Subgroups — C₁₉×Dic₅₅ #16862016

Order 4180.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×Dic₁₁	—	5	1	no	maximal, Hall
4	C₂×C₁₁×C₁₉	D₅	1	1	yes	characteristic
5	C₁₉×Dic₅	—	11	1	no	maximal, Hall
6	Dic₅₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₁₉	Dic₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×C₁₉	D₁₁	1	1	yes	characteristic
9	C₂×C₅×C₁₁	C₂×C₁₉	1	1	yes	characteristic
10	C₅×C₁₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₄×C₁₉	—	55	1	no	Hall
12	C₅×C₁₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
13	Dic₁₁	—	5	1	no	Hall
14	C₂×C₁₉	D₅₅	1	1	yes	characteristic
15	C₂×C₁₁	D₅×C₁₉	1	1	yes	characteristic
16	Dic₅	—	11	1	no	Hall
17	C₁₉	Dic₅₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₁	C₁₉×Dic₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	C₁₉×D₁₁	1	1	yes	characteristic
20	C₅	C₁₉×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	55	1	no	Sylow
22	C₂	C₁₉×D₅₅	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.