Subgroups — C₅×D₁₉×C₁₂₁ #37527353

Order 22990.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₁₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₂₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₁×D₁₉	C₁₁	1	1	yes	maximal, characteristic
5	C₂×C₅×C₁₂₁	—	19	1	no	maximal, Hall
6	C₅×C₁₁×C₁₉	C₂×C₁₁	1	1	yes	characteristic
7	C₅×C₁₂₁	D₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×D₁₉	C₅×C₁₁	1	1	yes	characteristic
9	C₂×C₁₂₁	—	19	1	no	Hall
10	C₁₁×C₁₉	C₂×C₅×C₁₁	1	1	yes	characteristic
11	C₅×D₁₉	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₂₁	C₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₅×C₁₁	—	19	1	no	—
14	C₅×C₁₉	C₂×C₁₂₁	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₁	C₁₁×D₁₉	1	1	yes	characteristic
16	D₁₉	C₅×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁	—	19	1	no	—
18	C₁₉	C₂×C₅×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
19	C₁₁	C₅×C₁₁×D₁₉	1	1	yes	characteristic
20	C₂×C₅	—	19	1	no	Hall
21	C₅	D₁₉×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	19	1	no	Sylow

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.