Subgroups — C₁₆₉×D₃₁⋊C₃ #44537616

Order 31434.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊C₃×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁×C₁₆₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₃₁⋊C₃	C₁₃	1	1	yes	maximal, characteristic
5	C₁₃×C₃₁⋊C₃	C₂×C₁₃	1	1	yes	characteristic
6	C₂×C₃×C₁₆₉	—	31	1	no	maximal, Hall
7	C₁₃×D₃₁	C₃×C₁₃	1	1	yes	characteristic
8	C₃×C₁₆₉	—	31	1	no	Hall
9	C₁₃×C₃₁	C₂×C₃×C₁₃	1	1	yes	characteristic
10	C₂×C₁₆₉	—	31	1	no	Hall
11	D₃₁⋊C₃	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
12	C₁₆₉	D₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃₁⋊C₃	C₂×C₁₆₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₃	—	31	1	no	—
15	D₃₁	C₃×C₁₆₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₃	—	31	1	no	—
17	C₃₁	C₂×C₃×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₃	—	31	1	no	—
19	C₁₃	C₁₃×D₃₁⋊C₃	1	1	yes	characteristic
20	C₂×C₃	—	31	1	no	Hall
21	C₃	—	31	1	no	Sylow
22	C₂	—	31	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.