Subgroups — #28355716

Order 13851.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987358	C₃	1	9	yes	maximal, complemented
2	#17987341	C₃	1	3	yes	maximal
3	C₁₉×#6887	C₃	1	1	yes	maximal, characteristic
4	#13095312	C₃²	1	9	yes	—
5	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₁₉×C₉⋊C₉	—	3	1	no	—
7	C₁₉×C₉⋊C₉	C₃²	1	3	yes	—
8	C₁₉×C₃²⋊C₉	—	3	1	no	—
9	C₉²×C₁₉	—	3	1	no	—
10	#10624830	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	3₋¹⁺²	1	1	yes	characteristic
12	C₃×C₉×C₁₉	—	3	3	no	—
13	C₃×C₉×C₁₉	—	3	3	no	—
14	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉×C₁₉	3₋¹⁺²	1	1	yes	characteristic
16	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
17	#10587018	—	3	9	no	—
18	#6887	C₁₉⋊C₃	1	1	yes	characteristic
19	#6875	—	19	9	no	—
20	#6869	—	19	3	no	—
21	C₃²×C₁₉	—	3	1	no	—
22	C₃²×C₁₉	—	9	1	no	—
23	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
24	C₉×C₁₉	—	3	1	no	—
25	C₉×C₁₉	—	3	1	no	—
26	C₉×C₁₉	—	9	3	no	—
27	C₉×C₁₉	#737	1	3	yes	—
28	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
29	C₂₇⋊C₃	—	19	9	no	—
30	C₉⋊C₉	—	3	1	no	—
31	C₉⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	—
32	C₃²⋊C₉	—	3	1	no	—
33	C₉²	—	3	1	no	—
34	C₃×C₁₉	—	3	1	no	—
35	C₃×C₁₉	—	9	1	no	—
36	C₃×C₁₉	#6895	1	1	yes	characteristic
37	C₃³	#10587025	1	1	yes	characteristic
38	C₃×C₉	—	3	3	no	—
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	#10587025	1	1	yes	characteristic
41	C₃×C₉	#10587025	1	1	yes	characteristic
42	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
43	C₂₇	—	57	9	no	—
44	C₁₉	#10624830	1	1	yes	characteristic, complemented, Sylow
45	C₃²	—	3	1	no	—
46	C₃²	—	9	1	no	—
47	C₃²	C₃×#10587025	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	#13095332	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	C₃	#17987445	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987445
commutator, cosocle	C₃×C₉×C₁₉	C₃³
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#6887	C₃
socle	C₃×C₁₉	#6895
prime radical	C₃³×C₁₉	3₋¹⁺²
hypercenter	#6887	C₁₉⋊C₃
hypocenter	C₁₉	#10624830
LCS	G ▷ C₃×C₉×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. #17987358	C₃	semidirect
44. C₁₉	#10624830	semidirect

Maximal subgroups

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

subgroup	index
#17987358	3
#17987341	3
C₁₉×#6887	3
#10624830	19