Subgroups — C₂×C₃³×C₅×C₈₉ #72201313

Order 24030.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅×C₈₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃³×C₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃²×C₅×C₈₉	C₃	1	13	yes	maximal, direct product factor
4	C₃²×C₅×C₈₉	C₂×C₃	1	13	yes	direct product factor
5	C₂×C₃×C₅×C₈₉	C₃²	1	13	yes	direct product factor
6	C₃³×C₈₉	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₈₉	C₃×C₅	1	13	yes	direct product factor
8	C₃×C₅×C₈₉	C₂×C₃²	1	13	yes	direct product factor
9	C₂×C₅×C₈₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₈₉	C₂×C₃×C₅	1	13	yes	direct product factor
11	C₂×C₃×C₈₉	C₃²×C₅	1	13	yes	direct product factor
12	C₅×C₈₉	C₂×C₃³	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃³×C₅	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₈₉	C₂×C₃²×C₅	1	13	yes	direct product factor
15	C₂×C₈₉	C₃³×C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃³×C₅	C₂×C₈₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²×C₅	C₃×C₈₉	1	13	yes	direct product factor
18	C₈₉	C₂×C₃³×C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃³	C₅×C₈₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃²×C₅	C₂×C₃×C₈₉	1	13	yes	direct product factor
21	C₂×C₃×C₅	C₃²×C₈₉	1	13	yes	direct product factor
22	C₃³	C₂×C₅×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₃²	C₃×C₅×C₈₉	1	13	yes	direct product factor
24	C₃×C₅	C₂×C₃²×C₈₉	1	13	yes	direct product factor
25	C₂×C₅	C₃³×C₈₉	1	1	yes	characteristic, direct product factor, Hall
26	C₃²	C₂×C₃×C₅×C₈₉	1	13	yes	direct product factor
27	C₂×C₃	C₃²×C₅×C₈₉	1	13	yes	direct product factor
28	C₅	C₂×C₃³×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₃²×C₅×C₈₉	1	13	yes	direct product factor
30	C₂	C₃³×C₅×C₈₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃³×C₅×C₈₉	C₂	direct (N × H)
2. C₂×C₃³×C₈₉	C₅	direct (N × H)
3. C₂×C₃²×C₅×C₈₉	C₃	direct (N × H)
4. C₃²×C₅×C₈₉	C₂×C₃	direct (N × H)
5. C₂×C₃×C₅×C₈₉	C₃²	direct (N × H)
6. C₃³×C₈₉	C₂×C₅	direct (N × H)
7. C₂×C₃²×C₈₉	C₃×C₅	direct (N × H)
8. C₃×C₅×C₈₉	C₂×C₃²	direct (N × H)
9. C₂×C₅×C₈₉	C₃³	direct (N × H)
10. C₃²×C₈₉	C₂×C₃×C₅	direct (N × H)
11. C₂×C₃×C₈₉	C₃²×C₅	direct (N × H)
12. C₅×C₈₉	C₂×C₃³	direct (N × H)
13. C₂×C₃³×C₅	C₈₉	direct (N × H)
14. C₃×C₈₉	C₂×C₃²×C₅	direct (N × H)
15. C₂×C₈₉	C₃³×C₅	direct (N × H)
16. C₃³×C₅	C₂×C₈₉	direct (N × H)
17. C₂×C₃²×C₅	C₃×C₈₉	direct (N × H)
18. C₈₉	C₂×C₃³×C₅	direct (N × H)
19. C₂×C₃³	C₅×C₈₉	direct (N × H)
20. C₃²×C₅	C₂×C₃×C₈₉	direct (N × H)
21. C₂×C₃×C₅	C₃²×C₈₉	direct (N × H)
22. C₃³	C₂×C₅×C₈₉	direct (N × H)
23. C₂×C₃²	C₃×C₅×C₈₉	direct (N × H)
24. C₃×C₅	C₂×C₃²×C₈₉	direct (N × H)
25. C₂×C₅	C₃³×C₈₉	direct (N × H)
26. C₃²	C₂×C₃×C₅×C₈₉	direct (N × H)
27. C₂×C₃	C₃²×C₅×C₈₉	direct (N × H)
28. C₅	C₂×C₃³×C₈₉	direct (N × H)
29. C₃	C₂×C₃²×C₅×C₈₉	direct (N × H)
30. C₂	C₃³×C₅×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₅×C₈₉	2
C₂×C₃³×C₈₉	5
C₂×C₃²×C₅×C₈₉	3
C₂×C₃³×C₅	89

Subgroups — C2×C33×C5×C89 #72201313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₅×C₈₉ #72201313