Subgroups — A₄×C₁₉×C₁₃⋊C₃ #22580312

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₂²⋊(C₁₃⋊C₃)	C₃	1	2	yes	maximal, complemented
2	A₄×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₁₃⋊C₃	—	4	1	no	maximal, Hall
5	C₂×C₁₉×C₁₃⋊C₃	—	3	1	no	—
6	C₂²×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×C₁₉	—	4	1	no	—
8	C₁₉×C₁₃⋊C₃	—	4	2	no	—
9	C₁₉×C₁₃⋊C₃	A₄	1	1	yes	characteristic, direct product factor
10	C₃×A₄×C₁₉	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₁₉	—	3	1	no	—
12	A₄×C₁₃⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₃×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₃×C₁₉	—	13	1	no	—
15	A₄×C₁₉	—	13	2	no	—
16	A₄×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
17	C₃²×C₁₉	—	52	1	no	Hall
18	C₂²⋊(C₁₃⋊C₃)	C₃×C₁₉	1	2	yes	complemented
19	A₄×C₁₃	C₃×C₁₉	1	1	yes	characteristic, complemented
20	C₂²×C₁₃⋊C₃	C₃×C₁₉	1	1	yes	characteristic, complemented
21	C₃×C₁₃⋊C₃	—	4	1	no	Hall
22	C₂×C₃×C₁₉	—	39	1	no	—
23	C₂×C₁₃⋊C₃	—	3	1	no	—
24	C₂²×C₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₉	—	4	1	no	—
26	C₃×C₁₉	—	13	1	no	—
27	C₃×C₁₉	—	52	2	no	—
28	C₂²×C₁₃	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₃	—	4	1	no	—
30	C₁₃⋊C₃	—	4	2	no	—
31	C₁₃⋊C₃	A₄×C₁₉	1	1	yes	characteristic, direct product factor
32	C₂×C₁₉	—	3	1	no	—
33	C₃×A₄	—	13	1	no	Hall
34	C₂×C₁₃	—	3	1	no	—
35	C₁₉	A₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₃	C₃×A₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₃	—	13	1	no	—
38	A₄	—	13	2	no	—
39	A₄	C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	52	1	no	Sylow
41	C₂×C₃	—	39	1	no	—
42	C₂²	C₃×C₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	13	1	no	—
45	C₃	—	52	2	no	—
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	A₄×C₁₃⋊C₃
commutator, hypocenter	C₂²×C₁₃	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₁₉	C₃²
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₂²⋊(C₁₃⋊C₃)	C₃	semidirect
2. A₄×C₁₃×C₁₉	C₃	semidirect
3. C₂²×C₁₉×C₁₃⋊C₃	C₃	semidirect
6. C₂²×C₁₃×C₁₉	C₃²	semidirect
9. C₁₉×C₁₃⋊C₃	A₄	direct (N × H)
12. A₄×C₁₃⋊C₃	C₁₉	direct (N × H)
13. C₁₃×C₁₉	C₃×A₄	semidirect
16. A₄×C₁₉	C₁₃⋊C₃	direct (N × H)
18. C₂²⋊(C₁₃⋊C₃)	C₃×C₁₉	semidirect
19. A₄×C₁₃	C₃×C₁₉	semidirect
20. C₂²×C₁₃⋊C₃	C₃×C₁₉	semidirect
24. C₂²×C₁₉	C₃×C₁₃⋊C₃	semidirect
28. C₂²×C₁₃	C₃²×C₁₉	semidirect
31. C₁₃⋊C₃	A₄×C₁₉	direct (N × H)
35. C₁₉	A₄×C₁₃⋊C₃	direct (N × H)
36. C₁₃	C₃×A₄×C₁₉	semidirect
39. A₄	C₁₉×C₁₃⋊C₃	direct (N × H)
42. C₂²	C₃×C₁₉×C₁₃⋊C₃	semidirect

Subgroups — A4×C19×C13⋊C3 #22580312

Conjugacy classes of subgroups

Complements

Subgroups — A₄×C₁₉×C₁₃⋊C₃ #22580312