Subgroups — C₁₉×#10624649 #28352845

Order 13851.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#6894	C₃	1	3	yes	maximal
2	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
3	C₁₉×#6861	C₃	1	3	yes	maximal
4	C₁₉×#6860	C₃	1	3	yes	maximal
5	C₁₉×#6858	C₃	1	3	yes	maximal
6	C₃×C₁₉×3₋¹⁺²	C₃²	1	3	yes	—
7	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×C₉⋊C₉	—	3	2	no	—
9	C₁₉×C₉⋊C₉	—	3	6	no	—
10	C₁₉×C₉⋊C₉	—	3	3	no	—
11	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
12	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
13	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₉²×C₁₉	—	3	1	no	—
15	#10624649	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₁₉×3₋¹⁺²	—	9	3	no	—
18	C₃×C₉×C₁₉	—	3	3	no	—
19	C₃×C₉×C₁₉	—	3	3	no	—
20	C₃×C₉×C₁₉	—	3	3	no	—
21	C₃×C₉×C₁₉	—	3	3	no	—
22	C₃×C₉×C₁₉	—	3	3	no	—
23	C₃×C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
24	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
25	#6894	C₃×C₁₉	1	3	yes	—
26	#6887	C₃×C₁₉	1	1	yes	characteristic
27	#6861	C₃×C₁₉	1	3	yes	—
28	#6860	C₃×C₁₉	1	3	yes	—
29	#6858	C₃×C₁₉	1	3	yes	—
30	C₃²×C₁₉	—	3	3	no	—
31	C₃²×C₁₉	—	3	1	no	—
32	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₉×C₁₉	—	3	2	no	—
34	C₉×C₁₉	—	9	3	no	—
35	C₉×C₁₉	—	9	3	no	—
36	C₉×C₁₉	—	9	3	no	—
37	C₉×C₁₉	—	9	3	no	—
38	C₉×C₁₉	#733	1	3	yes	—
39	C₃×3₋¹⁺²	C₃²×C₁₉	1	3	yes	—
40	C₃²×C₉	C₃²×C₁₉	1	1	yes	characteristic
41	C₉⋊C₉	—	3	2	no	—
42	C₉⋊C₉	—	3	6	no	—
43	C₉⋊C₉	—	3	3	no	—
44	C₃²⋊C₉	C₃²×C₁₉	1	3	yes	—
45	C₃²⋊C₉	C₃²×C₁₉	1	3	yes	—
46	C₃²⋊C₉	C₃²×C₁₉	1	3	yes	—
47	C₉²	—	3	1	no	—
48	C₃×C₁₉	—	9	1	no	—
49	C₃×C₁₉	C₃×#733	1	1	yes	characteristic
50	C₃×C₁₉	#6913	1	3	yes	—
51	C₃³	C₃³×C₁₉	1	1	yes	characteristic
52	3₋¹⁺²	—	9	3	no	—
53	C₃×C₉	—	3	3	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	3	3	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	C₁₉×H(3,𝔽₃)	1	2	yes	—
59	C₃×C₉	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
60	C₁₉	#10624649	1	1	yes	characteristic, direct product factor, Sylow
61	C₃²	—	3	1	no	—
62	C₃²	—	3	3	no	—
63	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
64	C₉	—	3	2	no	—
65	C₉	—	9	3	no	—
66	C₉	—	9	3	no	—
67	C₉	—	9	3	no	—
68	C₉	—	9	3	no	—
69	C₉	C₁₉×#733	1	3	yes	—
70	C₃	—	9	1	no	—
71	C₃	C₃×C₁₉×#733	1	1	yes	characteristic
72	C₃	C₁₉×#6913	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
15. #10624649	C₁₉	direct (N × H)
60. C₁₉	#10624649	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#6894	3
C₁₉×#6887	3
C₁₉×#6861	3
C₁₉×#6860	3
C₁₉×#6858	3
#10624649	19

Subgroups — C19×#10624649 #28352845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624649 #28352845