Subgroups — C₆₁×C₁₉⋊AGL(1,𝔽₅) #37550811

Order 23180.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₆₁×Dic₁₉	—	5	1	no	maximal, Hall
4	C₂×C₁₉×C₆₁	—	5	1	no	—
5	AGL(1,𝔽₅)×C₆₁	—	19	1	no	maximal, Hall
6	C₁₉×C₆₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₆₁	D₁₉	1	1	yes	characteristic
8	C₁₉⋊AGL(1,𝔽₅)	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₆₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	C₄×C₆₁	—	95	1	no	Hall
11	D₅×C₁₉	C₂×C₆₁	1	1	yes	characteristic
12	C₂×C₆₁	—	5	1	no	—
13	C₅×C₁₉	C₄×C₆₁	1	1	yes	characteristic, complemented, Hall
14	Dic₁₉	—	5	1	no	Hall
15	C₆₁	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	—	5	1	no	—
17	AGL(1,𝔽₅)	—	19	1	no	Hall
18	C₁₉	AGL(1,𝔽₅)×C₆₁	1	1	yes	characteristic, complemented, Sylow
19	D₅	D₁₉×C₆₁	1	1	yes	characteristic
20	C₅	C₆₁×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	95	1	no	Sylow
22	C₂	—	5	1	no	—

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.