Subgroups — C₂×C₃×C₅×D₁₆₁ #23751656

Order 9660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₁₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₁₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₁₆₁	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×D₂₃	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×D₁₆₁	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₂₃	D₇	1	1	yes	characteristic, complemented
13	C₃×C₅×D₂₃	—	7	2	no	—
14	C₂×D₁₆₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇×C₂₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₂₃	—	7	1	no	Hall
17	C₂×C₃×C₅×D₇	—	23	1	no	maximal, Hall
18	C₃×C₅×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	D₁₆₁	C₂×C₃×C₅	1	2	yes	direct product factor
21	C₂×C₃×D₂₃	—	7	1	no	Hall
22	C₂×C₅×C₂₃	C₃×D₇	1	1	yes	characteristic, complemented
23	C₅×D₂₃	—	7	2	no	—
24	C₂×C₃×C₅×C₇	D₂₃	1	1	yes	characteristic, complemented
25	C₃×C₅×D₇	—	23	2	no	—
26	C₇×C₂₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×D₇	—	23	1	no	Hall
28	C₂×C₃×C₂₃	C₅×D₇	1	1	yes	characteristic, complemented
29	C₃×D₂₃	—	7	2	no	—
30	C₅×C₂₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
32	C₂×D₂₃	—	7	1	no	Hall
33	C₂×C₃×D₇	—	23	1	no	Hall
34	C₂×C₅×C₇	C₃×D₂₃	1	1	yes	characteristic, complemented
35	C₅×D₇	—	23	2	no	—
36	C₃×C₂₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃×C₅	—	161	1	no	Hall
38	C₂×C₂₃	C₃×C₅×D₇	1	1	yes	characteristic, complemented
39	D₂₃	—	7	2	no	—
40	C₂×C₃×C₇	C₅×D₂₃	1	1	yes	characteristic, complemented
41	C₃×D₇	—	23	2	no	—
42	C₅×C₇	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂×C₃×C₅	—	161	2	no	—
44	C₂×C₃×C₅	D₁₆₁	1	1	yes	characteristic, direct product factor
45	C₂×D₇	—	23	1	no	Hall
46	C₂₃	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₇	C₂×C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅	—	161	1	no	Hall
49	C₃×C₅	C₂×D₁₆₁	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₇	C₃×C₅×D₂₃	1	1	yes	characteristic, complemented
51	D₇	—	23	2	no	—
52	C₂²×C₃	—	161	1	no	Hall
53	C₂×C₅	—	161	2	no	—
54	C₂×C₅	C₃×D₁₆₁	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₃×C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	161	2	no	—
57	C₂×C₃	C₅×D₁₆₁	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	161	1	no	Sylow
60	C₃	C₂×C₅×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	161	2	no	—
62	C₂	C₃×C₅×D₁₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₁₆₁
commutator, cosocle, hypocenter	C₇×C₂₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₁₆₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₃	C₂	semidirect
3. C₂×C₅×D₁₆₁	C₃	direct (N × H)
4. C₃×C₅×C₇×C₂₃	C₂²	semidirect
5. C₂×C₃×D₁₆₁	C₅	direct (N × H)
6. C₂×C₅×C₇×C₂₃	C₂×C₃	semidirect
7. C₅×D₁₆₁	C₂×C₃	direct (N × H)
9. C₂×C₃×C₇×C₂₃	C₂×C₅	semidirect
10. C₃×D₁₆₁	C₂×C₅	direct (N × H)
11. C₅×C₇×C₂₃	C₂²×C₃	semidirect
12. C₂×C₃×C₅×C₂₃	D₇	semidirect
14. C₂×D₁₆₁	C₃×C₅	direct (N × H)
15. C₃×C₇×C₂₃	C₂²×C₅	semidirect
18. C₃×C₅×C₂₃	C₂×D₇	semidirect
19. C₂×C₇×C₂₃	C₂×C₃×C₅	semidirect
20. D₁₆₁	C₂×C₃×C₅	direct (N × H)
22. C₂×C₅×C₂₃	C₃×D₇	semidirect
24. C₂×C₃×C₅×C₇	D₂₃	semidirect
26. C₇×C₂₃	C₂²×C₃×C₅	semidirect
28. C₂×C₃×C₂₃	C₅×D₇	semidirect
30. C₅×C₂₃	C₂×C₃×D₇	semidirect
31. C₃×C₅×C₇	C₂×D₂₃	semidirect
34. C₂×C₅×C₇	C₃×D₂₃	semidirect
36. C₃×C₂₃	C₂×C₅×D₇	semidirect
38. C₂×C₂₃	C₃×C₅×D₇	semidirect
40. C₂×C₃×C₇	C₅×D₂₃	semidirect
42. C₅×C₇	C₂×C₃×D₂₃	semidirect
44. C₂×C₃×C₅	D₁₆₁	direct (N × H)
46. C₂₃	C₂×C₃×C₅×D₇	semidirect
47. C₃×C₇	C₂×C₅×D₂₃	semidirect
49. C₃×C₅	C₂×D₁₆₁	direct (N × H)
50. C₂×C₇	C₃×C₅×D₂₃	semidirect
54. C₂×C₅	C₃×D₁₆₁	direct (N × H)
55. C₇	C₂×C₃×C₅×D₂₃	semidirect
57. C₂×C₃	C₅×D₁₆₁	direct (N × H)
58. C₅	C₂×C₃×D₁₆₁	direct (N × H)
60. C₃	C₂×C₅×D₁₆₁	direct (N × H)
62. C₂	C₃×C₅×D₁₆₁	direct (N × H)

Subgroups — C2×C3×C5×D161 #23751656

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×D₁₆₁ #23751656