Subgroups — C₃×Dic₁₉×C₁₃₉ #44540069

Order 31692.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×C₁₃₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₁₃₉	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₁₃₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₁₃₉	—	19	1	no	maximal, Hall
7	C₂×C₃×C₁₃₉	D₁₉	1	1	yes	characteristic
8	C₄×C₁₃₉	—	19	1	no	Hall
9	C₃×C₁₃₉	Dic₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃₉	C₃×D₁₉	1	1	yes	characteristic
11	C₃×Dic₁₉	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₃₉	C₃×Dic₁₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₁₉	C₂×C₁₃₉	1	1	yes	characteristic
14	Dic₁₉	C₃×C₁₃₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₉	C₄×C₁₃₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₉	C₂×C₃×C₁₃₉	1	1	yes	characteristic
17	C₁₉	C₃×C₄×C₁₃₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	19	1	no	Hall
19	C₂×C₃	D₁₉×C₁₃₉	1	1	yes	characteristic
20	C₄	—	19	1	no	Sylow
21	C₃	Dic₁₉×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₁₉×C₁₃₉	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.