Subgroups — C₃×C₇×#6895 #19100280

Order 5103.

836 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
2	C₇×#6895	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₇×C₉⋊C₉	C₃	1	9	yes	maximal, complemented
4	C₃×C₇×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃×#6895	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃²×C₇×C₉	—	3	9	no	—
8	C₃²×C₇×C₉	C₃²	1	9	yes	—
9	C₃²×C₇×C₉	C₃²	1	9	yes	—
10	C₃²×C₇×C₉	C₃²	1	3	yes	—
11	C₇×C₉⋊C₉	C₃²	1	81	yes	complemented
12	C₇×C₃²⋊C₉	C₃²	1	27	yes	—
13	C₃³×C₉	C₃×C₇	1	1	yes	characteristic
14	#6895	C₃×C₇	1	27	yes	direct product factor
15	C₃×C₉⋊C₉	C₃×C₇	1	9	yes	complemented
16	C₃×C₃²⋊C₉	C₃×C₇	1	3	yes	—
17	C₃³×C₇	—	3	9	no	—
18	C₃³×C₇	3₋¹⁺²	1	9	yes	—
19	C₃³×C₇	C₃³	1	3	yes	—
20	C₃³×C₇	C₃³	1	1	yes	characteristic
21	C₃×C₇×C₉	—	3	27	no	—
22	C₃×C₇×C₉	—	3	9	no	—
23	C₃×C₇×C₉	—	3	27	no	—
24	C₃×C₇×C₉	C₃³	1	27	yes	—
25	C₃×C₇×C₉	C₃³	1	9	yes	—
26	C₃⁴	C₃²×C₇	1	1	yes	characteristic
27	C₃²×C₉	—	3	9	no	—
28	C₃²×C₉	C₃²×C₇	1	3	yes	—
29	C₃²×C₉	C₃²×C₇	1	9	yes	—
30	C₃²×C₉	C₃²×C₇	1	9	yes	—
31	C₉⋊C₉	C₃²×C₇	1	81	yes	complemented
32	C₃²⋊C₉	C₃²×C₇	1	27	yes	—
33	C₃²×C₇	—	3	9	no	—
34	C₃²×C₇	—	3	27	no	—
35	C₃²×C₇	C₃×3₋¹⁺²	1	9	yes	—
36	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
37	C₃²×C₇	#737	1	9	yes	—
38	C₃²×C₇	C₃⁴	1	1	yes	characteristic
39	C₇×C₉	—	3	9	no	—
40	C₇×C₉	—	3	27	no	—
41	C₃³	—	3	9	no	—
42	C₃³	C₇×3₋¹⁺²	1	9	yes	—
43	C₃³	C₃³×C₇	1	3	yes	—
44	C₃³	C₃³×C₇	1	1	yes	characteristic
45	C₃×C₉	—	3	27	no	—
46	C₃×C₉	—	3	9	no	—
47	C₃×C₉	—	3	27	no	—
48	C₃×C₉	C₃³×C₇	1	27	yes	—
49	C₃×C₉	C₃³×C₇	1	9	yes	—
50	C₃×C₇	—	3	9	no	—
51	C₃×C₇	#6895	1	9	yes	direct product factor
52	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
53	C₃×C₇	C₃×#737	1	3	yes	—
54	C₃²	—	3	27	no	—
55	C₃²	—	3	9	no	—
56	C₃²	C₃×C₇×3₋¹⁺²	1	9	yes	—
57	C₃²	C₃×C₇×3₋¹⁺²	1	3	yes	—
58	C₃²	C₇×#737	1	9	yes	—
59	C₃²	C₃⁴×C₇	1	1	yes	characteristic
60	C₉	—	3	9	no	—
61	C₉	—	3	27	no	—
62	C₇	C₃×#6895	1	1	yes	characteristic, direct product factor, Sylow
63	C₃	—	3	9	no	—
64	C₃	C₇×#6895	1	9	yes	direct product factor
65	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
66	C₃	C₃×C₇×#737	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×#6895	C₃	direct (N × H)
3. C₃×C₇×C₉⋊C₉	C₃	semidirect
5. C₃×#6895	C₇	direct (N × H)
11. C₇×C₉⋊C₉	C₃²	semidirect
14. #6895	C₃×C₇	direct (N × H)
15. C₃×C₉⋊C₉	C₃×C₇	semidirect
31. C₉⋊C₉	C₃²×C₇	semidirect
51. C₃×C₇	#6895	direct (N × H)
62. C₇	C₃×#6895	direct (N × H)
64. C₃	C₇×#6895	direct (N × H)

Subgroups — C3×C7×#6895 #19100280

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6895 #19100280