Subgroups — C₅×C₁₉×Dic₅₉ #36375758

Order 22420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×Dic₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₉×C₅₉	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₅₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₅₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₅₉	C₂×C₁₉	1	1	yes	characteristic
8	C₄×C₅×C₁₉	—	59	1	no	maximal, Hall
9	C₅×C₅₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
10	Dic₅₉	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₉	D₅₉	1	1	yes	characteristic
12	C₂×C₅₉	C₂×C₅×C₁₉	1	1	yes	characteristic
13	C₅×C₁₉	Dic₅₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₉	—	59	1	no	Hall
15	C₅₉	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₉	C₅×D₅₉	1	1	yes	characteristic
17	C₄×C₅	—	59	1	no	Hall
18	C₁₉	C₅×Dic₅₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₁₉×D₅₉	1	1	yes	characteristic
20	C₅	C₁₉×Dic₅₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	59	1	no	Sylow
22	C₂	C₅×C₁₉×D₅₉	1	1	yes	characteristic

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.