Subgroups — C₁₉×#10624670 #28352866

Order 13851.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#6891	C₃	1	4	yes	maximal
2	C₁₉×#6862	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
4	C₃×C₁₉×3₋¹⁺²	—	3	4	no	—
5	C₁₉×C₃²⋊C₉	—	3	4	no	—
6	C₁₉×C₃²⋊C₉	—	3	4	no	—
7	C₁₉×C₃²⋊C₉	C₃²	1	12	yes	—
8	#10624670	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃³×C₁₉	—	9	4	no	—
10	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃³×C₁₉	H(3,𝔽₃)	1	2	yes	—
12	C₃³×C₁₉	C₃³	1	1	yes	characteristic
13	C₁₉×3₋¹⁺²	—	9	12	no	—
14	C₃×C₉×C₁₉	—	3	12	no	—
15	#6891	C₃×C₁₉	1	4	yes	—
16	#6862	C₃×C₁₉	1	9	yes	complemented
17	C₃²×C₁₉	—	3	4	no	—
18	C₃²×C₁₉	—	3	4	no	—
19	C₃²×C₁₉	—	3	4	no	—
20	C₃²×C₁₉	—	3	4	no	—
21	C₃²×C₁₉	—	9	9	no	—
22	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₉×C₁₉	—	9	12	no	—
24	C₃⁴	C₃²×C₁₉	1	1	yes	characteristic
25	C₃×3₋¹⁺²	—	3	4	no	—
26	C₃²⋊C₉	—	3	4	no	—
27	C₃²⋊C₉	—	3	4	no	—
28	C₃²⋊C₉	C₃²×C₁₉	1	12	yes	—
29	C₃×C₁₉	—	9	2	no	—
30	C₃×C₁₉	—	9	1	no	—
31	C₃×C₁₉	—	9	1	no	—
32	C₃×C₁₉	#6910	1	4	yes	—
33	C₃³	—	9	4	no	—
34	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃³	C₁₉×H(3,𝔽₃)	1	2	yes	—
36	C₃³	C₃³×C₁₉	1	1	yes	characteristic
37	3₋¹⁺²	—	9	12	no	—
38	C₃×C₉	—	3	12	no	—
39	C₁₉	#10624670	1	1	yes	characteristic, direct product factor, Sylow
40	C₃²	—	3	4	no	—
41	C₃²	—	3	4	no	—
42	C₃²	—	3	4	no	—
43	C₃²	—	3	4	no	—
44	C₃²	—	9	9	no	—
45	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
46	C₉	—	9	12	no	—
47	C₃	—	9	2	no	—
48	C₃	—	9	1	no	—
49	C₃	—	9	1	no	—
50	C₃	C₁₉×#6910	1	4	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₉
prime radical	C₃⁴×C₁₉	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ C₃⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#6862	C₃	semidirect
8. #10624670	C₁₉	direct (N × H)
16. #6862	C₃×C₁₉	semidirect
39. C₁₉	#10624670	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×#6891	3
C₁₉×#6862	3
#10624670	19

Subgroups — C19×#10624670 #28352866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624670 #28352866