Subgroups — C₃×C₁₃²×D₃₁ #44537693

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	C₁₃²×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₃₁	C₁₃	1	14	yes	maximal, direct product factor
5	C₃×C₁₃×C₃₁	C₂×C₁₃	1	14	yes	complemented
6	C₂×C₃×C₁₃²	—	31	1	no	maximal, Hall
7	C₁₃×D₃₁	C₃×C₁₃	1	14	yes	direct product factor
8	C₃×C₁₃²	D₃₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₃×C₃₁	C₂×C₃×C₁₃	1	14	yes	complemented
10	C₂×C₁₃²	—	31	1	no	Hall
11	C₃×D₃₁	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃²	C₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₃₁	C₂×C₁₃²	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₃	—	31	14	no	—
15	D₃₁	C₃×C₁₃²	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃	C₁₃×D₃₁	1	14	yes	direct product factor
17	C₃₁	C₂×C₃×C₁₃²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₃	—	31	14	no	—
19	C₁₃	C₃×C₁₃×D₃₁	1	14	yes	direct product factor
20	C₂×C₃	—	31	1	no	Hall
21	C₃	C₁₃²×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃²	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₁₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₃²

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.