Subgroups — C₂×C₃²×C₅²×D₇ #20263172

Order 6300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅²×D₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×C₅×D₇	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₃×C₅²×C₇	C₂×C₃	1	4	yes	complemented
7	C₃×C₅²×D₇	C₂×C₃	1	8	yes	direct product factor
8	C₂²×C₃²×C₅²	—	7	1	no	maximal, Hall
9	C₂×C₅²×D₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃²×C₅×C₇	C₂×C₅	1	6	yes	complemented
11	C₃²×C₅×D₇	C₂×C₅	1	12	yes	direct product factor
12	C₃×C₅²×C₇	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃²×C₅²	—	7	2	no	—
14	C₂×C₃²×C₅²	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₃×C₅×D₇	C₃×C₅	1	24	yes	direct product factor
16	C₂×C₅²×C₇	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₅²×D₇	C₂×C₃²	1	2	yes	direct product factor
18	C₃²×C₅×C₇	C₂²×C₅	1	6	yes	complemented
19	C₂²×C₃×C₅²	—	7	4	no	—
20	C₂×C₃²×D₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
21	C₃²×C₅²	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₇	C₂×C₃×C₅	1	24	yes	complemented
23	C₃×C₅×D₇	C₂×C₃×C₅	1	48	yes	direct product factor
24	C₂²×C₃²×C₅	—	7	6	no	—
25	C₅²×C₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅²	—	7	8	no	—
27	C₂×C₃×C₅²	C₃×D₇	1	4	yes	direct product factor
28	C₂×C₅×D₇	C₃²×C₅	1	6	yes	direct product factor
29	C₂×C₃²×C₇	C₂×C₅²	1	1	yes	characteristic, complemented
30	C₃²×D₇	C₂×C₅²	1	2	yes	direct product factor
31	C₃×C₅×C₇	C₂²×C₃×C₅	1	24	yes	complemented
32	C₂²×C₅²	—	7	1	no	Hall
33	C₂×C₃²×C₅	—	7	12	no	—
34	C₂×C₃²×C₅	C₅×D₇	1	6	yes	direct product factor
35	C₂×C₃×D₇	C₃×C₅²	1	4	yes	direct product factor
36	C₃×C₅²	C₂×C₃×D₇	1	4	yes	direct product factor
37	C₂×C₅×C₇	C₂×C₃²×C₅	1	6	yes	complemented
38	C₅×D₇	C₂×C₃²×C₅	1	12	yes	direct product factor
39	C₃²×C₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₃×C₅	—	7	24	no	—
41	C₂×C₅²	—	7	2	no	—
42	C₂×C₅²	C₃²×D₇	1	1	yes	characteristic, direct product factor
43	C₃²×C₅	C₂×C₅×D₇	1	6	yes	direct product factor
44	C₂×C₃×C₇	C₂×C₃×C₅²	1	4	yes	complemented
45	C₃×D₇	C₂×C₃×C₅²	1	8	yes	direct product factor
46	C₂²×C₃²	—	7	1	no	Hall
47	C₅×C₇	C₂²×C₃²×C₅	1	6	yes	complemented
48	C₂×C₃×C₅	—	7	48	no	—
49	C₂×C₃×C₅	C₃×C₅×D₇	1	24	yes	direct product factor
50	C₂×D₇	C₃²×C₅²	1	1	yes	characteristic, direct product factor, Hall
51	C₅²	C₂×C₃²×D₇	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₇	C₂²×C₃×C₅²	1	4	yes	complemented
53	C₂²×C₅	—	7	6	no	—
54	C₂×C₃²	—	7	2	no	—
55	C₂×C₃²	C₅²×D₇	1	1	yes	characteristic, direct product factor
56	C₃×C₅	C₂×C₃×C₅×D₇	1	24	yes	direct product factor
57	C₂×C₇	C₂×C₃²×C₅²	1	1	yes	characteristic, complemented
