Subgroups — C₂×C₃×C₅²×D₃₁ #22604945

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₅×D₃₁	C₅	1	6	yes	maximal, direct product factor
6	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×D₃₁	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×C₃₁	C₂×C₅	1	6	yes	complemented
9	C₃×C₅×D₃₁	C₂×C₅	1	12	yes	direct product factor
10	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×D₃₁	C₃×C₅	1	6	yes	direct product factor
12	C₃×C₅×C₃₁	C₂²×C₅	1	6	yes	complemented
13	C₂×C₃×D₃₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₃₁	C₂×C₃×C₅	1	6	yes	complemented
15	C₅×D₃₁	C₂×C₃×C₅	1	12	yes	direct product factor
16	C₂²×C₃×C₅²	—	31	1	no	maximal, Hall
17	C₂×C₃×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
18	C₃×D₃₁	C₂×C₅²	1	2	yes	direct product factor
19	C₅×C₃₁	C₂²×C₃×C₅	1	6	yes	complemented
20	C₂×C₃×C₅²	—	31	2	no	—
21	C₂×C₃×C₅²	D₃₁	1	1	yes	characteristic, direct product factor
22	C₂×D₃₁	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₅²	—	31	1	no	Hall
24	C₃×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅²	C₂×D₃₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃₁	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
27	D₃₁	C₂×C₃×C₅²	1	2	yes	direct product factor
28	C₂²×C₃×C₅	—	31	6	no	—
29	C₂×C₅²	—	31	2	no	—
30	C₂×C₅²	C₃×D₃₁	1	1	yes	characteristic, direct product factor
31	C₃₁	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₅	—	31	12	no	—
33	C₂×C₃×C₅	C₅×D₃₁	1	6	yes	direct product factor
34	C₅²	C₂×C₃×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²×C₅	—	31	6	no	—
36	C₃×C₅	C₂×C₅×D₃₁	1	6	yes	direct product factor
37	C₂²×C₃	—	31	1	no	Hall
38	C₂×C₅	—	31	12	no	—
39	C₂×C₅	C₃×C₅×D₃₁	1	6	yes	direct product factor
40	C₂×C₃	—	31	2	no	—
41	C₂×C₃	C₅²×D₃₁	1	1	yes	characteristic, direct product factor
42	C₅	C₂×C₃×C₅×D₃₁	1	6	yes	direct product factor
43	C₂²	—	31	1	no	Sylow
44	C₃	C₂×C₅²×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	31	2	no	—
46	C₂	C₃×C₅²×D₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	D₃₁
commutator, hypocenter	C₃₁	C₂²×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×D₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₃₁	C₂	semidirect
3. C₂×C₅²×D₃₁	C₃	direct (N × H)
4. C₃×C₅²×C₃₁	C₂²	semidirect
5. C₂×C₃×C₅×D₃₁	C₅	direct (N × H)
6. C₂×C₅²×C₃₁	C₂×C₃	semidirect
7. C₅²×D₃₁	C₂×C₃	direct (N × H)
8. C₂×C₃×C₅×C₃₁	C₂×C₅	semidirect
9. C₃×C₅×D₃₁	C₂×C₅	direct (N × H)
10. C₅²×C₃₁	C₂²×C₃	semidirect
11. C₂×C₅×D₃₁	C₃×C₅	direct (N × H)
12. C₃×C₅×C₃₁	C₂²×C₅	semidirect
13. C₂×C₃×D₃₁	C₅²	direct (N × H)
14. C₂×C₅×C₃₁	C₂×C₃×C₅	semidirect
15. C₅×D₃₁	C₂×C₃×C₅	direct (N × H)
17. C₂×C₃×C₃₁	C₂×C₅²	semidirect
18. C₃×D₃₁	C₂×C₅²	direct (N × H)
19. C₅×C₃₁	C₂²×C₃×C₅	semidirect
21. C₂×C₃×C₅²	D₃₁	direct (N × H)
22. C₂×D₃₁	C₃×C₅²	direct (N × H)
24. C₃×C₃₁	C₂²×C₅²	semidirect
25. C₃×C₅²	C₂×D₃₁	direct (N × H)
26. C₂×C₃₁	C₂×C₃×C₅²	semidirect
27. D₃₁	C₂×C₃×C₅²	direct (N × H)
30. C₂×C₅²	C₃×D₃₁	direct (N × H)
31. C₃₁	C₂²×C₃×C₅²	semidirect
33. C₂×C₃×C₅	C₅×D₃₁	direct (N × H)
34. C₅²	C₂×C₃×D₃₁	direct (N × H)
36. C₃×C₅	C₂×C₅×D₃₁	direct (N × H)
39. C₂×C₅	C₃×C₅×D₃₁	direct (N × H)
41. C₂×C₃	C₅²×D₃₁	direct (N × H)
42. C₅	C₂×C₃×C₅×D₃₁	direct (N × H)
44. C₃	C₂×C₅²×D₃₁	direct (N × H)
46. C₂	C₃×C₅²×D₃₁	direct (N × H)

Subgroups — C2×C3×C52×D31 #22604945

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅²×D₃₁ #22604945