Subgroups — C₁₉⋊C₃×C₈₁⋊C₃ #28355719

Order 13851.

164 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	#17987367	C₃	1	2	yes	maximal, complemented
3	#17987366	C₃	1	3	yes	maximal, complemented
4	#17987365	C₃	1	3	yes	maximal, complemented
5	C₁₉⋊C₃×C₈₁	C₃	1	3	yes	maximal, complemented
6	C₁₉×C₈₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
8	C₃×#10587018	C₉	1	2	yes	—
9	C₂₇×C₁₉⋊C₃	C₉	1	2	yes	—
10	C₂₇×C₁₉⋊C₃	C₉	1	2	yes	—
11	C₂₇×C₁₉⋊C₃	C₉	1	2	yes	—
12	C₂₇×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
13	C₂₇×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
14	C₂₇×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
15	#13095301	C₃²	1	6	yes	complemented
16	C₃×C₁₉×C₂₇	C₃²	1	1	yes	characteristic
17	C₁₉×C₈₁	C₃²	1	3	yes	complemented
18	C₃×C₈₁⋊C₃	—	19	1	no	maximal, Sylow
19	C₃²×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
20	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
21	C₃×#4294	C₂₇	1	2	yes	—
22	C₉×C₁₉⋊C₃	C₂₇	1	2	yes	—
23	C₉×C₁₉⋊C₃	C₂₇	1	2	yes	—
24	C₉×C₁₉⋊C₃	C₂₇	1	2	yes	—
25	C₉×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
26	C₉×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
27	C₉×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
28	C₁₉×C₂₇	C₃×C₉	1	2	yes	—
29	C₁₉×C₂₇	C₃³	1	1	yes	characteristic
30	#10587018	C₃×C₉	1	2	yes	—
31	#10587018	C₃×C₉	1	2	yes	—
32	#10587018	C₃×C₉	1	2	yes	—
33	C₃²×C₂₇	—	19	1	no	—
34	C₈₁⋊C₃	—	19	2	no	—
35	C₈₁⋊C₃	—	19	3	no	—
36	C₈₁⋊C₃	—	19	3	no	—
37	C₈₁⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
38	C₃×C₈₁	—	19	3	no	—
39	C₃²×C₁₉	C₃×C₂₇	1	1	yes	characteristic
40	C₃×C₁₉⋊C₃	—	3	3	no	—
41	C₃×C₁₉⋊C₃	C₃×C₂₇	1	1	yes	characteristic
42	C₃×C₁₉⋊C₃	C₃×C₂₇	1	1	yes	characteristic
43	C₃×C₁₉⋊C₃	C₃×C₂₇	1	1	yes	characteristic
44	C₉×C₁₉	C₃×C₂₇	1	2	yes	—
45	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
46	#4294	C₃×C₂₇	1	2	yes	—
47	#4294	C₃×C₂₇	1	2	yes	—
48	#4294	C₃×C₂₇	1	2	yes	—
49	C₃²×C₉	—	19	1	no	—
50	C₃×C₂₇	—	19	2	no	—
51	C₃×C₂₇	—	19	2	no	—
52	C₃×C₂₇	—	19	2	no	—
53	C₃×C₂₇	—	19	2	no	—
54	C₃×C₂₇	—	19	1	no	—
55	C₃×C₂₇	—	19	1	no	—
56	C₃×C₂₇	—	19	1	no	—
57	C₃×C₂₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic
58	C₈₁	—	19	6	no	—
59	C₈₁	C₃×C₁₉⋊C₃	1	3	yes	complemented
60	C₃×C₁₉	—	3	1	no	—
61	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
62	C₁₉⋊C₃	—	3	1	no	—
63	C₁₉⋊C₃	—	3	1	no	—
64	C₁₉⋊C₃	C₈₁⋊C₃	1	3	yes	direct product factor
65	C₃³	—	19	1	no	—
66	C₃×C₉	—	19	2	no	—
67	C₃×C₉	—	19	2	no	—
68	C₃×C₉	—	19	2	no	—
69	C₃×C₉	—	19	2	no	—
70	C₃×C₉	—	19	1	no	—
71	C₃×C₉	—	19	1	no	—
72	C₃×C₉	—	19	1	no	—
73	C₃×C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
74	C₂₇	—	19	2	no	—
75	C₂₇	—	19	2	no	—
76	C₂₇	—	19	2	no	—
77	C₂₇	C₉×C₁₉⋊C₃	1	2	yes	—
78	C₂₇	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
79	C₁₉	C₃×C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
80	C₃²	—	19	1	no	—
81	C₃²	—	19	1	no	—
82	C₃²	—	19	1	no	—
83	C₃²	—	57	3	no	—
84	C₃²	C₂₇×C₁₉⋊C₃	1	1	yes	characteristic
85	C₉	—	19	2	no	—
86	C₉	—	19	2	no	—
87	C₉	—	19	2	no	—
88	C₉	C₂₇×C₁₉⋊C₃	1	2	yes	—
89	C₉	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
90	C₃	—	3	1	no	—
91	C₃	—	19	3	no	—
92	C₃	—	57	1	no	—
93	C₃	—	57	1	no	—
94	C₃	C₃×C₂₇×C₁₉⋊C₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #17987367	C₃	semidirect
3. #17987366	C₃	semidirect
4. #17987365	C₃	semidirect
5. C₁₉⋊C₃×C₈₁	C₃	semidirect
6. C₁₉×C₈₁⋊C₃	C₃	semidirect
15. #13095301	C₃²	semidirect
17. C₁₉×C₈₁	C₃²	semidirect
37. C₈₁⋊C₃	C₁₉⋊C₃	direct (N × H)
59. C₈₁	C₃×C₁₉⋊C₃	semidirect
64. C₁₉⋊C₃	C₈₁⋊C₃	direct (N × H)
79. C₁₉	C₃×C₈₁⋊C₃	semidirect

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
#17987367	3
#17987366	3
#17987365	3
C₁₉⋊C₃×C₈₁	3
C₁₉×C₈₁⋊C₃	3
C₃×C₈₁⋊C₃	19

Subgroups — C19⋊C3×C81⋊C3 #28355719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊C₃×C₈₁⋊C₃ #28355719