Subgroups — C₁₉⋊C₃×C₂²⋊(C₁₃⋊C₃) #22580311

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#10625203	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊#10625202	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉×C₂²⋊(C₁₃⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃⋊C₃×C₁₉⋊C₃	—	4	1	no	maximal, Hall
6	C₂×C₁₃×C₁₉⋊C₃	—	3	1	no	—
7	C₂²×C₁₃×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	#10625203	—	4	1	no	—
9	#10625202	—	4	1	no	—
10	C₁₃×C₁₉⋊C₃	A₄	1	1	yes	characteristic, complemented
11	C₁₉×C₁₃⋊C₃	—	4	1	no	—
12	A₄×C₁₉⋊C₃	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₁₉	—	3	1	no	—
14	C₃×C₂²⋊(C₁₃⋊C₃)	—	19	1	no	maximal, Hall
15	C₁₃×C₁₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
16	C₂²⋊(C₁₉⋊C₃)	—	13	1	no	—
17	C₂²⋊(C₁₉⋊C₃)	—	13	1	no	—
18	A₄×C₁₉	—	13	1	no	—
19	C₂²×C₁₉⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
20	C₃×C₁₉⋊C₃	—	52	1	no	Hall
21	C₂²×C₃×C₁₃	—	19	1	no	—
22	C₂²⋊(C₁₃⋊C₃)	—	19	1	no	—
23	C₂²⋊(C₁₃⋊C₃)	—	19	1	no	—
24	C₂²⋊(C₁₃⋊C₃)	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
25	C₃×C₁₃⋊C₃	—	76	1	no	Hall
26	C₂×C₁₉⋊C₃	—	3	1	no	—
27	C₂×C₃×C₁₃	—	57	1	no	—
28	C₂²×C₁₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₉	—	52	1	no	—
30	C₁₉⋊C₃	—	52	1	no	—
31	C₁₉⋊C₃	—	52	1	no	—
32	C₁₉⋊C₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
33	C₂²×C₁₃	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₃	—	19	1	no	—
35	C₁₃⋊C₃	—	4	1	no	—
36	C₁₃⋊C₃	—	76	1	no	—
37	C₁₃⋊C₃	—	76	1	no	—
38	C₂×C₁₉	—	3	1	no	—
39	C₃×A₄	—	247	1	no	Hall
40	C₂×C₁₃	—	3	1	no	—
41	C₁₉	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
42	C₁₃	A₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₃	—	19	1	no	—
44	A₄	—	13	1	no	—
45	A₄	—	247	1	no	—
46	A₄	—	247	1	no	—
47	C₃²	—	988	1	no	Sylow
48	C₂×C₃	—	57	1	no	—
49	C₂²	C₁₃⋊C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₃	—	19	1	no	—
51	C₃	—	52	1	no	—
52	C₃	—	988	1	no	—
53	C₃	—	988	1	no	—
54	C₂	—	3	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#10625203	C₃	semidirect
2. C₂²⋊#10625202	C₃	semidirect
3. C₁₉×C₂²⋊(C₁₃⋊C₃)	C₃	semidirect
4. C₂²×C₁₃×C₁₉⋊C₃	C₃	semidirect
7. C₂²×C₁₃×C₁₉	C₃²	semidirect
10. C₁₃×C₁₉⋊C₃	A₄	semidirect
15. C₁₃×C₁₉	C₃×A₄	semidirect
19. C₂²×C₁₉⋊C₃	C₁₃⋊C₃	semidirect
24. C₂²⋊(C₁₃⋊C₃)	C₁₉⋊C₃	direct (N × H)
28. C₂²×C₁₉	C₃×C₁₃⋊C₃	semidirect
32. C₁₉⋊C₃	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
33. C₂²×C₁₃	C₃×C₁₉⋊C₃	semidirect
41. C₁₉	C₃×C₂²⋊(C₁₃⋊C₃)	semidirect
42. C₁₃	A₄×C₁₉⋊C₃	semidirect
49. C₂²	C₁₃⋊C₃×C₁₉⋊C₃	semidirect

Subgroups — C19⋊C3×C22⋊(C13⋊C3) #22580311

Conjugacy classes of subgroups

Complements

Subgroups — C₁₉⋊C₃×C₂²⋊(C₁₃⋊C₃) #22580311