Subgroups — C₂×C₅²×D₃×C₃₁ #22604940

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₃×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅²×C₃₁	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₃×C₃₁	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₅²×C₃₁	—	3	2	no	—
7	C₂×C₅²×C₃₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₃×C₅×C₃₁	C₂×C₅	1	6	yes	complemented
9	C₅×D₃×C₃₁	C₂×C₅	1	12	yes	direct product factor
10	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₅×C₃₁	—	3	6	no	—
12	C₃×C₅×C₃₁	C₂²×C₅	1	6	yes	complemented
13	C₂×D₃×C₃₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₃₁	—	3	12	no	—
15	C₂×C₅×C₃₁	C₅×D₃	1	6	yes	direct product factor
16	C₂×C₅²×D₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
18	D₃×C₃₁	C₂×C₅²	1	2	yes	direct product factor
19	C₅×C₃₁	C₂×C₅×D₃	1	6	yes	direct product factor
20	C₂×C₃×C₅²	C₂×C₃₁	1	1	yes	characteristic, complemented
21	C₅²×D₃	C₂×C₃₁	1	2	yes	direct product factor
22	C₂²×C₃₁	—	3	1	no	Hall
23	C₂²×C₅²	—	3	1	no	Hall
24	C₃×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅²	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃₁	—	3	2	no	—
27	C₂×C₃₁	C₅²×D₃	1	1	yes	characteristic, direct product factor
28	C₂×C₅×D₃	C₅×C₃₁	1	6	yes	direct product factor
29	C₂×C₅²	—	3	2	no	—
30	C₂×C₅²	D₃×C₃₁	1	1	yes	characteristic, direct product factor
31	C₃₁	C₂×C₅²×D₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₅	C₂×C₅×C₃₁	1	6	yes	complemented
33	C₅×D₃	C₂×C₅×C₃₁	1	12	yes	direct product factor
34	C₅²	C₂×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²×C₅	—	3	6	no	—
36	C₃×C₅	C₂²×C₅×C₃₁	1	6	yes	complemented
37	C₂×D₃	C₅²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₅	—	3	12	no	—
39	C₂×C₅	C₅×D₃×C₃₁	1	6	yes	direct product factor
40	C₂×C₃	C₂×C₅²×C₃₁	1	1	yes	characteristic, complemented
41	D₃	C₂×C₅²×C₃₁	1	2	yes	direct product factor
42	C₅	C₂×C₅×D₃×C₃₁	1	6	yes	direct product factor
43	C₂²	—	3	1	no	Sylow
44	C₃	C₂²×C₅²×C₃₁	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	3	2	no	—
46	C₂	C₅²×D₃×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₃₁	D₃
commutator, hypocenter	C₃	C₂²×C₅²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅²×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅²×D₃×C₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₃₁	C₂	semidirect
4. C₃×C₅²×C₃₁	C₂²	semidirect
5. C₂×C₅×D₃×C₃₁	C₅	direct (N × H)
7. C₂×C₅²×C₃₁	D₃	direct (N × H)
8. C₂×C₃×C₅×C₃₁	C₂×C₅	semidirect
9. C₅×D₃×C₃₁	C₂×C₅	direct (N × H)
10. C₅²×C₃₁	C₂×D₃	direct (N × H)
12. C₃×C₅×C₃₁	C₂²×C₅	semidirect
13. C₂×D₃×C₃₁	C₅²	direct (N × H)
15. C₂×C₅×C₃₁	C₅×D₃	direct (N × H)
16. C₂×C₅²×D₃	C₃₁	direct (N × H)
17. C₂×C₃×C₃₁	C₂×C₅²	semidirect
18. D₃×C₃₁	C₂×C₅²	direct (N × H)
19. C₅×C₃₁	C₂×C₅×D₃	direct (N × H)
20. C₂×C₃×C₅²	C₂×C₃₁	semidirect
21. C₅²×D₃	C₂×C₃₁	direct (N × H)
24. C₃×C₃₁	C₂²×C₅²	semidirect
25. C₃×C₅²	C₂²×C₃₁	semidirect
27. C₂×C₃₁	C₅²×D₃	direct (N × H)
28. C₂×C₅×D₃	C₅×C₃₁	direct (N × H)
30. C₂×C₅²	D₃×C₃₁	direct (N × H)
31. C₃₁	C₂×C₅²×D₃	direct (N × H)
32. C₂×C₃×C₅	C₂×C₅×C₃₁	semidirect
33. C₅×D₃	C₂×C₅×C₃₁	direct (N × H)
34. C₅²	C₂×D₃×C₃₁	direct (N × H)
36. C₃×C₅	C₂²×C₅×C₃₁	semidirect
37. C₂×D₃	C₅²×C₃₁	direct (N × H)
39. C₂×C₅	C₅×D₃×C₃₁	direct (N × H)
40. C₂×C₃	C₂×C₅²×C₃₁	semidirect
41. D₃	C₂×C₅²×C₃₁	direct (N × H)
42. C₅	C₂×C₅×D₃×C₃₁	direct (N × H)
44. C₃	C₂²×C₅²×C₃₁	semidirect
46. C₂	C₅²×D₃×C₃₁	direct (N × H)

Subgroups — C2×C52×D3×C31 #22604940

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅²×D₃×C₃₁ #22604940