Subgroups — C₂×C₅²×C₃⋊D₂₁ #20263160

Order 6300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₂₁	—	3	4	no	maximal
4	C₃²×C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₃⋊D₂₁	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₃×C₅²×C₇	D₃	1	4	yes	complemented
7	C₅²×D₂₁	—	3	8	no	—
8	C₂×C₅²×C₃⋊D₃	—	7	1	no	maximal, Hall
9	C₂×C₅²×D₇	—	9	1	no	Hall
10	C₂×C₃²×C₅×C₇	C₂×C₅	1	6	yes	complemented
11	C₅×C₃⋊D₂₁	C₂×C₅	1	12	yes	direct product factor
12	C₃×C₅²×C₇	C₂×D₃	1	4	yes	complemented
13	C₂×C₃²×C₅²	D₇	1	1	yes	characteristic, complemented
14	C₅²×C₃⋊D₃	—	7	2	no	—
15	C₂×C₅×D₂₁	—	3	24	no	—
16	C₂×C₅²×C₇	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₅²×D₇	—	9	2	no	—
18	C₃²×C₅×C₇	C₂²×C₅	1	6	yes	complemented
19	C₂×C₅²×D₃	—	21	4	no	—
20	C₂×C₃⋊D₂₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
21	C₃²×C₅²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅×C₇	C₅×D₃	1	24	yes	complemented
23	C₅×D₂₁	—	3	48	no	—
24	C₂×C₅×C₃⋊D₃	—	7	6	no	—
25	C₅²×C₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅²	D₂₁	1	4	yes	complemented
27	C₅²×D₃	—	21	8	no	—
28	C₂×C₅×D₇	—	9	6	no	—
29	C₂×C₃²×C₇	C₂×C₅²	1	1	yes	characteristic, complemented
30	C₃⋊D₂₁	C₂×C₅²	1	2	yes	direct product factor
31	C₃×C₅×C₇	C₂×C₅×D₃	1	24	yes	complemented
32	C₂²×C₅²	—	63	1	no	Hall
33	C₂×C₃²×C₅	C₅×D₇	1	6	yes	complemented
34	C₅×C₃⋊D₃	—	7	12	no	—
35	C₂×D₂₁	—	3	4	no	—
36	C₃×C₅²	C₂×D₂₁	1	4	yes	complemented
37	C₂×C₅×C₇	C₅×C₃⋊D₃	1	6	yes	complemented
38	C₅×D₇	—	9	12	no	—
39	C₃²×C₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
40	C₂×C₅×D₃	—	21	24	no	—
41	C₂×C₅²	—	63	2	no	—
42	C₂×C₅²	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
43	C₃²×C₅	C₂×C₅×D₇	1	6	yes	complemented
44	C₂×C₃×C₇	C₅²×D₃	1	4	yes	complemented
45	D₂₁	—	3	8	no	—
46	C₂×C₃⋊D₃	—	7	1	no	Hall
47	C₅×C₇	C₂×C₅×C₃⋊D₃	1	6	yes	complemented
48	C₂×C₃×C₅	C₅×D₂₁	1	24	yes	complemented
49	C₅×D₃	—	21	48	no	—
50	C₂×D₇	—	9	1	no	Hall
51	C₅²	C₂×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₇	C₂×C₅²×D₃	1	4	yes	complemented
53	C₂²×C₅	—	63	6	no	—
54	C₂×C₃²	C₅²×D₇	1	1	yes	characteristic, complemented
55	C₃⋊D₃	—	7	2	no	—
56	C₃×C₅	C₂×C₅×D₂₁	1	24	yes	complemented
57	C₂×C₇	C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented
58	D₇	—	9	2	no	—
59	C₂×D₃	—	21	4	no	—
60	C₂×C₅	—	63	12	no	—
61	C₂×C₅	C₅×C₃⋊D₂₁	1	6	yes	direct product factor
62	C₃²	C₂×C₅²×D₇	1	1	yes	characteristic, complemented, Sylow
63	C₇	C₂×C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₅²×D₂₁	1	4	yes	complemented
65	D₃	—	21	8	no	—
66	C₅	C₂×C₅×C₃⋊D₂₁	1	6	yes	direct product factor
67	C₂²	—	63	1	no	Sylow
68	C₃	C₂×C₅²×D₂₁	1	4	yes	complemented
69	C₂	—	63	2	no	—
70	C₂	C₅²×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²	C₃⋊D₂₁
commutator, hypocenter	C₃²×C₇	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×C₃⋊D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₇	C₂	semidirect
4. C₃²×C₅²×C₇	C₂²	semidirect
5. C₂×C₅×C₃⋊D₂₁	C₅	direct (N × H)
6. C₂×C₃×C₅²×C₇	D₃	semidirect
10. C₂×C₃²×C₅×C₇	C₂×C₅	semidirect
11. C₅×C₃⋊D₂₁	C₂×C₅	direct (N × H)
12. C₃×C₅²×C₇	C₂×D₃	semidirect
13. C₂×C₃²×C₅²	D₇	semidirect
16. C₂×C₅²×C₇	C₃⋊D₃	semidirect
18. C₃²×C₅×C₇	C₂²×C₅	semidirect
20. C₂×C₃⋊D₂₁	C₅²	direct (N × H)
21. C₃²×C₅²	C₂×D₇	semidirect
22. C₂×C₃×C₅×C₇	C₅×D₃	semidirect
25. C₅²×C₇	C₂×C₃⋊D₃	semidirect
26. C₂×C₃×C₅²	D₂₁	semidirect
29. C₂×C₃²×C₇	C₂×C₅²	semidirect
30. C₃⋊D₂₁	C₂×C₅²	direct (N × H)
31. C₃×C₅×C₇	C₂×C₅×D₃	semidirect
33. C₂×C₃²×C₅	C₅×D₇	semidirect
36. C₃×C₅²	C₂×D₂₁	semidirect
37. C₂×C₅×C₇	C₅×C₃⋊D₃	semidirect
39. C₃²×C₇	C₂²×C₅²	semidirect
42. C₂×C₅²	C₃⋊D₂₁	direct (N × H)
43. C₃²×C₅	C₂×C₅×D₇	semidirect
44. C₂×C₃×C₇	C₅²×D₃	semidirect
47. C₅×C₇	C₂×C₅×C₃⋊D₃	semidirect
48. C₂×C₃×C₅	C₅×D₂₁	semidirect
51. C₅²	C₂×C₃⋊D₂₁	direct (N × H)
52. C₃×C₇	C₂×C₅²×D₃	semidirect
54. C₂×C₃²	C₅²×D₇	semidirect
56. C₃×C₅	C₂×C₅×D₂₁	semidirect
57. C₂×C₇	C₅²×C₃⋊D₃	semidirect
61. C₂×C₅	C₅×C₃⋊D₂₁	direct (N × H)
62. C₃²	C₂×C₅²×D₇	semidirect
63. C₇	C₂×C₅²×C₃⋊D₃	semidirect
64. C₂×C₃	C₅²×D₂₁	semidirect
66. C₅	C₂×C₅×C₃⋊D₂₁	direct (N × H)
68. C₃	C₂×C₅²×D₂₁	semidirect
70. C₂	C₅²×C₃⋊D₂₁	direct (N × H)

Subgroups — C2×C52×C3⋊D21 #20263160

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×C₃⋊D₂₁ #20263160