Subgroups — #17987429

Order 4617.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587025	C₃	1	2	yes	maximal, complemented
2	C₃²×#4294	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊#4294	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃³×C₁₉	C₃²	1	3	yes	—
6	C₃³×C₁₉	C₃²	1	1	yes	characteristic
7	C₁₉×H(3,𝔽₃)	—	3	3	no	—
8	#10587025	—	3	6	no	—
9	C₃×#4294	—	3	3	no	—
10	C₃×#4294	C₃²	1	3	yes	—
11	C₃×#4294	C₃²	1	6	yes	—
12	#6893	—	19	1	no	maximal, Sylow
13	C₃²×C₁₉	—	3	3	no	—
14	C₃²×C₁₉	—	3	3	no	—
15	C₃²×C₁₉	—	3	9	no	—
16	C₃²×C₁₉	H(3,𝔽₃)	1	3	yes	—
17	C₃²×C₁₉	C₃³	1	1	yes	characteristic
18	#4294	—	3	3	no	—
19	#4294	—	3	6	no	—
20	C₃×3₋¹⁺²	—	19	2	no	—
21	C₃×H(3,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic
22	C₃²×C₉	—	19	1	no	—
23	C₃²⋊C₉	—	19	9	no	—
24	C₃×C₁₉	—	3	3	no	—
25	C₃×C₁₉	—	9	3	no	—
26	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₁₉	#737	1	3	yes	—
28	C₃³	C₃×C₁₉⋊C₃	1	3	yes	—
29	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
30	3₋¹⁺²	—	57	6	no	—
31	H(3,𝔽₃)	—	3	3	no	—
32	C₃×C₉	—	19	3	no	—
33	C₃×C₉	—	19	6	no	—
34	C₃×C₉	—	57	3	no	—
35	C₁₉	#6893	1	1	yes	characteristic, complemented, Sylow
36	C₃²	—	3	3	no	—
37	C₃²	—	3	3	no	—
38	C₃²	—	3	9	no	—
39	C₃²	C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
40	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
41	C₉	—	57	3	no	—
42	C₉	—	57	6	no	—
43	C₃	—	3	3	no	—
44	C₃	—	9	3	no	—
45	C₃	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
46	C₃	#13095331	1	3	yes	—

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.