Subgroups — C₁₉×#10624840 #28353036

Order 13851.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#733	C₃	1	3	yes	maximal
2	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#6880	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₉×3₋¹⁺²	—	3	3	no	—
5	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₁₉×#733	—	3	6	no	—
7	C₁₉×#733	C₃²	1	9	yes	—
8	C₁₉×C₉⋊C₉	—	3	2	no	—
9	C₁₉×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₁₉	C₃²	1	3	yes	—
11	#10624840	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₁₉×3₋¹⁺²	—	3	9	no	—
14	C₁₉×3₋¹⁺²	—	9	6	no	—
15	C₃×C₉×C₁₉	—	3	3	no	—
16	C₃×C₉×C₁₉	—	3	3	no	—
17	C₃×C₉×C₁₉	—	9	3	no	—
18	C₃×C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
19	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
20	C₃×#733	C₃×C₁₉	1	3	yes	—
21	#6887	C₃×C₁₉	1	1	yes	characteristic
22	#6880	C₃×C₁₉	1	9	yes	complemented
23	C₃²×C₁₉	—	9	1	no	—
24	C₃²×C₁₉	#732	1	3	yes	—
25	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
26	C₉×C₁₉	—	3	2	no	—
27	C₉×C₁₉	—	3	1	no	—
28	C₉×C₁₉	—	9	3	no	—
29	C₉×C₁₉	—	9	9	no	—
30	C₃×3₋¹⁺²	—	3	3	no	—
31	C₃²×C₉	C₃²×C₁₉	1	1	yes	characteristic
32	#733	—	3	6	no	—
33	#733	C₃²×C₁₉	1	9	yes	—
34	C₉⋊C₉	—	3	2	no	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₉²	C₃²×C₁₉	1	3	yes	—
37	C₃×C₁₉	—	3	1	no	—
38	C₃×C₁₉	—	3	3	no	—
39	C₃×C₁₉	C₃×#732	1	1	yes	characteristic
40	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
41	3₋¹⁺²	—	3	9	no	—
42	3₋¹⁺²	—	9	6	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	9	3	no	—
46	C₃×C₉	C₁₉×H(3,𝔽₃)	1	2	yes	—
47	C₃×C₉	C₃³×C₁₉	1	1	yes	characteristic
48	C₁₉	#10624840	1	1	yes	characteristic, direct product factor, Sylow
49	C₃²	—	9	1	no	—
50	C₃²	C₁₉×#732	1	3	yes	—
51	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
52	C₉	—	3	2	no	—
53	C₉	—	3	1	no	—
54	C₉	—	9	3	no	—
55	C₉	—	9	9	no	—
56	C₃	—	3	1	no	—
57	C₃	—	3	3	no	—
58	C₃	C₃×C₁₉×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₉	C₃×#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₉
prime radical	C₃³×C₁₉	H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₉ ◁ C₃³×C₁₉ ◁ C₃²×C₉×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#6880	C₃	semidirect
11. #10624840	C₁₉	direct (N × H)
22. #6880	C₃×C₁₉	semidirect
48. C₁₉	#10624840	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#733	3
C₁₉×#6887	3
C₁₉×#6880	3
#10624840	19

Subgroups — C19×#10624840 #28353036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624840 #28353036