Subgroups — C₁₉⋊#10624562 #28353587

Order 13851.

2138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃²⋊(C₁₉⋊C₃)	C₃	1	12	yes	maximal, complemented
2	C₃²×C₁₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₁₉⋊C₃	C₃²	1	9	yes	—
4	C₃×C₃²⋊(C₁₉⋊C₃)	—	3	36	no	—
5	C₃×C₃²⋊(C₁₉⋊C₃)	—	3	108	no	—
6	C₃⁴×C₁₉	C₃²	1	4	yes	—
7	C₃×C₁₉×H(3,𝔽₃)	—	3	12	no	—
8	#10624562	—	19	1	no	maximal, Sylow
9	C₃³×C₁₉	—	3	12	no	—
10	C₃³×C₁₉	—	3	36	no	—
11	C₃³×C₁₉	H(3,𝔽₃)	1	12	yes	complemented
12	C₃³×C₁₉	C₃³	1	1	yes	characteristic
13	C₃²×C₁₉⋊C₃	—	3	72	no	—
14	C₃²×C₁₉⋊C₃	—	3	36	no	—
15	C₃²×C₁₉⋊C₃	H(3,𝔽₃)	1	27	yes	complemented
16	C₁₉×H(3,𝔽₃)	—	3	27	no	—
17	C₃²⋊(C₁₉⋊C₃)	—	3	324	no	—
18	C₃²×H(3,𝔽₃)	—	19	12	no	—
19	C₃²×H(3,𝔽₃)	C₁₉⋊C₃	1	1	yes	characteristic, complemented
20	C₃²×C₁₉	—	3	36	no	—
21	C₃²×C₁₉	—	3	12	no	—
22	C₃²×C₁₉	—	9	36	no	—
23	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	9	yes	—
24	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	4	yes	—
25	C₃×C₁₉⋊C₃	—	3	108	no	—
26	C₃×C₁₉⋊C₃	—	9	72	no	—
27	C₃×C₁₉⋊C₃	—	9	9	no	—
28	C₃⁴	—	19	9	no	—
29	C₃⁴	C₃×C₁₉⋊C₃	1	4	yes	—
30	C₃×H(3,𝔽₃)	—	3	12	no	—
31	C₃×H(3,𝔽₃)	—	57	108	no	—
32	C₃×H(3,𝔽₃)	—	57	36	no	—
33	C₃×C₁₉	—	9	12	no	—
34	C₃×C₁₉	C₃²⋊H(3,𝔽₃)	1	12	yes	—
35	C₃×C₁₉	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
36	C₁₉⋊C₃	—	9	27	no	—
37	C₃³	—	3	36	no	—
38	C₃³	—	3	12	no	—
39	C₃³	—	19	27	no	—
40	C₃³	—	57	72	no	—
41	C₃³	—	57	36	no	—
42	C₃³	C₃²⋊(C₁₉⋊C₃)	1	12	yes	complemented
43	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
44	H(3,𝔽₃)	—	3	27	no	—
45	H(3,𝔽₃)	—	57	324	no	—
46	C₁₉	#10624562	1	1	yes	characteristic, complemented, Sylow
47	C₃²	—	3	36	no	—
48	C₃²	—	3	12	no	—
49	C₃²	—	9	36	no	—
50	C₃²	—	57	108	no	—
51	C₃²	—	171	72	no	—
52	C₃²	—	171	9	no	—
53	C₃²	H(3,𝔽₃)×C₁₉⋊C₃	1	9	yes	—
54	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	4	yes	—
55	C₃	—	9	12	no	—
56	C₃	—	171	27	no	—
57	C₃	(C₃×C₁₉⋊C₃)⋊H(3,𝔽₃)	1	12	yes	—
58	C₃	#17987417	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₁₉⋊C₃
commutator, socle, cosocle	C₃³×C₁₉	C₃³
Fitting	C₃²×C₁₉×H(3,𝔽₃)	C₃
hypercenter	C₃²×H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	#10624562
LCS	G ▷ C₃³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃²⋊(C₁₉⋊C₃)	C₃	semidirect
2. C₃²×C₁₉×H(3,𝔽₃)	C₃	semidirect
11. C₃³×C₁₉	H(3,𝔽₃)	semidirect
15. C₃²×C₁₉⋊C₃	H(3,𝔽₃)	semidirect
19. C₃²×H(3,𝔽₃)	C₁₉⋊C₃	semidirect
42. C₃³	C₃²⋊(C₁₉⋊C₃)	semidirect
46. C₁₉	#10624562	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₃²⋊(C₁₉⋊C₃)	3
C₃²×C₁₉×H(3,𝔽₃)	3
#10624562	19

Subgroups — C19⋊#10624562 #28353587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#10624562 #28353587