Subgroups — C₃×C₄₇×Dic₁₉ #24924261

Order 10716.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×Dic₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₉×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₄₇	—	19	1	no	maximal, Hall
7	C₂×C₃×C₄₇	D₁₉	1	1	yes	characteristic
8	C₃×Dic₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₄₇	—	19	1	no	Hall
10	C₃×C₄₇	Dic₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₁₉	C₂×C₄₇	1	1	yes	characteristic
12	C₂×C₄₇	C₃×D₁₉	1	1	yes	characteristic
13	Dic₁₉	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₉	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
15	C₄₇	C₃×Dic₁₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₉	C₂×C₃×C₄₇	1	1	yes	characteristic
17	C₁₉	C₃×C₄×C₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	19	1	no	Hall
19	C₂×C₃	D₁₉×C₄₇	1	1	yes	characteristic
20	C₄	—	19	1	no	Sylow
21	C₃	C₄₇×Dic₁₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₁₉×C₄₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.