Subgroups — D₃×C₁₃²×C₃₁ #44537698

Order 31434.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃²×C₃₁	—	3	1	no	maximal, Hall
3	C₁₃²×C₃₁	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₃×C₃₁	C₁₃	1	14	yes	maximal, direct product factor
5	C₃×C₁₃×C₃₁	C₂×C₁₃	1	14	yes	complemented
6	D₃×C₁₃²	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₃₁	—	3	14	no	—
8	C₃×C₁₃²	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	D₃×C₁₃	1	14	yes	direct product factor
10	C₂×C₁₃²	—	3	1	no	Hall
11	D₃×C₃₁	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃²	D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₃₁	C₂×C₁₃²	1	1	yes	characteristic, complemented, Hall
14	D₃×C₁₃	C₁₃×C₃₁	1	14	yes	direct product factor
15	C₂×C₃₁	—	3	1	no	Hall
16	C₃×C₁₃	C₂×C₁₃×C₃₁	1	14	yes	complemented
17	C₃₁	D₃×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₃	—	3	14	no	—
19	C₁₃	D₃×C₁₃×C₃₁	1	14	yes	direct product factor
20	D₃	C₁₃²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×C₁₃²×C₃₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃²×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₃²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₃²×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.