Subgroups — #13095321

Order 1539.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	#10587025	C₃	1	2	yes	maximal
3	C₃×#4294	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₁₉	C₃²	1	1	yes	characteristic
5	C₉×C₁₉	—	3	1	no	—
6	#4294	—	3	1	no	—
7	#4294	—	3	2	no	—
8	#733	—	19	1	no	maximal, Sylow
9	C₃×C₁₉	—	3	1	no	—
10	C₃×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
11	3₋¹⁺²	—	19	2	no	—
12	3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
13	C₃×C₉	—	19	1	no	—
14	C₁₉	#733	1	1	yes	characteristic, complemented, Sylow
15	C₃²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
16	C₉	—	3	1	no	—
17	C₉	—	57	1	no	—
18	C₉	—	57	2	no	—
19	C₃	—	3	1	no	—
20	C₃	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²⋊(C₁₉⋊C₃)
commutator, prime radical, cosocle	C₃²×C₁₉	C₃²
Frattini	C₃²	C₃×C₁₉⋊C₃
Fitting	C₁₉×3₋¹⁺²	C₃
socle	C₃×C₁₉	H(3,𝔽₃)
hypercenter	3₋¹⁺²	C₁₉⋊C₃
hypocenter	C₁₉	#733
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ 3₋¹⁺²

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
14. C₁₉	#733	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.