Subgroups — C₃×C₇×C₉×H(3,𝔽₃) #19100268

Order 5103.

1688 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₇×C₉	C₃	1	4	yes	maximal, complemented
3	C₇×C₉×H(3,𝔽₃)	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₇×C₃²⋊C₉	C₃	1	8	yes	maximal, complemented
5	C₃×C₉×H(3,𝔽₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	4	yes	—
7	C₃×C₇×H(3,𝔽₃)	C₉	1	27	yes	direct product factor
8	C₃×C₇×H(3,𝔽₃)	C₃²	1	9	yes	—
9	C₃²×C₇×C₉	—	3	36	no	—
10	C₃²×C₇×C₉	C₃²	1	8	yes	—
11	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
12	C₃²×C₇×C₉	C₃²	1	36	yes	complemented
13	C₇×C₃²⋊C₉	C₃²	1	72	yes	complemented
14	C₃²×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
15	C₃³×C₉	C₃×C₇	1	4	yes	complemented
16	C₉×H(3,𝔽₃)	C₃×C₇	1	27	yes	direct product factor
17	C₃×C₃²⋊C₉	C₃×C₇	1	8	yes	complemented
18	C₃³×C₇	—	3	12	no	—
19	C₃³×C₇	—	3	24	no	—
20	C₃³×C₇	C₃×C₉	1	36	yes	complemented
21	C₃³×C₇	C₃³	1	12	yes	—
22	C₃³×C₇	C₃³	1	1	yes	characteristic
23	C₇×H(3,𝔽₃)	C₃×C₉	1	81	yes	direct product factor
24	C₃×C₇×C₉	—	3	24	no	—
25	C₃×C₇×C₉	—	3	108	no	—
26	C₃×C₇×C₉	H(3,𝔽₃)	1	9	yes	direct product factor
27	C₃×C₇×C₉	C₃³	1	24	yes	—
28	C₃×C₇×C₉	C₃³	1	3	yes	—
29	C₃⁴	C₃²×C₇	1	4	yes	—
30	C₃×H(3,𝔽₃)	C₇×C₉	1	27	yes	direct product factor
31	C₃×H(3,𝔽₃)	C₃²×C₇	1	9	yes	—
32	C₃²×C₉	—	3	36	no	—
33	C₃²×C₉	C₃²×C₇	1	8	yes	—
34	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
35	C₃²×C₉	C₃²×C₇	1	36	yes	complemented
36	C₃²⋊C₉	C₃²×C₇	1	72	yes	complemented
37	C₃²×C₇	—	3	12	no	—
38	C₃²×C₇	—	3	24	no	—
39	C₃²×C₇	—	3	108	no	—
40	C₃²×C₇	C₃²×C₉	1	3	yes	—
41	C₃²×C₇	C₃²×C₉	1	36	yes	complemented
42	C₃²×C₇	C₃×H(3,𝔽₃)	1	3	yes	—
43	C₃²×C₇	#737	1	6	yes	—
44	C₃²×C₇	C₃⁴	1	1	yes	characteristic
45	C₇×C₉	—	3	24	no	—
46	C₇×C₉	C₃×H(3,𝔽₃)	1	9	yes	direct product factor
47	C₃³	—	3	12	no	—
48	C₃³	—	3	24	no	—
49	C₃³	C₃×C₇×C₉	1	36	yes	complemented
50	C₃³	C₃³×C₇	1	12	yes	—
51	C₃³	C₃³×C₇	1	1	yes	characteristic
52	H(3,𝔽₃)	C₃×C₇×C₉	1	81	yes	direct product factor
53	C₃×C₉	—	3	24	no	—
54	C₃×C₉	—	3	108	no	—
55	C₃×C₉	C₇×H(3,𝔽₃)	1	9	yes	direct product factor
56	C₃×C₉	C₃³×C₇	1	24	yes	—
57	C₃×C₉	C₃³×C₇	1	3	yes	—
58	C₃×C₇	—	3	36	no	—
59	C₃×C₇	C₉×H(3,𝔽₃)	1	9	yes	direct product factor
60	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
61	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
62	C₃×C₇	C₃×#737	1	2	yes	—
63	C₃²	—	3	108	no	—
64	C₃²	—	3	12	no	—
65	C₃²	—	3	24	no	—
66	C₃²	C₃²×C₇×C₉	1	3	yes	—
67	C₃²	C₃²×C₇×C₉	1	36	yes	complemented
68	C₃²	C₃×C₇×H(3,𝔽₃)	1	3	yes	—
69	C₃²	C₇×#737	1	6	yes	—
70	C₃²	C₃⁴×C₇	1	1	yes	characteristic
71	C₉	—	3	24	no	—
72	C₉	C₃×C₇×H(3,𝔽₃)	1	9	yes	direct product factor
73	C₇	C₃×C₉×H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
74	C₃	—	3	36	no	—
75	C₃	C₇×C₉×H(3,𝔽₃)	1	9	yes	direct product factor
76	C₃	C₃³×C₇×C₉	1	1	yes	characteristic
77	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic
78	C₃	C₃×C₇×#737	1	2	yes	—

	subgroup	G/H
center	C₃²×C₇×C₉	C₃²
commutator	C₃	C₃³×C₇×C₉
Frattini	C₃²	C₃⁴×C₇
socle	C₃³×C₇	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₇×C₉	C₃	semidirect
3. C₇×C₉×H(3,𝔽₃)	C₃	direct (N × H)
4. C₃×C₇×C₃²⋊C₉	C₃	semidirect
5. C₃×C₉×H(3,𝔽₃)	C₇	direct (N × H)
7. C₃×C₇×H(3,𝔽₃)	C₉	direct (N × H)
12. C₃²×C₇×C₉	C₃²	semidirect
13. C₇×C₃²⋊C₉	C₃²	semidirect
15. C₃³×C₉	C₃×C₇	semidirect
16. C₉×H(3,𝔽₃)	C₃×C₇	direct (N × H)
17. C₃×C₃²⋊C₉	C₃×C₇	semidirect
20. C₃³×C₇	C₃×C₉	semidirect
23. C₇×H(3,𝔽₃)	C₃×C₉	direct (N × H)
26. C₃×C₇×C₉	H(3,𝔽₃)	direct (N × H)
30. C₃×H(3,𝔽₃)	C₇×C₉	direct (N × H)
35. C₃²×C₉	C₃²×C₇	semidirect
36. C₃²⋊C₉	C₃²×C₇	semidirect
41. C₃²×C₇	C₃²×C₉	semidirect
46. C₇×C₉	C₃×H(3,𝔽₃)	direct (N × H)
49. C₃³	C₃×C₇×C₉	semidirect
52. H(3,𝔽₃)	C₃×C₇×C₉	direct (N × H)
55. C₃×C₉	C₇×H(3,𝔽₃)	direct (N × H)
59. C₃×C₇	C₉×H(3,𝔽₃)	direct (N × H)
67. C₃²	C₃²×C₇×C₉	semidirect
72. C₉	C₃×C₇×H(3,𝔽₃)	direct (N × H)
73. C₇	C₃×C₉×H(3,𝔽₃)	direct (N × H)
75. C₃	C₇×C₉×H(3,𝔽₃)	direct (N × H)

Subgroups — C3×C7×C9×H(3,𝔽3) #19100268

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×C₉×H(3,𝔽₃) #19100268