Subgroups — #17987515

Order 4617.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₁₉⋊C₃)	C₃	1	3	yes	maximal, complemented
2	#13095320	C₃	1	9	yes	maximal, complemented
3	C₃×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₁₉	C₃²	1	1	yes	characteristic
5	C₃²×C₁₉⋊C₃	—	3	3	no	—
6	C₁₉×3₋¹⁺²	—	3	3	no	—
7	C₃×C₉×C₁₉	C₃²	1	3	yes	complemented
8	C₃²⋊(C₁₉⋊C₃)	—	3	6	no	—
9	C₃²⋊(C₁₉⋊C₃)	C₃²	1	9	yes	complemented
10	#6911	—	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	C₃×C₁₉⋊C₃	—	3	9	no	—
15	C₃×C₁₉⋊C₃	—	9	9	no	—
16	C₉×C₁₉	—	3	3	no	—
17	C₃×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
18	C₃×H(3,𝔽₃)	—	19	3	no	—
19	#732	—	19	9	no	—
20	C₃×C₁₉	—	3	3	no	—
21	C₃×C₁₉	—	3	1	no	—
22	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₁₉⋊C₃	—	9	9	no	—
24	C₃³	—	57	3	no	—
25	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
26	3₋¹⁺²	—	3	3	no	—
27	H(3,𝔽₃)	—	19	9	no	—
28	H(3,𝔽₃)	—	57	6	no	—
29	C₃×C₉	C₃×C₁₉⋊C₃	1	3	yes	complemented
30	C₁₉	#6911	1	1	yes	characteristic, complemented, Sylow
31	C₃²	—	9	1	no	—
32	C₃²	—	57	9	no	—
33	C₃²	—	171	9	no	—
34	C₃²	C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
35	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
36	C₉	—	3	3	no	—
37	C₃	—	3	3	no	—
38	C₃	—	3	1	no	—
39	C₃	—	171	9	no	—
40	C₃	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic

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.