Subgroups — D₃×C₃₁×C₁₆₉ #44537612

Order 31434.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₁×C₁₆₉	—	3	1	no	maximal, Hall
3	C₃₁×C₁₆₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₃×C₃₁	C₁₃	1	1	yes	maximal, characteristic
5	C₃×C₁₃×C₃₁	C₂×C₁₃	1	1	yes	characteristic
6	D₃×C₁₆₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₃₁	—	3	1	no	—
8	C₃×C₁₆₉	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	D₃×C₁₃	1	1	yes	characteristic
10	C₂×C₁₆₉	—	3	1	no	Hall
11	D₃×C₃₁	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
12	C₁₆₉	D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₃₁	C₂×C₁₆₉	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₃	C₁₃×C₃₁	1	1	yes	characteristic
15	C₂×C₃₁	—	3	1	no	Hall
16	C₃×C₁₃	C₂×C₁₃×C₃₁	1	1	yes	characteristic
17	C₃₁	D₃×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₃	—	3	1	no	—
19	C₁₃	D₃×C₁₃×C₃₁	1	1	yes	characteristic
20	D₃	C₃₁×C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₃₁×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

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.