Subgroups — C₁₉⋊(C₅₉⋊AGL(1,𝔽₅)) #36375770

Order 22420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₂₁	—	5	1	no	maximal, Hall
4	C₂×C₁₉×C₅₉	—	5	1	no	—
5	C₅₉⋊AGL(1,𝔽₅)	—	19	1	no	maximal, Hall
6	C₁₉×C₅₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₅₉	D₁₉	1	1	yes	characteristic
8	C₁₉⋊AGL(1,𝔽₅)	—	59	1	no	maximal, Hall
9	C₅×C₅₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	Dic₅₉	—	95	1	no	Hall
11	D₅×C₁₉	D₅₉	1	1	yes	characteristic
12	C₂×C₅₉	—	5	1	no	—
13	C₅×C₁₉	Dic₅₉	1	1	yes	characteristic, complemented, Hall
14	Dic₁₉	—	295	1	no	Hall
15	C₅₉	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	—	5	1	no	—
17	AGL(1,𝔽₅)	—	1121	1	no	Hall
18	C₁₉	C₅₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	D₅	D₁₁₂₁	1	1	yes	characteristic
20	C₅	Dic₁₁₂₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5605	1	no	Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉×C₅₉	C₄
prime radical, cosocle	D₅×C₁₉×C₅₉	C₂
LCS	G ▷ C₅×C₁₉×C₅₉
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.