Subgroups — C₃₁×D₅₀₇ #44537614

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	C₃₁×D₁₆₉	—	3	1	no	maximal, Hall
3	C₃₁×C₁₆₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₃₁×D₃₉	—	13	1	no	maximal
5	C₃×C₁₃×C₃₁	D₁₃	1	1	yes	characteristic
6	D₅₀₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₁₃×C₃₁	—	39	1	no	—
8	C₃×C₁₆₉	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₃₁	D₃₉	1	1	yes	characteristic
10	D₁₆₉	—	3	1	no	Hall
11	D₃×C₃₁	—	169	1	no	Hall
12	C₁₆₉	D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₃₁	D₁₆₉	1	1	yes	characteristic, complemented, Hall
14	D₃₉	—	13	1	no	—
15	C₂×C₃₁	—	507	1	no	Hall
16	C₃×C₁₃	D₁₃×C₃₁	1	1	yes	characteristic
17	C₃₁	D₅₀₇	1	1	yes	characteristic, direct product factor, Sylow
18	D₁₃	—	39	1	no	—
19	C₁₃	C₃₁×D₃₉	1	1	yes	characteristic
20	D₃	—	169	1	no	Hall
21	C₃	C₃₁×D₁₆₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	507	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁	D₅₀₇
commutator, cosocle, hypocenter	C₃×C₁₆₉	C₂×C₃₁
Frattini	C₁₃	C₃₁×D₃₉
Fitting	C₃×C₃₁×C₁₆₉	C₂
socle	C₃×C₁₃×C₃₁	D₁₃
LCS	G ▷ C₃×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.