Subgroups — AGL(1,𝔽₅)×C₅₃⋊C₁₃ #28351925

Order 13780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₅₃⋊C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₅₃⋊C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₅₃⋊C₁₃	—	5	1	no	maximal, Hall
4	C₂×C₅₃⋊C₁₃	—	5	1	no	—
5	AGL(1,𝔽₅)×C₅₃	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₅₃⋊C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
7	D₅×C₅₃	C₂×C₁₃	1	1	yes	characteristic
8	C₅×C₅₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×AGL(1,𝔽₅)	—	53	1	no	maximal, Hall
10	C₄×C₅₃	—	5	1	no	Hall
11	D₅×C₁₃	—	53	1	no	—
12	C₂×C₅₃	—	5	1	no	—
13	C₅×C₁₃	—	53	1	no	Hall
14	C₅₃	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₁₃	—	265	1	no	Hall
16	C₂×C₁₃	—	265	1	no	—
17	AGL(1,𝔽₅)	C₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃	—	53	1	no	Sylow
19	D₅	C₂×C₅₃⋊C₁₃	1	1	yes	characteristic
20	C₅	C₄×C₅₃⋊C₁₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	1	no	Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₅₃	C₄×C₁₃
prime radical	D₅×C₅₃⋊C₁₃	C₂
cosocle	D₅×C₅₃	C₂×C₁₃
LCS	G ▷ C₅×C₅₃
UCS	C₁

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

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