Subgroups — C₁₉×#6900 #17987286

Order 4617.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×3₋¹⁺²	C₃	1	4	yes	maximal
2	C₁₉×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₁₉	C₃²	1	1	yes	characteristic
5	C₁₉×3₋¹⁺²	—	3	12	no	—
6	C₃×C₉×C₁₉	C₃²	1	8	yes	—
7	C₃×C₉×C₁₉	C₃²	1	4	yes	—
8	#6900	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃²×C₁₉	—	3	4	no	—
10	C₃²×C₁₉	C₃³	1	1	yes	characteristic
11	C₉×C₁₉	—	3	8	no	—
12	C₉×C₁₉	3₋¹⁺²	1	12	yes	complemented
13	C₃×3₋¹⁺²	C₃×C₁₉	1	4	yes	—
14	C₉⋊C₉	C₃×C₁₉	1	8	yes	complemented
15	C₉²	C₃×C₁₉	1	1	yes	characteristic, complemented
16	C₃×C₁₉	—	9	1	no	—
17	C₃×C₁₉	C₃×3₋¹⁺²	1	4	yes	—
18	C₃³	C₃²×C₁₉	1	1	yes	characteristic
19	3₋¹⁺²	—	3	12	no	—
20	C₃×C₉	C₃²×C₁₉	1	8	yes	—
21	C₃×C₉	C₃²×C₁₉	1	4	yes	—
22	C₁₉	#6900	1	1	yes	characteristic, direct product factor, Sylow
23	C₃²	—	3	4	no	—
24	C₃²	C₃³×C₁₉	1	1	yes	characteristic
25	C₉	—	3	8	no	—
26	C₉	C₁₉×3₋¹⁺²	1	12	yes	complemented
27	C₃	—	9	1	no	—
28	C₃	C₃×C₁₉×3₋¹⁺²	1	4	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₉	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₁₉
prime radical	C₃³×C₁₉	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ G

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.