Subgroups — C₃×C₅₂₉⋊AGL(1,𝔽₅) #44540673

Order 31740.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₅₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅₂₉⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₅₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₅₂₉	—	5	1	no	maximal, Hall
5	D₅×C₅₂₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₅₂₉	—	5	1	no	—
7	C₅×C₅₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₅₂₉	—	5	1	no	Hall
9	C₃×C₅₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	C₃×C₂₃⋊AGL(1,𝔽₅)	—	23	1	no	maximal
11	C₂×C₅₂₉	—	5	1	no	—
12	C₃×D₅×C₂₃	D₂₃	1	1	yes	characteristic
13	C₅₂₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
14	C₂₃⋊AGL(1,𝔽₅)	—	23	1	no	—
15	C₃×C₅×C₂₃	Dic₂₃	1	1	yes	characteristic
16	C₃×Dic₂₃	—	115	1	no	—
17	D₅×C₂₃	C₃×D₂₃	1	1	yes	characteristic
18	C₂×C₃×C₂₃	—	5	1	no	—
19	C₅×C₂₃	C₃×Dic₂₃	1	1	yes	characteristic
20	Dic₂₃	—	115	1	no	—
21	C₃×C₂₃	C₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
22	C₃×AGL(1,𝔽₅)	—	529	1	no	Hall
23	C₂×C₂₃	—	5	1	no	—
24	C₃×D₅	D₅₂₉	1	1	yes	characteristic
25	C₂₃	C₃×C₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
26	AGL(1,𝔽₅)	—	529	1	no	Hall
27	C₃×C₅	Dic₅₂₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₄	—	2645	1	no	Hall
29	D₅	C₃×D₅₂₉	1	1	yes	characteristic
30	C₂×C₃	—	5	1	no	—
31	C₅	C₃×Dic₅₂₉	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	2645	1	no	Sylow
33	C₃	C₅₂₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅₂₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₅₂₉	C₃×C₄
Frattini	C₂₃	C₃×C₂₃⋊AGL(1,𝔽₅)
Fitting	C₃×C₅×C₅₂₉	C₄
socle	C₃×C₅×C₂₃	Dic₂₃
prime radical	C₃×D₅×C₂₃	D₂₃
cosocle	D₅×C₅₂₉	C₂×C₃
LCS	G ▷ C₅×C₅₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₅₂₉⋊AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃×C₅×C₅₂₉	C₄	semidirect
7. C₅×C₅₂₉	C₃×C₄	semidirect
9. C₃×C₅₂₉	AGL(1,𝔽₅)	semidirect
13. C₅₂₉	C₃×AGL(1,𝔽₅)	semidirect
27. C₃×C₅	Dic₅₂₉	semidirect
31. C₅	C₃×Dic₅₂₉	semidirect
33. C₃	C₅₂₉⋊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×C₅₂₉	2
C₅₂₉⋊AGL(1,𝔽₅)	3
C₃×Dic₅₂₉	5
C₃×C₂₃⋊AGL(1,𝔽₅)	23

Subgroups — C3×C529⋊AGL(1,𝔽5) #44540673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅₂₉⋊AGL(1,𝔽₅) #44540673