Subgroups — C₃×#20264263 #34063373

Order 19197.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264263	C₃	1	27	yes	maximal, direct product factor
2	C₃×#14523840	C₃	1	2	yes	maximal, complemented
3	C₃×#14523839	C₃	1	3	yes	maximal, complemented
4	C₃×#14523838	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊(C₇₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₇₉⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃²×C₉×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₇₉⋊C₃	C₃²	1	3	yes	—
9	#14523840	C₃²	1	18	yes	complemented
10	#14523839	C₃²	1	27	yes	complemented
11	#14523838	C₃²	1	27	yes	complemented
12	C₃²⋊(C₇₉⋊C₃)	C₃²	1	9	yes	—
13	C₃×C₇₉⋊C₉	C₃²	1	6	yes	—
14	C₉×C₇₉⋊C₃	C₃²	1	27	yes	complemented
15	C₃³×C₇₉	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₇₉	C₃²	1	9	yes	complemented
20	C₃²×C₇₉	—	3	3	no	—
21	C₃²×C₇₉	C₃³	1	3	yes	—
22	C₃²×C₇₉	C₃³	1	1	yes	characteristic
23	C₃×C₇₉⋊C₃	—	3	9	no	—
24	C₃×C₇₉⋊C₃	C₃³	1	9	yes	—
25	C₉×C₇₉	C₃³	1	3	yes	—
26	C₉×C₇₉	C₃³	1	3	yes	—
27	C₉×C₇₉	C₃³	1	3	yes	—
28	C₇₉⋊C₉	C₃³	1	18	yes	—
29	C₃×#737	—	79	1	no	maximal, Sylow
30	C₃×C₇₉	—	3	3	no	—
31	C₃×C₇₉	#737	1	3	yes	complemented
32	C₃×C₇₉	C₃⁴	1	1	yes	characteristic
33	C₇₉⋊C₃	—	3	9	no	—
34	#737	—	79	27	no	—
35	C₃×3₋¹⁺²	—	79	2	no	—
36	C₃×3₋¹⁺²	—	79	3	no	—
37	C₃×3₋¹⁺²	—	79	3	no	—
38	C₃×H(3,𝔽₃)	—	79	1	no	—
39	C₃²×C₉	—	79	3	no	—
40	C₃²×C₉	C₇₉⋊C₃	1	1	yes	characteristic, complemented
41	C₇₉	C₃×#737	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	79	3	no	—
43	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	79	18	no	—
45	3₋¹⁺²	—	79	27	no	—
46	3₋¹⁺²	—	79	27	no	—
47	H(3,𝔽₃)	—	79	9	no	—
48	C₃×C₉	—	79	6	no	—
49	C₃×C₉	—	79	27	no	—
50	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₇₉⋊C₃	1	9	yes	complemented
54	C₃²	—	3	3	no	—
55	C₃²	—	79	9	no	—
56	C₃²	—	237	9	no	—
57	C₃²	C₃²×C₇₉⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
59	C₉	—	79	18	no	—
60	C₉	C₃²×C₇₉⋊C₃	1	3	yes	—
61	C₉	C₃²×C₇₉⋊C₃	1	3	yes	—
62	C₉	C₃²×C₇₉⋊C₃	1	3	yes	—
63	C₃	—	3	3	no	—
64	C₃	—	237	9	no	—
65	C₃	#20264263	1	3	yes	direct product factor
66	C₃	C₃³×C₇₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₇₉⋊C₃
commutator, cosocle	C₃×C₇₉	C₃⁴
Frattini	C₃	C₃³×C₇₉⋊C₃
Fitting	C₃²×C₉×C₇₉	C₃
socle	C₃²×C₇₉	C₃³
prime radical	C₃×C₃²⋊(C₇₉⋊C₃)	C₃
hypercenter	C₃²×C₉	C₇₉⋊C₃
hypocenter	C₇₉	C₃×#737
LCS	G ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #20264263	C₃	direct (N × H)
2. C₃×#14523840	C₃	semidirect
3. C₃×#14523839	C₃	semidirect
4. C₃×#14523838	C₃	semidirect
6. C₃×C₉×C₇₉⋊C₃	C₃	semidirect
7. C₃²×C₉×C₇₉	C₃	semidirect
9. #14523840	C₃²	semidirect
10. #14523839	C₃²	semidirect
11. #14523838	C₃²	semidirect
14. C₉×C₇₉⋊C₃	C₃²	semidirect
19. C₃×C₉×C₇₉	C₃²	semidirect
31. C₃×C₇₉	#737	semidirect
40. C₃²×C₉	C₇₉⋊C₃	semidirect
41. C₇₉	C₃×#737	semidirect
53. C₃×C₉	C₃×C₇₉⋊C₃	semidirect
65. C₃	#20264263	direct (N × H)

Maximal subgroups

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

subgroup	index
#20264263	3
C₃×#14523840	3
C₃×#14523839	3
C₃×#14523838	3
C₃×C₃²⋊(C₇₉⋊C₃)	3
C₃×C₉×C₇₉⋊C₃	3
C₃²×C₉×C₇₉	3
C₃×#737	79

Subgroups — C3×#20264263 #34063373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20264263 #34063373