Subgroups — C₃₁×D₁₆₉⋊C₃ #44537621

Order 31434.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₁₆₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₆₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₁×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃₁×D₁₃⋊C₃	—	13	1	no	maximal
5	C₃₁×C₁₃⋊C₃	—	13	1	no	—
6	D₁₆₉⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₁₃×C₃₁	—	13	1	no	—
8	C₁₆₉⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	D₁₃⋊C₃	1	1	yes	characteristic
10	D₁₆₉	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₃₁	—	169	1	no	Hall
12	C₁₆₉	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₁	—	169	1	no	Hall
14	D₁₃⋊C₃	—	13	1	no	—
15	C₂×C₃₁	—	169	1	no	Hall
16	C₁₃⋊C₃	—	13	1	no	—
17	C₃₁	D₁₆₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	D₁₃	—	13	1	no	—
19	C₁₃	C₃₁×D₁₃⋊C₃	1	1	yes	characteristic
20	C₂×C₃	—	169	1	no	Hall
21	C₃	—	169	1	no	Sylow
22	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₁₆₉⋊C₃
commutator, cosocle, hypocenter	C₁₆₉	C₂×C₃×C₃₁
Frattini	C₁₃	C₃₁×D₁₃⋊C₃
Fitting	C₃₁×C₁₆₉	C₂×C₃
socle	C₁₃×C₃₁	D₁₃⋊C₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₃₁

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.