×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃²×C₁₃	—	19	1	no	Hall
22	C₂×C₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
23	C₂×C₁₉⋊C₃	C₂×C₃×C₁₃	1	3	yes	—
24	C₂×C₃×C₁₃	—	19	3	no	—
25	C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
26	C₄×C₁₉	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₃×C₁₉	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented
28	C₁₉⋊C₃	C₃×C₄×C₁₃	1	3	yes	direct product factor
29	C₄×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₃	—	19	3	no	—
31	C₃×C₁₃	C₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
32	C₂×C₁₉	C₂×C₃²×C₁₃	1	1	yes	characteristic
33	C₃²×C₄	—	19	1	no	Hall
34	C₂×C₁₃	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic
35	C₁₉	C₃²×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	19	1	no	—
37	C₁₃	C₃×C₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₄	—	19	3	no	—
39	C₃×C₄	C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	19	1	no	Sylow
41	C₂×C₃	—	19	3	no	—
42	C₂×C₃	C₂×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic
43	C₄	C₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	19	3	no	—
45	C₃	C₄×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₃	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃²×C₄×C₁₃
Frattini	C₂	C₂×C₃×C₁₃×C₁₉⋊C₃
Fitting	C₃×C₄×C₁₃×C₁₉	C₃
socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₁₉⋊C₃	C₃	direct (N × H)
3. C₃×C₄×C₁₃×C₁₉	C₃	semidirect
4. C₃×C₁₃×C₁₉⋊C₃	C₄	direct (N × H)
7. C₄×C₁₃×C₁₉	C₃²	semidirect
8. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
9. C₁₃×C₁₉⋊C₃	C₃×C₄	direct (N × H)
10. C₃×C₄×C₁₉⋊C₃	C₁₃	direct (N × H)
14. C₁₃×C₁₉	C₃²×C₄	semidirect
16. C₃×C₄×C₁₉	C₃×C₁₃	semidirect
17. C₄×C₁₉⋊C₃	C₃×C₁₃	direct (N × H)
18. C₃×C₁₉⋊C₃	C₄×C₁₃	direct (N × H)
20. C₃×C₄×C₁₃	C₁₉⋊C₃	direct (N × H)
26. C₄×C₁₉	C₃²×C₁₃	semidirect
27. C₃×C₁₉	C₃×C₄×C₁₃	semidirect
28. C₁₉⋊C₃	C₃×C₄×C₁₃	direct (N × H)
29. C₄×C₁₃	C₃×C₁₉⋊C₃	direct (N × H)
31. C₃×C₁₃	C₄×C₁₉⋊C₃	direct (N × H)
35. C₁₉	C₃²×C₄×C₁₃	semidirect
37. C₁₃	C₃×C₄×C₁₉⋊C₃	direct (N × H)
39. C₃×C₄	C₁₃×C₁₉⋊C₃	direct (N × H)
43. C₄	C₃×C₁₃×C₁₉⋊C₃	direct (N × H)
45. C₃	C₄×C₁₃×C₁₉⋊C₃	direct (N × H)

Subgroups — C3×C4×C13×C19⋊C3 #22580219

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₄×C₁₃×C₁₉⋊C₃ #22580219