Subgroups — C₃×#20264264 #34063374

Order 19197.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264264	C₃	1	27	yes	maximal, direct product factor
2	C₃×#14523840	C₃	1	1	yes	maximal, characteristic, 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	C₃²×C₇₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×C₇₉⋊C₃	C₃	1	3	yes	maximal, complemented
8	C₃×3₋¹⁺²×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃²×C₇₉⋊C₃	C₃²	1	3	yes	—
10	#14523840	C₃²	1	9	yes	complemented
11	#14523839	C₃²	1	27	yes	complemented
12	#14523838	C₃²	1	27	yes	complemented
13	C₃²⋊(C₇₉⋊C₃)	C₃²	1	9	yes	—
14	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
15	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
16	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
17	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₇₉⋊C₉	C₃²	1	9	yes	complemented
19	C₉×C₇₉⋊C₃	C₃²	1	27	yes	complemented
20	C₃³×C₇₉	C₃²	1	1	yes	characteristic
21	3₋¹⁺²×C₇₉	C₃²	1	9	yes	complemented
22	C₃×C₉×C₇₉	C₃²	1	3	yes	—
23	C₃²×C₇₉	—	3	3	no	—
24	C₃²×C₇₉	C₃³	1	3	yes	—
25	C₃²×C₇₉	C₃³	1	1	yes	characteristic
26	C₃×C₇₉⋊C₃	—	3	9	no	—
27	C₃×C₇₉⋊C₃	C₃³	1	9	yes	—
28	C₉×C₇₉	C₃³	1	9	yes	—
29	C₇₉⋊C₉	C₃³	1	3	yes	—
30	C₇₉⋊C₉	C₃³	1	9	yes	—
31	C₇₉⋊C₉	C₃³	1	3	yes	—
32	C₇₉⋊C₉	C₃³	1	3	yes	—
33	C₃×#737	—	79	1	no	maximal, Sylow
34	C₃×C₇₉	—	3	3	no	—
35	C₃×C₇₉	#737	1	3	yes	complemented
36	C₃×C₇₉	C₃⁴	1	1	yes	characteristic
37	C₇₉⋊C₃	—	3	9	no	—
38	#737	—	79	27	no	—
39	C₃×3₋¹⁺²	—	79	1	no	—
40	C₃×3₋¹⁺²	—	79	3	no	—
41	C₃×3₋¹⁺²	—	79	3	no	—
42	C₃×3₋¹⁺²	C₇₉⋊C₃	1	1	yes	characteristic, complemented
43	C₃×H(3,𝔽₃)	—	79	1	no	—
44	C₃²×C₉	—	79	1	no	—
45	C₃²×C₉	—	79	3	no	—
46	C₇₉	C₃×#737	1	1	yes	characteristic, complemented, Sylow
47	C₃³	—	79	3	no	—
48	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
49	3₋¹⁺²	—	79	9	no	—
50	3₋¹⁺²	—	79	27	no	—
51	3₋¹⁺²	—	79	27	no	—
52	3₋¹⁺²	C₃×C₇₉⋊C₃	1	9	yes	complemented
53	H(3,𝔽₃)	—	79	9	no	—
54	C₃×C₉	—	79	9	no	—
55	C₃×C₉	—	79	1	no	—
56	C₃×C₉	—	79	3	no	—
57	C₃×C₉	—	79	1	no	—
58	C₃×C₉	—	79	1	no	—
59	C₃×C₉	—	79	27	no	—
60	C₃×C₉	C₃×C₇₉⋊C₃	1	3	yes	—
61	C₃²	—	3	3	no	—
62	C₃²	—	79	9	no	—
63	C₃²	—	237	9	no	—
64	C₃²	C₃²×C₇₉⋊C₃	1	3	yes	—
65	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
66	C₉	—	79	3	no	—
67	C₉	—	79	9	no	—
68	C₉	—	79	3	no	—
69	C₉	—	79	3	no	—
70	C₉	C₃²×C₇₉⋊C₃	1	9	yes	—
71	C₃	—	3	3	no	—
72	C₃	—	237	9	no	—
73	C₃	#20264264	1	3	yes	direct product factor
74	C₃	C₃³×C₇₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²×C₇₉⋊C₃
commutator, cosocle	C₃×C₇₉	C₃⁴
Frattini	C₃	C₃³×C₇₉⋊C₃
Fitting	C₃×3₋¹⁺²×C₇₉	C₃
socle	C₃²×C₇₉	C₃³
prime radical	C₃×C₃²⋊(C₇₉⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₇₉⋊C₃
hypocenter	C₇₉	C₃×#737
LCS	G ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #20264264	C₃	direct (N × H)
2. C₃×#14523840	C₃	semidirect
3. C₃×#14523839	C₃	semidirect
4. C₃×#14523838	C₃	semidirect
6. C₃²×C₇₉⋊C₉	C₃	semidirect
7. C₃×C₉×C₇₉⋊C₃	C₃	semidirect
8. C₃×3₋¹⁺²×C₇₉	C₃	semidirect
10. #14523840	C₃²	semidirect
11. #14523839	C₃²	semidirect
12. #14523838	C₃²	semidirect
18. C₃×C₇₉⋊C₉	C₃²	semidirect
19. C₉×C₇₉⋊C₃	C₃²	semidirect
21. 3₋¹⁺²×C₇₉	C₃²	semidirect
35. C₃×C₇₉	#737	semidirect
42. C₃×3₋¹⁺²	C₇₉⋊C₃	semidirect
46. C₇₉	C₃×#737	semidirect
52. 3₋¹⁺²	C₃×C₇₉⋊C₃	semidirect
73. C₃	#20264264	direct (N × H)

Maximal subgroups

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

subgroup	index
#20264264	3
C₃×#14523840	3
C₃×#14523839	3
C₃×#14523838	3
C₃×C₃²⋊(C₇₉⋊C₃)	3
C₃²×C₇₉⋊C₉	3
C₃×C₉×C₇₉⋊C₃	3
C₃×3₋¹⁺²×C₇₉	3
C₃×#737	79

Subgroups — C3×#20264264 #34063374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20264264 #34063374