Subgroups — #37589481

Order 24548.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇⋊(C₁₉⋊D₁₉)	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₉²	C₄	1	1	yes	characteristic, complemented, Hall
3	#13089659	—	17	1	no	maximal, Hall
4	C₁₉⋊D₁₉	—	17	1	no	—
5	D₃₂₃	—	38	10	no	—
6	C₁₉²	#595	1	1	yes	characteristic, complemented, Sylow
7	C₁₇×C₁₉	—	2	10	no	—
8	#595	—	361	1	no	maximal, Hall
9	D₁₉	—	646	10	no	—
10	D₁₇	—	361	1	no	—
11	C₁₉	—	2	10	no	—
12	C₁₇	#13089659	1	1	yes	characteristic, complemented, Sylow
13	C₄	—	6137	1	no	Sylow
14	C₂	—	6137	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₁₉²	C₄
prime radical, cosocle	C₁₇⋊(C₁₉⋊D₁₉)	C₂
LCS	G ▷ C₁₇×C₁₉²
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.