58	D₇	C₂×C₃²×C₅²	1	2	yes	direct product factor
59	C₂²×C₃	—	7	4	no	—
60	C₂×C₅	—	7	12	no	—
61	C₂×C₅	C₃²×C₅×D₇	1	6	yes	direct product factor
62	C₃²	C₂×C₅²×D₇	1	1	yes	characteristic, direct product factor, Sylow
63	C₇	C₂²×C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	7	8	no	—
65	C₂×C₃	C₃×C₅²×D₇	1	4	yes	direct product factor
66	C₅	C₂×C₃²×C₅×D₇	1	6	yes	direct product factor
67	C₂²	—	7	1	no	Sylow
68	C₃	C₂×C₃×C₅²×D₇	1	4	yes	direct product factor
69	C₂	—	7	2	no	—
70	C₂	C₃²×C₅²×D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅²	D₇
commutator, hypocenter	C₇	C₂²×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃²×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×D₇	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₇	C₂	semidirect
3. C₂×C₃×C₅²×D₇	C₃	direct (N × H)
4. C₃²×C₅²×C₇	C₂²	semidirect
5. C₂×C₃²×C₅×D₇	C₅	direct (N × H)
6. C₂×C₃×C₅²×C₇	C₂×C₃	semidirect
7. C₃×C₅²×D₇	C₂×C₃	direct (N × H)
9. C₂×C₅²×D₇	C₃²	direct (N × H)
10. C₂×C₃²×C₅×C₇	C₂×C₅	semidirect
11. C₃²×C₅×D₇	C₂×C₅	direct (N × H)
12. C₃×C₅²×C₇	C₂²×C₃	semidirect
14. C₂×C₃²×C₅²	D₇	direct (N × H)
15. C₂×C₃×C₅×D₇	C₃×C₅	direct (N × H)
16. C₂×C₅²×C₇	C₂×C₃²	semidirect
17. C₅²×D₇	C₂×C₃²	direct (N × H)
18. C₃²×C₅×C₇	C₂²×C₅	semidirect
20. C₂×C₃²×D₇	C₅²	direct (N × H)
21. C₃²×C₅²	C₂×D₇	direct (N × H)
22. C₂×C₃×C₅×C₇	C₂×C₃×C₅	semidirect
23. C₃×C₅×D₇	C₂×C₃×C₅	direct (N × H)
25. C₅²×C₇	C₂²×C₃²	semidirect
27. C₂×C₃×C₅²	C₃×D₇	direct (N × H)
28. C₂×C₅×D₇	C₃²×C₅	direct (N × H)
29. C₂×C₃²×C₇	C₂×C₅²	semidirect
30. C₃²×D₇	C₂×C₅²	direct (N × H)
31. C₃×C₅×C₇	C₂²×C₃×C₅	semidirect
34. C₂×C₃²×C₅	C₅×D₇	direct (N × H)
35. C₂×C₃×D₇	C₃×C₅²	direct (N × H)
36. C₃×C₅²	C₂×C₃×D₇	direct (N × H)
37. C₂×C₅×C₇	C₂×C₃²×C₅	semidirect
38. C₅×D₇	C₂×C₃²×C₅	direct (N × H)
39. C₃²×C₇	C₂²×C₅²	semidirect
42. C₂×C₅²	C₃²×D₇	direct (N × H)
43. C₃²×C₅	C₂×C₅×D₇	direct (N × H)
44. C₂×C₃×C₇	C₂×C₃×C₅²	semidirect
45. C₃×D₇	C₂×C₃×C₅²	direct (N × H)
47. C₅×C₇	C₂²×C₃²×C₅	semidirect
49. C₂×C₃×C₅	C₃×C₅×D₇	direct (N × H)
50. C₂×D₇	C₃²×C₅²	direct (N × H)
51. C₅²	C₂×C₃²×D₇	direct (N × H)
52. C₃×C₇	C₂²×C₃×C₅²	semidirect
55. C₂×C₃²	C₅²×D₇	direct (N × H)
56. C₃×C₅	C₂×C₃×C₅×D₇	direct (N × H)
57. C₂×C₇	C₂×C₃²×C₅²	semidirect
58. D₇	C₂×C₃²×C₅²	direct (N × H)
61. C₂×C₅	C₃²×C₅×D₇	direct (N × H)
62. C₃²	C₂×C₅²×D₇	direct (N × H)
63. C₇	C₂²×C₃²×C₅²	semidirect
65. C₂×C₃	C₃×C₅²×D₇	direct (N × H)
66. C₅	C₂×C₃²×C₅×D₇	direct (N × H)
68. C₃	C₂×C₃×C₅²×D₇	direct (N × H)
70. C₂	C₃²×C₅²×D₇	direct (N × H)

Subgroups — C2×C32×C52×D7 #20263172

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₅²×D₇ #20263172