Subgroups — #28353474

Order 13851.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987377	C₃	1	1	yes	maximal, characteristic, complemented
2	#17987374	C₃	1	1	yes	maximal, characteristic
3	C₉×#10587018	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#6880	C₃	1	1	yes	maximal, characteristic, complemented
5	#13095322	—	3	1	no	—
6	#13095320	—	3	1	no	—
7	C₃×#10587018	—	3	1	no	—
8	C₁₉×#733	—	3	1	no	—
9	C₉²×C₁₉	C₃²	1	1	yes	characteristic
10	#10624537	—	19	1	no	maximal, Sylow
11	C₁₉×3₋¹⁺²	—	9	1	no	—
12	C₃×C₉×C₁₉	—	3	1	no	—
13	C₃×C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃²⋊(C₁₉⋊C₃)	—	9	1	no	—
15	#10587025	—	9	1	no	—
16	#10587018	—	3	3	no	—
17	#6880	—	19	1	no	—
18	#6880	C₁₉⋊C₃	1	1	yes	characteristic, complemented
19	#6879	—	19	1	no	—
20	C₉×C₂₇	—	19	1	no	—
21	C₃²×C₁₉	#732	1	1	yes	characteristic
22	C₃×C₁₉⋊C₃	—	27	1	no	—
23	C₉×C₁₉	—	3	3	no	—
24	C₉×C₁₉	—	3	1	no	—
25	C₉×C₁₉	—	27	1	no	—
26	#4294	—	27	1	no	—
27	#733	—	3	1	no	—
28	#733	—	57	1	no	—
29	#732	—	57	1	no	—
30	C₃×C₂₇	—	57	1	no	—
31	C₉²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
32	C₃×C₁₉	—	3	1	no	—
33	C₃×C₁₉	#6879	1	1	yes	characteristic
34	C₁₉⋊C₃	—	81	1	no	—
35	3₋¹⁺²	—	9	1	no	—
36	3₋¹⁺²	—	171	1	no	—
37	H(3,𝔽₃)	—	171	1	no	—
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
40	C₂₇	—	57	3	no	—
41	C₁₉	#10624537	1	1	yes	characteristic, complemented, Sylow
42	C₃²	—	513	1	no	—
43	C₃²	#13095319	1	1	yes	characteristic
44	C₉	—	513	1	no	—
45	C₉	—	3	3	no	—
46	C₉	—	3	1	no	—
47	C₉	—	27	1	no	—
48	C₃	—	3	1	no	—
49	C₃	—	1539	1	no	—
50	C₃	#17987373	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987373
commutator, cosocle	C₉²×C₁₉	C₃²
Frattini	C₉²	C₃×C₁₉⋊C₃
Fitting	C₁₉×#6880	C₃
socle	C₃×C₁₉	#6879
prime radical	#17987374	C₃
hypercenter	#6880	C₁₉⋊C₃
hypocenter	C₁₉	#10624537
LCS	G ▷ C₉²×C₁₉ ▷ C₃×C₉×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉² ◁ #6880

Complements

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

N	H ≅ G/N	type
1. #17987377	C₃	semidirect
3. C₉×#10587018	C₃	semidirect
4. C₁₉×#6880	C₃	semidirect
18. #6880	C₁₉⋊C₃	semidirect
41. C₁₉	#10624537	semidirect

Maximal subgroups

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

subgroup	index
#17987377	3
#17987374	3
C₉×#10587018	3
C₁₉×#6880	3
#10624537	19