Subgroups — Dic₃×C₁₉×C₇₁ #30633679

Order 16188.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×C₇₁	—	3	1	no	maximal, Hall
3	C₃×C₁₉×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₇₁	D₃	1	1	yes	characteristic
5	C₁₉×C₇₁	Dic₃	1	1	yes	characteristic, direct product factor, Hall
6	Dic₃×C₇₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇₁	C₂×C₁₉	1	1	yes	characteristic
8	C₄×C₇₁	—	3	1	no	Hall
9	Dic₃×C₁₉	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇₁	D₃×C₁₉	1	1	yes	characteristic
12	C₂×C₃×C₁₉	C₂×C₇₁	1	1	yes	characteristic
13	C₄×C₁₉	—	3	1	no	Hall
14	C₇₁	Dic₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₉	C₄×C₇₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₉	D₃×C₇₁	1	1	yes	characteristic
17	C₁₉	Dic₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
18	Dic₃	C₁₉×C₇₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃	C₂×C₁₉×C₇₁	1	1	yes	characteristic
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₁₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₁₉×C₇₁	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.