Subgroups — C₃³×C₇×3₋¹⁺² #19100348

Order 5103.

7208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₇	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₇×3₋¹⁺²	C₃	1	117	yes	maximal, direct product factor
3	C₃³×C₇×C₉	C₃	1	3	yes	maximal, complemented
4	C₃³×3₋¹⁺²	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	—	3	27	no	—
6	C₃⁴×C₇	C₃²	1	39	yes	—
7	C₃⁴×C₇	C₃²	1	1	yes	characteristic
8	C₃×C₇×3₋¹⁺²	C₃²	1	1053	yes	direct product factor
9	C₃²×C₇×C₉	C₃²	1	117	yes	complemented
10	C₃⁵	C₃×C₇	1	1	yes	characteristic
11	C₃²×3₋¹⁺²	C₃×C₇	1	117	yes	direct product factor
12	C₃³×C₉	C₃×C₇	1	3	yes	complemented
13	C₃³×C₇	—	3	351	no	—
14	C₃³×C₇	3₋¹⁺²	1	27	yes	direct product factor
15	C₃³×C₇	C₃³	1	117	yes	—
16	C₃³×C₇	C₃³	1	13	yes	—
17	C₇×3₋¹⁺²	C₃³	1	729	yes	direct product factor
18	C₃×C₇×C₉	C₃³	1	351	yes	complemented
19	C₃⁴	—	3	27	no	—
20	C₃⁴	C₃²×C₇	1	39	yes	—
21	C₃⁴	C₃²×C₇	1	1	yes	characteristic
22	C₃×3₋¹⁺²	C₃²×C₇	1	1053	yes	direct product factor
23	C₃²×C₉	C₃²×C₇	1	117	yes	complemented
24	C₃²×C₇	—	3	351	no	—
25	C₃²×C₇	C₃×3₋¹⁺²	1	117	yes	direct product factor
26	C₃²×C₇	C₃⁴	1	27	yes	—
27	C₃²×C₇	C₃⁴	1	13	yes	—
28	C₇×C₉	C₃⁴	1	81	yes	complemented
29	C₃³	—	3	351	no	—
30	C₃³	C₇×3₋¹⁺²	1	27	yes	direct product factor
31	C₃³	C₃³×C₇	1	117	yes	—
32	C₃³	C₃³×C₇	1	13	yes	—
33	3₋¹⁺²	C₃³×C₇	1	729	yes	direct product factor
34	C₃×C₉	C₃³×C₇	1	351	yes	complemented
35	C₃×C₇	—	3	27	no	—
36	C₃×C₇	C₃²×3₋¹⁺²	1	39	yes	direct product factor
37	C₃×C₇	C₃⁵	1	1	yes	characteristic
38	C₃²	—	3	351	no	—
39	C₃²	C₃×C₇×3₋¹⁺²	1	117	yes	direct product factor
40	C₃²	C₃⁴×C₇	1	27	yes	—
41	C₃²	C₃⁴×C₇	1	13	yes	—
42	C₉	C₃⁴×C₇	1	81	yes	complemented
43	C₇	C₃³×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	3	27	no	—
45	C₃	C₃²×C₇×3₋¹⁺²	1	39	yes	direct product factor
46	C₃	C₃⁵×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃⁴×C₇	C₃²
commutator, Frattini	C₃	C₃⁵×C₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇×3₋¹⁺²	C₃	direct (N × H)
3. C₃³×C₇×C₉	C₃	semidirect
4. C₃³×3₋¹⁺²	C₇	direct (N × H)
8. C₃×C₇×3₋¹⁺²	C₃²	direct (N × H)
9. C₃²×C₇×C₉	C₃²	semidirect
11. C₃²×3₋¹⁺²	C₃×C₇	direct (N × H)
12. C₃³×C₉	C₃×C₇	semidirect
14. C₃³×C₇	3₋¹⁺²	direct (N × H)
17. C₇×3₋¹⁺²	C₃³	direct (N × H)
18. C₃×C₇×C₉	C₃³	semidirect
22. C₃×3₋¹⁺²	C₃²×C₇	direct (N × H)
23. C₃²×C₉	C₃²×C₇	semidirect
25. C₃²×C₇	C₃×3₋¹⁺²	direct (N × H)
28. C₇×C₉	C₃⁴	semidirect
30. C₃³	C₇×3₋¹⁺²	direct (N × H)
33. 3₋¹⁺²	C₃³×C₇	direct (N × H)
34. C₃×C₉	C₃³×C₇	semidirect
36. C₃×C₇	C₃²×3₋¹⁺²	direct (N × H)
39. C₃²	C₃×C₇×3₋¹⁺²	direct (N × H)
42. C₉	C₃⁴×C₇	semidirect
43. C₇	C₃³×3₋¹⁺²	direct (N × H)
45. C₃	C₃²×C₇×3₋¹⁺²	direct (N × H)

Subgroups — C33×C7×3−1+2 #19100348

Conjugacy classes of subgroups

Complements

Subgroups — C₃³×C₇×3₋¹⁺² #19100348