Subgroups — C₁₉²×D₃₁ #36375511

Order 22382.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₃₁	C₁₉	1	20	yes	maximal, direct product factor
3	C₂×C₁₉²	—	31	1	no	maximal, Hall
4	C₁₉×C₃₁	C₂×C₁₉	1	20	yes	complemented
5	C₁₉²	D₃₁	1	1	yes	characteristic, direct product factor, Sylow
6	D₃₁	C₁₉²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₉	—	31	20	no	—
8	C₃₁	C₂×C₁₉²	1	1	yes	characteristic, complemented, Sylow
9	C₁₉	C₁₉×D₃₁	1	20	yes	direct product factor
10	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉²	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₁₉²
Frattini	C₁	G
Fitting, socle	C₁₉²×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₉²

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.