Subgroups — C₂×C₃²×C₅×D₈₉ #30630907

Order 16020.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₈₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₈₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×D₈₉	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₈₉	C₂×C₃	1	4	yes	complemented
8	C₂×C₅×D₈₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₈₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃²×D₈₉	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅×C₈₉	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₈₉	C₃×C₅	1	4	yes	direct product factor
13	C₂×C₅×C₈₉	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₅×D₈₉	C₂×C₃²	1	2	yes	direct product factor
15	C₃²×C₈₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₈₉	C₂×C₃×C₅	1	4	yes	complemented
17	C₃×D₈₉	C₂×C₃×C₅	1	8	yes	direct product factor
18	C₅×C₈₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
19	C₂×D₈₉	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₈₉	C₂²×C₃×C₅	1	4	yes	complemented
21	C₂²×C₃²×C₅	—	89	1	no	maximal, Hall
22	C₂×C₈₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
23	D₈₉	C₂×C₃²×C₅	1	2	yes	direct product factor
24	C₂×C₃²×C₅	—	89	2	no	—
25	C₂×C₃²×C₅	D₈₉	1	1	yes	characteristic, direct product factor
26	C₈₉	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₃×C₅	—	89	4	no	—
28	C₃²×C₅	C₂×D₈₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃²	—	89	1	no	Hall
30	C₂×C₃×C₅	—	89	8	no	—
31	C₂×C₃×C₅	C₃×D₈₉	1	4	yes	direct product factor
32	C₂²×C₅	—	89	1	no	Hall
33	C₂×C₃²	—	89	2	no	—
34	C₂×C₃²	C₅×D₈₉	1	1	yes	characteristic, direct product factor
35	C₃×C₅	C₂×C₃×D₈₉	1	4	yes	direct product factor
36	C₂²×C₃	—	89	4	no	—
37	C₂×C₅	—	89	2	no	—
38	C₂×C₅	C₃²×D₈₉	1	1	yes	characteristic, direct product factor
39	C₃²	C₂×C₅×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	89	8	no	—
41	C₂×C₃	C₃×C₅×D₈₉	1	4	yes	direct product factor
42	C₅	C₂×C₃²×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	89	1	no	Sylow
44	C₃	C₂×C₃×C₅×D₈₉	1	4	yes	direct product factor
45	C₂	—	89	2	no	—
46	C₂	C₃²×C₅×D₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×D₈₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₈₉	C₂	semidirect
3. C₂×C₃×C₅×D₈₉	C₃	direct (N × H)
4. C₃²×C₅×C₈₉	C₂²	semidirect
5. C₂×C₃²×D₈₉	C₅	direct (N × H)
6. C₃×C₅×D₈₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₈₉	C₂×C₃	semidirect
8. C₂×C₅×D₈₉	C₃²	direct (N × H)
9. C₂×C₃²×C₈₉	C₂×C₅	semidirect
10. C₃²×D₈₉	C₂×C₅	direct (N × H)
11. C₃×C₅×C₈₉	C₂²×C₃	semidirect
12. C₂×C₃×D₈₉	C₃×C₅	direct (N × H)
13. C₂×C₅×C₈₉	C₂×C₃²	semidirect
14. C₅×D₈₉	C₂×C₃²	direct (N × H)
15. C₃²×C₈₉	C₂²×C₅	semidirect
16. C₂×C₃×C₈₉	C₂×C₃×C₅	semidirect
17. C₃×D₈₉	C₂×C₃×C₅	direct (N × H)
18. C₅×C₈₉	C₂²×C₃²	semidirect
19. C₂×D₈₉	C₃²×C₅	direct (N × H)
20. C₃×C₈₉	C₂²×C₃×C₅	semidirect
22. C₂×C₈₉	C₂×C₃²×C₅	semidirect
23. D₈₉	C₂×C₃²×C₅	direct (N × H)
25. C₂×C₃²×C₅	D₈₉	direct (N × H)
26. C₈₉	C₂²×C₃²×C₅	semidirect
28. C₃²×C₅	C₂×D₈₉	direct (N × H)
31. C₂×C₃×C₅	C₃×D₈₉	direct (N × H)
34. C₂×C₃²	C₅×D₈₉	direct (N × H)
35. C₃×C₅	C₂×C₃×D₈₉	direct (N × H)
38. C₂×C₅	C₃²×D₈₉	direct (N × H)
39. C₃²	C₂×C₅×D₈₉	direct (N × H)
41. C₂×C₃	C₃×C₅×D₈₉	direct (N × H)
42. C₅	C₂×C₃²×D₈₉	direct (N × H)
44. C₃	C₂×C₃×C₅×D₈₉	direct (N × H)
46. C₂	C₃²×C₅×D₈₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅×D₈₉	2
C₂×C₃²×C₅×C₈₉	2
C₂×C₃×C₅×D₈₉	3
C₂×C₃²×D₈₉	5
C₂²×C₃²×C₅	89

Subgroups — C2×C32×C5×D89 #30630907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×D₈₉ #30630907