Subgroups — C₃×C₁₃×C₄₃⋊AGL(1,𝔽₅) #46776538

Order 33540.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₃×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₄₃⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×Dic₄₃	—	5	1	no	maximal, Hall
5	D₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₃×C₄₃	—	5	1	no	—
7	C₅×C₁₃×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄₃⋊AGL(1,𝔽₅)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₃×Dic₄₃	—	5	1	no	Hall
10	C₃×C₁₃×C₄₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₄₃	C₂×C₁₃	1	1	yes	characteristic
12	C₂×C₁₃×C₄₃	—	5	1	no	—
13	C₄₃⋊AGL(1,𝔽₅)	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₃×AGL(1,𝔽₅)	—	43	1	no	maximal, Hall
15	C₃×C₅×C₄₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×Dic₄₃	—	5	1	no	Hall
18	D₅×C₄₃	C₂×C₃×C₁₃	1	1	yes	characteristic
19	C₃×D₅×C₁₃	D₄₃	1	1	yes	characteristic
20	C₁₃×AGL(1,𝔽₅)	—	43	1	no	Hall
21	C₂×C₃×C₄₃	—	5	1	no	—
22	C₅×C₄₃	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	Dic₄₃	1	1	yes	characteristic, complemented, Hall
24	Dic₄₃	—	5	1	no	Hall
25	C₃×C₄×C₁₃	—	215	1	no	Hall
26	D₅×C₁₃	C₃×D₄₃	1	1	yes	characteristic
27	C₃×C₄₃	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₃	—	5	1	no	—
29	C₂×C₃×C₁₃	—	5	1	no	—
30	C₅×C₁₃	C₃×Dic₄₃	1	1	yes	characteristic, complemented, Hall
31	C₃×AGL(1,𝔽₅)	—	43	1	no	Hall
32	C₄×C₁₃	—	215	1	no	Hall
33	C₄₃	C₃×C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	C₄₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
35	C₃×D₅	C₁₃×D₄₃	1	1	yes	characteristic
36	C₂×C₁₃	—	5	1	no	—
37	AGL(1,𝔽₅)	—	43	1	no	Hall
38	C₃×C₅	C₁₃×Dic₄₃	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×C₄₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	—	215	1	no	Hall
41	D₅	C₃×C₁₃×D₄₃	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₃×C₁₃×Dic₄₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	215	1	no	Sylow
45	C₃	C₁₃×C₄₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₄₃⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₄₃	C₃×C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₃	C₄
prime radical	C₃×D₅×C₁₃×C₄₃	C₂
cosocle	D₅×C₄₃	C₂×C₃×C₁₃
LCS	G ▷ C₅×C₄₃
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₄₃⋊AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₄₃	C₄	semidirect
7. C₅×C₁₃×C₄₃	C₃×C₄	semidirect
8. C₃×C₄₃⋊AGL(1,𝔽₅)	C₁₃	direct (N × H)
10. C₃×C₁₃×C₄₃	AGL(1,𝔽₅)	semidirect
13. C₄₃⋊AGL(1,𝔽₅)	C₃×C₁₃	direct (N × H)
15. C₃×C₅×C₄₃	C₄×C₁₃	semidirect
16. C₁₃×C₄₃	C₃×AGL(1,𝔽₅)	semidirect
22. C₅×C₄₃	C₃×C₄×C₁₃	semidirect
23. C₃×C₅×C₁₃	Dic₄₃	semidirect
27. C₃×C₄₃	C₁₃×AGL(1,𝔽₅)	semidirect
30. C₅×C₁₃	C₃×Dic₄₃	semidirect
33. C₄₃	C₃×C₁₃×AGL(1,𝔽₅)	semidirect
34. C₃×C₁₃	C₄₃⋊AGL(1,𝔽₅)	direct (N × H)
38. C₃×C₅	C₁₃×Dic₄₃	semidirect
39. C₁₃	C₃×C₄₃⋊AGL(1,𝔽₅)	direct (N × H)
43. C₅	C₃×C₁₃×Dic₄₃	semidirect
45. C₃	C₁₃×C₄₃⋊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×C₄₃	2
C₁₃×C₄₃⋊AGL(1,𝔽₅)	3
C₃×C₁₃×Dic₄₃	5
C₃×C₄₃⋊AGL(1,𝔽₅)	13
C₃×C₁₃×AGL(1,𝔽₅)	43

Subgroups — C3×C13×C43⋊AGL(1,𝔽5) #46776538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₄₃⋊AGL(1,𝔽₅) #46776538