Subgroups — #28356666

Order 13851.

5490 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987547	C₃	1	80	yes	maximal, complemented
2	C₃×#13095331	C₃	1	40	yes	maximal, complemented
3	C₁₉×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	#13095331	C₃²	1	90	yes	complemented
5	#13095331	C₃²	1	720	yes	complemented
6	C₃×#10587025	C₃²	1	320	yes	complemented
7	C₃²×#4294	C₃²	1	40	yes	complemented
8	C₃×C₁₉×H(3,𝔽₃)	C₃²	1	40	yes	—
9	#10624943	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	C₃³	1	40	yes	—
11	C₁₉×H(3,𝔽₃)	C₃³	1	90	yes	—
12	#10587025	C₃³	1	720	yes	—
13	C₃×#4294	C₃³	1	40	yes	—
14	C₃×#4294	C₃³	1	320	yes	—
15	3₋¹⁺⁴	—	19	80	no	—
16	H(5,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic
17	C₃×#737	—	19	40	no	—
18	C₃²×C₁₉	—	9	40	no	—
19	C₃²×C₁₉	C₃⁴	1	40	yes	—
20	#4294	C₃⁴	1	1	yes	characteristic
21	#4294	C₃⁴	1	80	yes	—
22	#737	—	19	90	no	—
23	#737	—	19	720	no	—
24	C₃×3₋¹⁺²	—	19	320	no	—
25	C₃×H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	40	yes	—
26	C₃²×C₉	—	19	40	no	—
27	C₃×C₁₉	—	3	40	no	—
28	C₃×C₁₉	C₃⁵	1	1	yes	characteristic
29	C₃³	C₃²×C₁₉⋊C₃	1	40	yes	—
30	3₋¹⁺²	—	19	720	no	—
31	H(3,𝔽₃)	C₃²×C₁₉⋊C₃	1	90	yes	—
32	C₃×C₉	—	19	40	no	—
33	C₃×C₉	—	19	320	no	—
34	C₁₉	#10624943	1	1	yes	characteristic, complemented, Sylow
35	C₃²	—	9	40	no	—
36	C₃²	C₃³×C₁₉⋊C₃	1	40	yes	—
37	C₉	—	19	1	no	—
38	C₉	—	19	80	no	—
39	C₃	—	3	40	no	—
40	C₃	C₃⁴×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.