Subgroups — C₃×C₁₉⋊C₃×C₈₁ #28355717

Order 13851.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×#13095301	C₃	1	2	yes	maximal, complemented
3	C₁₉⋊C₃×C₈₁	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₁₉×C₈₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
6	C₃×#10587018	C₉	1	2	yes	—
7	C₂₇×C₁₉⋊C₃	C₉	1	6	yes	—
8	C₂₇×C₁₉⋊C₃	C₃²	1	3	yes	—
9	#13095301	C₃²	1	6	yes	complemented
10	C₃×C₁₉×C₂₇	C₃²	1	1	yes	characteristic
11	C₁₉×C₈₁	C₃²	1	3	yes	complemented
12	C₃²×C₈₁	—	19	1	no	maximal, Sylow
13	C₃²×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
14	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃×#4294	C₂₇	1	2	yes	—
16	C₉×C₁₉⋊C₃	C₂₇	1	6	yes	—
17	C₉×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
18	C₁₉×C₂₇	C₃×C₉	1	2	yes	—
19	C₁₉×C₂₇	C₃³	1	1	yes	characteristic
20	#10587018	C₃×C₉	1	6	yes	—
21	C₃²×C₂₇	—	19	1	no	—
22	C₃×C₈₁	—	19	2	no	—
23	C₃×C₈₁	—	19	9	no	—
24	C₃×C₈₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
25	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
26	C₃×C₁₉⋊C₃	C₈₁	1	9	yes	direct product factor
27	C₃×C₁₉⋊C₃	C₃×C₂₇	1	3	yes	—
28	C₉×C₁₉	C₃×C₂₇	1	2	yes	—
29	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
30	#4294	C₃×C₂₇	1	6	yes	—
31	C₃²×C₉	—	19	1	no	—
32	C₃×C₂₇	—	19	2	no	—
33	C₃×C₂₇	—	19	6	no	—
34	C₃×C₂₇	—	19	3	no	—
35	C₃×C₂₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic
36	C₈₁	—	19	6	no	—
37	C₈₁	C₃×C₁₉⋊C₃	1	3	yes	direct product factor
38	C₃×C₁₉	C₃×C₈₁	1	3	yes	complemented
39	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
40	C₁₉⋊C₃	C₃×C₈₁	1	9	yes	direct product factor
41	C₃³	—	19	1	no	—
42	C₃×C₉	—	19	2	no	—
43	C₃×C₉	—	19	6	no	—
44	C₃×C₉	—	19	3	no	—
45	C₃×C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
46	C₂₇	—	19	6	no	—
47	C₂₇	C₉×C₁₉⋊C₃	1	2	yes	—
48	C₂₇	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
49	C₁₉	C₃²×C₈₁	1	1	yes	characteristic, complemented, Sylow
50	C₃²	—	19	9	no	—
51	C₃²	—	19	3	no	—
52	C₃²	C₂₇×C₁₉⋊C₃	1	1	yes	characteristic
53	C₉	—	19	6	no	—
54	C₉	C₂₇×C₁₉⋊C₃	1	2	yes	—
55	C₉	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
56	C₃	—	19	9	no	—
57	C₃	C₁₉⋊C₃×C₈₁	1	3	yes	direct product factor
58	C₃	C₃×C₂₇×C₁₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₈₁	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃²×C₈₁
Frattini	C₂₇	C₃²×C₁₉⋊C₃
Fitting	C₃×C₁₉×C₈₁	C₃
socle	C₃²×C₁₉	C₃×C₂₇
prime radical	C₃²×C₁₉⋊C₃	C₂₇
cosocle	C₁₉×C₂₇	C₃³
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₈₁

Complements

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

N	H ≅ G/N	type
2. C₃×#13095301	C₃	semidirect
3. C₁₉⋊C₃×C₈₁	C₃	direct (N × H)
4. C₃×C₁₉×C₈₁	C₃	semidirect
9. #13095301	C₃²	semidirect
11. C₁₉×C₈₁	C₃²	semidirect
24. C₃×C₈₁	C₁₉⋊C₃	direct (N × H)
26. C₃×C₁₉⋊C₃	C₈₁	direct (N × H)
37. C₈₁	C₃×C₁₉⋊C₃	direct (N × H)
38. C₃×C₁₉	C₃×C₈₁	semidirect
40. C₁₉⋊C₃	C₃×C₈₁	direct (N × H)
49. C₁₉	C₃²×C₈₁	semidirect
57. C₃	C₁₉⋊C₃×C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₂₇×C₁₉⋊C₃	3
C₃×#13095301	3
C₁₉⋊C₃×C₈₁	3
C₃×C₁₉×C₈₁	3
C₃²×C₈₁	19

Subgroups — C3×C19⋊C3×C81 #28355717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉⋊C₃×C₈₁ #28355717