Subgroups — C₇×#10624932 #19100341

Order 5103.

1062 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×H(5,𝔽₃)	C₃	1	3	yes	maximal, complemented
2	C₃×C₇×#737	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#6911	C₃	1	24	yes	maximal, complemented
4	C₃×C₇×#732	C₃	1	12	yes	maximal, complemented
5	#10624932	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₇×#737	—	3	9	no	—
7	C₃×C₇×3₋¹⁺²	C₃²	1	8	yes	complemented
8	C₃×C₇×H(3,𝔽₃)	—	3	27	no	—
9	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
10	C₃×C₇×H(3,𝔽₃)	C₃²	1	36	yes	complemented
11	C₃²×C₇×C₉	C₃²	1	4	yes	complemented
12	C₇×#732	C₃²	1	9	yes	complemented
13	C₇×#732	C₃²	1	72	yes	complemented
14	H(5,𝔽₃)	C₃×C₇	1	3	yes	complemented
15	C₃×#737	C₃×C₇	1	1	yes	characteristic, complemented
16	#6911	C₃×C₇	1	24	yes	complemented
17	C₃×#732	C₃×C₇	1	12	yes	complemented
18	C₃³×C₇	—	3	36	no	—
19	C₃³×C₇	C₃³	1	4	yes	—
20	C₇×3₋¹⁺²	—	3	24	no	—
21	C₇×H(3,𝔽₃)	—	3	72	no	—
22	C₇×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
23	C₇×H(3,𝔽₃)	C₃³	1	27	yes	—
24	C₃×C₇×C₉	—	3	12	no	—
25	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
26	C₃×C₇×C₉	C₃³	1	8	yes	—
27	#737	—	3	9	no	—
28	C₃×3₋¹⁺²	C₃²×C₇	1	8	yes	complemented
29	C₃×H(3,𝔽₃)	—	3	27	no	—
30	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
31	C₃×H(3,𝔽₃)	C₃²×C₇	1	36	yes	complemented
32	C₃²×C₉	C₃²×C₇	1	4	yes	complemented
33	#732	C₃²×C₇	1	9	yes	complemented
34	#732	C₃²×C₇	1	72	yes	complemented
35	C₃²×C₇	—	3	27	no	—
36	C₃²×C₇	—	9	4	no	—
37	C₃²×C₇	—	27	36	no	—
38	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
39	C₃²×C₇	C₃⁴	1	1	yes	characteristic
40	C₇×C₉	—	3	1	no	—
41	C₇×C₉	—	3	8	no	—
42	C₃³	—	3	36	no	—
43	C₃³	C₃³×C₇	1	4	yes	—
44	3₋¹⁺²	—	3	24	no	—
45	H(3,𝔽₃)	—	3	72	no	—
46	H(3,𝔽₃)	C₇×H(3,𝔽₃)	1	9	yes	—
47	H(3,𝔽₃)	C₃³×C₇	1	27	yes	—
48	C₃×C₉	—	3	12	no	—
49	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
50	C₃×C₉	C₃³×C₇	1	8	yes	—
51	C₃×C₇	—	3	1	no	—
52	C₃×C₇	—	3	12	no	—
53	C₃×C₇	—	9	27	no	—
54	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
55	C₃²	—	3	27	no	—
56	C₃²	—	9	4	no	—
57	C₃²	—	27	36	no	—
58	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
59	C₃²	C₃⁴×C₇	1	1	yes	characteristic
60	C₉	—	3	1	no	—
61	C₉	—	3	8	no	—
62	C₇	#10624932	1	1	yes	characteristic, direct product factor, Sylow
63	C₃	—	3	1	no	—
64	C₃	—	3	12	no	—
65	C₃	—	9	27	no	—
66	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₇	C₃²×H(3,𝔽₃)
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ C₃×C₇×H(3,𝔽₃) ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×H(5,𝔽₃)	C₃	semidirect
2. C₃×C₇×#737	C₃	semidirect
3. C₇×#6911	C₃	semidirect
4. C₃×C₇×#732	C₃	semidirect
5. #10624932	C₇	direct (N × H)
7. C₃×C₇×3₋¹⁺²	C₃²	semidirect
10. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
11. C₃²×C₇×C₉	C₃²	semidirect
12. C₇×#732	C₃²	semidirect
13. C₇×#732	C₃²	semidirect
14. H(5,𝔽₃)	C₃×C₇	semidirect
15. C₃×#737	C₃×C₇	semidirect
16. #6911	C₃×C₇	semidirect
17. C₃×#732	C₃×C₇	semidirect
28. C₃×3₋¹⁺²	C₃²×C₇	semidirect
31. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
32. C₃²×C₉	C₃²×C₇	semidirect
33. #732	C₃²×C₇	semidirect
34. #732	C₃²×C₇	semidirect
62. C₇	#10624932	direct (N × H)

Subgroups — C7×#10624932 #19100341

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624932 #19100341