Subgroups — C₁₉×#10624554 #28352750

Order 13851.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₉⋊C₉	C₃	1	12	yes	maximal
2	C₃×C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₉×C₁₉	C₃²	1	9	yes	—
4	C₃²×C₉×C₁₉	C₃²	1	4	yes	—
5	C₁₉×C₉⋊C₉	—	3	36	no	—
6	C₉²×C₁₉	C₉	1	9	yes	complemented
7	#10624554	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₉	C₃³	1	1	yes	characteristic
9	C₃×C₉×C₁₉	—	3	36	no	—
10	C₃×C₉×C₁₉	C₃×C₉	1	12	yes	—
11	C₃×C₉×C₁₉	3₋¹⁺²	1	36	yes	—
12	C₃×C₉⋊C₉	C₃×C₁₉	1	12	yes	—
13	C₃×C₉²	C₃×C₁₉	1	1	yes	characteristic
14	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
15	C₃²×C₁₉	C₃×3₋¹⁺²	1	12	yes	—
16	C₉×C₁₉	—	9	9	no	—
17	C₉×C₁₉	C₉⋊C₉	1	36	yes	complemented
18	C₃²×C₉	C₃²×C₁₉	1	9	yes	—
19	C₃²×C₉	C₃²×C₁₉	1	4	yes	—
20	C₉⋊C₉	—	3	36	no	—
21	C₉²	C₉×C₁₉	1	9	yes	complemented
22	C₃×C₁₉	C₃×C₉⋊C₉	1	4	yes	—
23	C₃×C₁₉	#6900	1	9	yes	—
24	C₃³	C₃³×C₁₉	1	1	yes	characteristic
25	C₃×C₉	—	3	36	no	—
26	C₃×C₉	C₃×C₉×C₁₉	1	12	yes	—
27	C₃×C₉	C₁₉×3₋¹⁺²	1	36	yes	—
28	C₁₉	#10624554	1	1	yes	characteristic, direct product factor, Sylow
29	C₃²	C₃²×C₉×C₁₉	1	1	yes	characteristic
30	C₃²	C₃×C₁₉×3₋¹⁺²	1	12	yes	—
31	C₉	—	9	9	no	—
32	C₉	C₁₉×C₉⋊C₉	1	36	yes	complemented
33	C₃	C₃×C₁₉×C₉⋊C₉	1	4	yes	—
34	C₃	C₁₉×#6900	1	9	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.