Subgroups — C₇×#10624910 #19100319

Order 5103.

740 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6893	C₃	1	9	yes	maximal, complemented
2	C₇×C₉⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
3	C₇×#6891	C₃	1	3	yes	maximal, complemented
4	C₇×C₃²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	#10624910	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
8	C₃×C₇×3₋¹⁺²	C₃²	1	18	yes	complemented
9	C₃×C₇×H(3,𝔽₃)	C₃²	1	9	yes	—
10	C₃×C₇×H(3,𝔽₃)	C₃²	1	3	yes	—
11	C₃²×C₇×C₉	C₃²	1	9	yes	complemented
12	C₇×C₃²⋊C₉	C₃²	1	18	yes	—
13	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
14	C₇×C₃²⋊C₉	C₃²	1	54	yes	complemented
15	#6893	C₃×C₇	1	9	yes	complemented
16	C₉⋊H(3,𝔽₃)	C₃×C₇	1	27	yes	complemented
17	#6891	C₃×C₇	1	3	yes	complemented
18	C₃²⋊H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
19	C₃³×C₇	—	9	1	no	—
20	C₃³×C₇	—	9	3	no	—
21	C₃³×C₇	C₃³	1	1	yes	characteristic
22	C₃³×C₇	C₃³	1	3	yes	—
23	C₃³×C₇	C₃³	1	9	yes	—
24	C₇×3₋¹⁺²	—	9	9	no	—
25	C₇×3₋¹⁺²	—	9	18	no	—
26	C₇×H(3,𝔽₃)	—	9	3	no	—
27	C₇×H(3,𝔽₃)	—	9	9	no	—
28	C₃×C₇×C₉	—	9	9	no	—
29	C₃×C₇×C₉	C₃³	1	27	yes	—
30	C₃⁴	C₃²×C₇	1	1	yes	characteristic
31	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
32	C₃×3₋¹⁺²	C₃²×C₇	1	18	yes	complemented
33	C₃×H(3,𝔽₃)	C₃²×C₇	1	9	yes	—
34	C₃×H(3,𝔽₃)	C₃²×C₇	1	3	yes	—
35	C₃²×C₉	C₃²×C₇	1	9	yes	complemented
36	C₃²⋊C₉	C₃²×C₇	1	18	yes	—
37	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
38	C₃²⋊C₉	C₃²×C₇	1	54	yes	complemented
39	C₃²×C₇	—	3	9	no	—
40	C₃²×C₇	—	3	1	no	—
41	C₃²×C₇	—	3	3	no	—
42	C₃²×C₇	—	3	3	no	—
43	C₃²×C₇	—	3	27	no	—
44	C₃²×C₇	—	3	3	no	—
45	C₃²×C₇	—	3	6	no	—
46	C₃²×C₇	—	9	9	no	—
47	C₃²×C₇	C₃⁴	1	1	yes	characteristic
48	C₇×C₉	—	3	27	no	—
49	C₃³	—	9	1	no	—
50	C₃³	—	9	3	no	—
51	C₃³	C₃³×C₇	1	1	yes	characteristic
52	C₃³	C₃³×C₇	1	3	yes	—
53	C₃³	C₃³×C₇	1	9	yes	—
54	3₋¹⁺²	—	9	9	no	—
55	3₋¹⁺²	—	9	18	no	—
56	H(3,𝔽₃)	—	9	3	no	—
57	H(3,𝔽₃)	—	9	9	no	—
58	C₃×C₉	—	9	9	no	—
59	C₃×C₉	C₃³×C₇	1	27	yes	—
60	C₃×C₇	—	9	9	no	—
61	C₃×C₇	—	9	1	no	—
62	C₃×C₇	—	9	3	no	—
63	C₃×C₇	H(5,𝔽₃)	1	1	yes	characteristic
64	C₃×C₇	3₋¹⁺⁴	1	3	yes	—
65	C₃²	—	3	9	no	—
66	C₃²	—	3	1	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	3	no	—
69	C₃²	—	3	27	no	—
70	C₃²	—	3	3	no	—
71	C₃²	—	3	6	no	—
72	C₃²	—	9	9	no	—
73	C₃²	C₃⁴×C₇	1	1	yes	characteristic
74	C₉	—	3	27	no	—
75	C₇	#10624910	1	1	yes	characteristic, direct product factor, Sylow
76	C₃	—	9	1	no	—
77	C₃	—	9	3	no	—
78	C₃	—	9	9	no	—
79	C₃	C₇×H(5,𝔽₃)	1	1	yes	characteristic
80	C₃	C₇×3₋¹⁺⁴	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₇×#6893	C₃	semidirect
2. C₇×C₉⋊H(3,𝔽₃)	C₃	semidirect
3. C₇×#6891	C₃	semidirect
5. #10624910	C₇	direct (N × H)
8. C₃×C₇×3₋¹⁺²	C₃²	semidirect
11. C₃²×C₇×C₉	C₃²	semidirect
14. C₇×C₃²⋊C₉	C₃²	semidirect
15. #6893	C₃×C₇	semidirect
16. C₉⋊H(3,𝔽₃)	C₃×C₇	semidirect
17. #6891	C₃×C₇	semidirect
32. C₃×3₋¹⁺²	C₃²×C₇	semidirect
35. C₃²×C₉	C₃²×C₇	semidirect
38. C₃²⋊C₉	C₃²×C₇	semidirect
75. C₇	#10624910	direct (N × H)

Subgroups — C7×#10624910 #19100319

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624910 #19100319