Subgroups — C₁₉×AGL(1,𝔽₅)×C₄₁ #29509999

Order 15580.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₉×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₉×C₄₁	—	5	1	no	maximal, Hall
4	C₂×C₁₉×C₄₁	—	5	1	no	—
5	AGL(1,𝔽₅)×C₄₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
7	D₅×C₄₁	C₂×C₁₉	1	1	yes	characteristic
8	C₁₉×AGL(1,𝔽₅)	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	D₅×C₁₉	C₂×C₄₁	1	1	yes	characteristic
11	C₄×C₄₁	—	5	1	no	Hall
12	C₅×C₁₉	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₁	—	5	1	no	—
14	C₄×C₁₉	—	5	1	no	Hall
15	C₄₁	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	—	5	1	no	—
17	AGL(1,𝔽₅)	C₁₉×C₄₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₉	AGL(1,𝔽₅)×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
19	D₅	C₂×C₁₉×C₄₁	1	1	yes	characteristic
20	C₅	C₄×C₁₉×C₄₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	5	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.