Subgroups — A₄×C₁₃×C₁₉⋊C₃ #22580308

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂²⋊(C₁₉⋊C₃)	C₃	1	2	yes	maximal, complemented
2	A₄×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₉⋊C₃	—	4	1	no	maximal, Hall
5	C₂×C₁₃×C₁₉⋊C₃	—	3	1	no	—
6	C₂²×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×C₁₉	—	4	1	no	—
8	C₁₃×C₁₉⋊C₃	—	4	2	no	—
9	C₁₃×C₁₉⋊C₃	A₄	1	1	yes	characteristic, direct product factor
10	A₄×C₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₃×C₁₉	—	3	1	no	—
12	C₃×A₄×C₁₃	—	19	1	no	maximal, Hall
13	C₁₃×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
14	C₂²⋊(C₁₉⋊C₃)	C₃×C₁₃	1	2	yes	complemented
15	A₄×C₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₂²×C₁₉⋊C₃	C₃×C₁₃	1	1	yes	characteristic, complemented
17	C₃×C₁₉⋊C₃	—	4	1	no	Hall
18	C₂²×C₃×C₁₃	—	19	1	no	—
19	A₄×C₁₃	—	19	2	no	—
20	A₄×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃²×C₁₃	—	76	1	no	Hall
22	C₂×C₁₉⋊C₃	—	3	1	no	—
23	C₂×C₃×C₁₃	—	57	1	no	—
24	C₂²×C₁₉	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₉	—	4	1	no	—
26	C₁₉⋊C₃	—	4	2	no	—
27	C₁₉⋊C₃	A₄×C₁₃	1	1	yes	characteristic, direct product factor
28	C₂²×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₃	—	4	1	no	—
30	C₃×C₁₃	—	19	1	no	—
31	C₃×C₁₃	—	76	2	no	—
32	C₂×C₁₉	—	3	1	no	—
33	C₃×A₄	—	19	1	no	Hall
34	C₂×C₁₃	—	3	1	no	—
35	C₁₉	C₃×A₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₁₃	A₄×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	—	19	1	no	—
38	A₄	—	19	2	no	—
39	A₄	C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	76	1	no	Sylow
41	C₂×C₃	—	57	1	no	—
42	C₂²	C₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	4	1	no	—
44	C₃	—	19	1	no	—
45	C₃	—	76	2	no	—
46	C₂	—	3	1	no	—

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

Complements

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

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

Subgroups — A4×C13×C19⋊C3 #22580308

Conjugacy classes of subgroups

Complements

Subgroups — A₄×C₁₃×C₁₉⋊C₃ #22580308