Subgroups — (C₁₉⋊C₃)⋊(C₂₇⋊C₃) #17987595

Order 4617.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095344	C₃	1	3	yes	maximal, complemented
2	#13095343	C₃	1	3	yes	maximal, complemented
3	#13095342	C₃	1	3	yes	maximal, complemented
4	(C₁₉⋊C₃)⋊C₂₇	C₃	1	3	yes	maximal, complemented
5	C₃×C₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
6	C₃²×C₁₉⋊C₃	C₉	1	1	yes	characteristic
7	C₃×C₉×C₁₉	C₉	1	1	yes	characteristic
8	C₃×#4294	C₉	1	1	yes	characteristic
9	C₃×#4294	C₃²	1	1	yes	characteristic
10	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
11	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
12	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
13	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
14	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
15	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
16	C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
17	C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
18	C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
19	#10587020	C₃²	1	9	yes	complemented
20	C₃×C₂₇⋊C₃	—	19	1	no	maximal, Sylow
21	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
22	C₃×C₁₉⋊C₃	—	3	3	no	—
23	C₃×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
24	C₃×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
25	C₃×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
26	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
27	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
28	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
29	#4294	C₃×C₉	1	1	yes	characteristic
30	#4294	C₃×C₉	1	1	yes	characteristic
31	#4294	C₃×C₉	1	1	yes	characteristic
32	#4294	C₃×C₉	1	1	yes	characteristic
33	#4294	C₃×C₉	1	1	yes	characteristic
34	#4294	C₃³	1	1	yes	characteristic
35	C₃²×C₉	—	19	1	no	—
36	C₂₇⋊C₃	—	19	3	no	—
37	C₂₇⋊C₃	—	19	3	no	—
38	C₂₇⋊C₃	—	19	3	no	—
39	C₃×C₂₇	—	19	3	no	—
40	C₃×C₁₉	—	3	1	no	—
41	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
42	C₁₉⋊C₃	—	3	1	no	—
43	C₁₉⋊C₃	—	3	1	no	—
44	C₁₉⋊C₃	C₂₇⋊C₃	1	3	yes	complemented
45	C₃³	—	19	1	no	—
46	C₃×C₉	—	19	1	no	—
47	C₃×C₉	—	19	1	no	—
48	C₃×C₉	—	19	1	no	—
49	C₃×C₉	—	19	1	no	—
50	C₃×C₉	—	19	1	no	—
51	C₃×C₉	—	19	1	no	—
52	C₃×C₉	—	19	1	no	—
53	C₃×C₉	—	19	1	no	—
54	C₃×C₉	—	19	1	no	—
55	C₃×C₉	—	19	1	no	—
56	C₃×C₉	—	19	1	no	—
57	C₃×C₉	#4296	1	1	yes	characteristic
58	C₂₇	—	19	9	no	—
59	C₁₉	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃²	—	19	1	no	—
61	C₃²	—	19	1	no	—
62	C₃²	—	19	1	no	—
63	C₃²	—	57	3	no	—
64	C₃²	C₃×#4296	1	1	yes	characteristic
65	C₉	—	19	1	no	—
66	C₉	—	19	1	no	—
67	C₉	—	19	1	no	—
68	C₉	—	19	1	no	—
69	C₉	—	19	1	no	—
70	C₉	—	19	1	no	—
71	C₉	C₃×#4296	1	1	yes	characteristic
72	C₉	C₃×#4296	1	1	yes	characteristic
73	C₉	C₃×#4296	1	1	yes	characteristic
74	C₃	—	3	1	no	—
75	C₃	—	19	3	no	—
76	C₃	—	57	1	no	—
77	C₃	—	57	1	no	—
78	C₃	C₃²×#4296	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃×#4296
commutator, socle	C₃×C₁₉	C₃²×C₉
Frattini	C₃	C₃²×#4296
Fitting	C₃×C₉×C₁₉	C₉
prime radical	C₃²×C₁₉⋊C₃	C₉
cosocle	#4294	C₃³
hypercenter	C₃×C₉	#4296
hypocenter	C₁₉	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
1. #13095344	C₃	semidirect
2. #13095343	C₃	semidirect
3. #13095342	C₃	semidirect
4. (C₁₉⋊C₃)⋊C₂₇	C₃	semidirect
19. #10587020	C₃²	semidirect
44. C₁₉⋊C₃	C₂₇⋊C₃	semidirect
59. C₁₉	C₃×C₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#13095344	3
#13095343	3
#13095342	3
(C₁₉⋊C₃)⋊C₂₇	3
C₃×C₉×C₁₉⋊C₃	3
C₃×C₂₇⋊C₃	19

Subgroups — (C19⋊C3)⋊(C27⋊C3) #17987595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₁₉⋊C₃)⋊(C₂₇⋊C₃) #17987595