Subgroups — C₃×D₅₂₃₉ #44537611

Order 31434.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₄₀₃	—	13	1	no	maximal
5	C₃×C₁₃×C₃₁	D₁₃	1	1	yes	characteristic
6	C₃×D₁₆₉	—	31	1	no	maximal, Hall
7	D₄₀₃	—	13	1	no	—
8	C₃×C₁₆₉	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	C₃×D₁₃	1	1	yes	characteristic
10	D₁₆₉	—	31	1	no	Hall
11	C₃×D₃₁	—	169	1	no	Hall
12	C₁₆₉	C₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₁	D₁₆₉	1	1	yes	characteristic, complemented, Hall
14	C₃×D₁₃	—	403	1	no	—
15	D₃₁	—	169	1	no	Hall
16	C₃×C₁₃	D₄₀₃	1	1	yes	characteristic
17	C₃₁	C₃×D₁₆₉	1	1	yes	characteristic, complemented, Sylow
18	D₁₃	—	403	1	no	—
19	C₁₃	C₃×D₄₀₃	1	1	yes	characteristic
20	C₂×C₃	—	5239	1	no	Hall
21	C₃	D₅₂₃₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	5239	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₂₃₉
commutator, cosocle, hypocenter	C₃₁×C₁₆₉	C₂×C₃
Frattini	C₁₃	C₃×D₄₀₃
Fitting	C₃×C₃₁×C₁₆₉	C₂
socle	C₃×C₁₃×C₃₁	D₁₃
LCS	G ▷ C₃₁×C₁₆₉
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.