Subgroups — C₃₁⋊C₃×D₁₆₉ #44537620

Order 31434.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃₁×C₁₆₉	C₂×C₃
Frattini	C₁₃	D₁₃×C₃₁⋊C₃
socle	C₁₃×C₃₁	C₃×D₁₃
LCS	G ▷ C₃₁×C₁₆₉
UCS	C₁

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.