Subgroups — #17987519

Order 4617.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587025	C₃	1	3	yes	maximal
2	#13095322	C₃	1	9	yes	maximal, complemented
3	C₃×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
4	C₃³×C₁₉	C₃²	1	1	yes	characteristic
5	C₁₉×3₋¹⁺²	—	3	3	no	—
6	C₃×C₉×C₁₉	C₃²	1	3	yes	—
7	#10587025	—	3	6	no	—
8	#10587025	C₃²	1	9	yes	—
9	C₃×#4294	—	3	3	no	—
10	#6912	—	19	1	no	maximal, Sylow
11	C₃²×C₁₉	—	9	1	no	—
12	C₃²×C₁₉	H(3,𝔽₃)	1	3	yes	—
13	C₃²×C₁₉	C₃³	1	1	yes	characteristic
14	C₉×C₁₉	—	3	3	no	—
15	#4294	—	3	9	no	—
16	C₃×3₋¹⁺²	—	19	3	no	—
17	C₃×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
18	#733	—	19	9	no	—
19	C₃×C₁₉	—	3	3	no	—
20	C₃×C₁₉	—	3	1	no	—
21	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
22	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
23	3₋¹⁺²	—	3	3	no	—
24	3₋¹⁺²	—	19	9	no	—
25	3₋¹⁺²	—	57	6	no	—
26	C₃×C₉	—	57	3	no	—
27	C₃×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
28	C₁₉	#6912	1	1	yes	characteristic, complemented, Sylow
29	C₃²	—	9	1	no	—
30	C₃²	C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
31	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
32	C₉	—	3	3	no	—
33	C₉	—	57	9	no	—
34	C₃	—	3	3	no	—
35	C₃	—	3	1	no	—
36	C₃	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #13095322	C₃	semidirect
28. C₁₉	#6912	semidirect

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