Subgroups — C₁₉×C₃⋊#63120 #28414901

Order 14820.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#63120	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×Dic₃₉	—	5	1	no	maximal, Hall
5	D₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₁₉	—	5	1	no	—
7	C₅×C₁₃×C₁₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₁₉×ΓL(1,𝔽₁₆)	—	13	1	no	maximal, Hall
9	C₁₉×Dic₁₃	—	15	1	no	Hall
10	C₃⋊#63120	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₃×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₅×C₁₉	D₁₃	1	1	yes	characteristic
13	C₂×C₁₃×C₁₉	—	5	1	no	—
14	C₃×D₅×C₁₃	C₂×C₁₉	1	1	yes	characteristic
15	C₁₉×AGL(1,𝔽₅)	—	39	1	no	Hall
16	C₃×C₅×C₁₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
17	#63120	—	3	1	no	Hall
18	C₁₃×C₁₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
19	Dic₃×C₁₉	—	65	1	no	Hall
20	C₃×C₅×C₁₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
21	D₅×C₁₉	D₃₉	1	1	yes	characteristic
22	Dic₃₉	—	5	1	no	Hall
23	D₅×C₁₃	D₃×C₁₉	1	1	yes	characteristic
24	C₂×C₃×C₁₉	—	5	1	no	—
25	C₅×C₁₉	Dic₃₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₃	—	5	1	no	—
27	C₄×C₁₉	—	195	1	no	Hall
28	C₅×C₁₃	Dic₃×C₁₉	1	1	yes	characteristic, complemented, Hall
29	ΓL(1,𝔽₁₆)	—	13	1	no	Hall
30	C₃×C₁₉	#63120	1	1	yes	characteristic, complemented, Hall
31	Dic₁₃	—	15	1	no	Hall
32	C₃×C₁₃	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉	—	5	1	no	—
34	C₃×D₅	C₁₉×D₁₃	1	1	yes	characteristic
35	C₂×C₁₃	—	5	1	no	—
36	AGL(1,𝔽₅)	—	39	1	no	Hall
37	C₁₉	C₃⋊#63120	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₁₉×Dic₁₃	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₁₉×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
40	Dic₃	—	65	1	no	Hall
41	D₅	C₁₉×D₃₉	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₁₉×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	195	1	no	Sylow
45	C₃	C₁₉×#63120	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊#63120
commutator, hypocenter	C₃×C₅×C₁₃	C₄×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₉	C₄
prime radical	C₃×D₅×C₁₃×C₁₉	C₂
cosocle	C₃×D₅×C₁₃	C₂×C₁₉
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₃×C₁₉	C₄	semidirect
7. C₅×C₁₃×C₁₉	Dic₃	semidirect
10. C₃⋊#63120	C₁₉	direct (N × H)
11. C₃×C₁₃×C₁₉	AGL(1,𝔽₅)	semidirect
16. C₃×C₅×C₁₉	Dic₁₃	semidirect
18. C₁₃×C₁₉	ΓL(1,𝔽₁₆)	semidirect
20. C₃×C₅×C₁₃	C₄×C₁₉	semidirect
25. C₅×C₁₉	Dic₃₉	semidirect
28. C₅×C₁₃	Dic₃×C₁₉	semidirect
30. C₃×C₁₉	#63120	semidirect
32. C₃×C₁₃	C₁₉×AGL(1,𝔽₅)	semidirect
37. C₁₉	C₃⋊#63120	direct (N × H)
38. C₃×C₅	C₁₉×Dic₁₃	semidirect
39. C₁₃	C₁₉×ΓL(1,𝔽₁₆)	semidirect
43. C₅	C₁₉×Dic₃₉	semidirect
45. C₃	C₁₉×#63120	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₅×C₁₃×C₁₉	2
C₁₉×#63120	3
C₁₉×Dic₃₉	5
C₁₉×ΓL(1,𝔽₁₆)	13
C₃⋊#63120	19

Subgroups — C19×C3⋊#63120 #28414901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#63120 #28414901