Subgroups — C₃₇×C₁₇²⋊C₃ #44545513

Order 32079.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇²⋊C₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₃₇	—	3	6	no	—
4	C₁₇²	C₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
5	C₃×C₃₇	—	289	1	no	maximal, Hall
6	C₃₇	C₁₇²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₁₇	—	3	6	no	—
8	C₃	—	289	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	C₁₇²⋊C₃
commutator, cosocle, hypocenter	C₁₇²	C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₇²×C₃₇	C₃
LCS	G ▷ C₁₇²
UCS	C₁ ◁ C₃₇

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.