Subgroups — C₃×C₁₃⋊D₄₀₃ #44537697

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	C₁₃⋊D₄₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₄₀₃	—	13	14	no	maximal
5	C₃×C₁₃×C₃₁	D₁₃	1	14	yes	complemented
6	C₃×C₁₃⋊D₁₃	—	31	1	no	maximal, Hall
7	D₄₀₃	—	13	14	no	—
8	C₃×C₁₃²	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	C₃×D₁₃	1	14	yes	complemented
10	C₁₃⋊D₁₃	—	31	1	no	Hall
11	C₃×D₃₁	—	169	1	no	Hall
12	C₁₃²	C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₁	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₁₃	—	403	14	no	—
15	D₃₁	—	169	1	no	Hall
16	C₃×C₁₃	D₄₀₃	1	14	yes	complemented
17	C₃₁	C₃×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
18	D₁₃	—	403	14	no	—
19	C₁₃	C₃×D₄₀₃	1	14	yes	complemented
20	C₂×C₃	—	5239	1	no	Hall
21	C₃	C₁₃⋊D₄₀₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	5239	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊D₄₀₃
commutator, cosocle, hypocenter	C₁₃²×C₃₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₃₁	C₂
LCS	G ▷ C₁₃²×C₃₁
UCS	C₁ ◁ C₃

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.