Subgroups — C₃×C₁₃×C₁₉×AGL(1,𝔽₅) #28414871

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	C₁₃×C₁₉×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄×C₁₃×C₁₉	—	5	1	no	maximal, Hall
5	D₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₁₉	—	5	1	no	—
7	C₅×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×AGL(1,𝔽₅)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₁₃×C₁₉	—	5	1	no	Hall
10	C₃×C₁₃×AGL(1,𝔽₅)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₃×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
12	C₃×D₅×C₁₉	C₂×C₁₃	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)	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅×C₁₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
17	C₁₃×AGL(1,𝔽₅)	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄×C₁₉	—	5	1	no	Hall
20	C₃×C₅×C₁₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
21	D₅×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
22	C₃×C₄×C₁₃	—	5	1	no	Hall
23	D₅×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic
24	C₂×C₃×C₁₉	—	5	1	no	—
25	C₅×C₁₉	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₃	—	5	1	no	—
27	C₄×C₁₉	—	5	1	no	Hall
28	C₅×C₁₃	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×AGL(1,𝔽₅)	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₉	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
31	C₄×C₁₃	—	5	1	no	Hall
32	C₃×C₁₃	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₉	—	5	1	no	—
34	C₃×D₅	C₂×C₁₃×C₁₉	1	1	yes	characteristic
35	C₂×C₁₃	—	5	1	no	—
36	AGL(1,𝔽₅)	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
37	C₁₉	C₃×C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₅	C₄×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	—	5	1	no	Hall
41	D₅	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₃×C₄×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	5	1	no	Sylow
45	C₃	C₁₃×C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₃×C₄×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₉	C₄
prime radical	C₃×D₅×C₁₃×C₁₉	C₂
cosocle	D₅	C₂×C₃×C₁₃×C₁₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₁₉×AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₁₉	C₄	semidirect
7. C₅×C₁₃×C₁₉	C₃×C₄	semidirect
8. C₃×C₁₉×AGL(1,𝔽₅)	C₁₃	direct (N × H)
10. C₃×C₁₃×AGL(1,𝔽₅)	C₁₉	direct (N × H)
11. C₃×C₁₃×C₁₉	AGL(1,𝔽₅)	direct (N × H)
15. C₁₉×AGL(1,𝔽₅)	C₃×C₁₃	direct (N × H)
16. C₃×C₅×C₁₉	C₄×C₁₃	semidirect
17. C₁₃×AGL(1,𝔽₅)	C₃×C₁₉	direct (N × H)
18. C₁₃×C₁₉	C₃×AGL(1,𝔽₅)	direct (N × H)
20. C₃×C₅×C₁₃	C₄×C₁₉	semidirect
25. C₅×C₁₉	C₃×C₄×C₁₃	semidirect
28. C₅×C₁₃	C₃×C₄×C₁₉	semidirect
29. C₃×AGL(1,𝔽₅)	C₁₃×C₁₉	direct (N × H)
30. C₃×C₁₉	C₁₃×AGL(1,𝔽₅)	direct (N × H)
32. C₃×C₁₃	C₁₉×AGL(1,𝔽₅)	direct (N × H)
36. AGL(1,𝔽₅)	C₃×C₁₃×C₁₉	direct (N × H)
37. C₁₉	C₃×C₁₃×AGL(1,𝔽₅)	direct (N × H)
38. C₃×C₅	C₄×C₁₃×C₁₉	semidirect
39. C₁₃	C₃×C₁₉×AGL(1,𝔽₅)	direct (N × H)
43. C₅	C₃×C₄×C₁₃×C₁₉	semidirect
45. C₃	C₁₃×C₁₉×AGL(1,𝔽₅)	direct (N × H)

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
C₁₃×C₁₉×AGL(1,𝔽₅)	3
C₃×C₄×C₁₃×C₁₉	5
C₃×C₁₉×AGL(1,𝔽₅)	13
C₃×C₁₃×AGL(1,𝔽₅)	19

Subgroups — C3×C13×C19×AGL(1,𝔽5) #28414871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₁₉×AGL(1,𝔽₅) #28414871