Subgroups — C₃²×C₅×Dic₈₉ #30630833

Order 16020.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×Dic₈₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×Dic₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₈₉	C₂×C₃	1	4	yes	—
6	C₅×Dic₈₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₈₉	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₈₉	C₃×C₄	1	4	yes	complemented
9	C₃×Dic₈₉	C₃×C₅	1	4	yes	direct product factor
10	C₂×C₅×C₈₉	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₈₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₈₉	C₂×C₃×C₅	1	4	yes	—
13	C₅×C₈₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	Dic₈₉	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₈₉	C₃×C₄×C₅	1	4	yes	complemented
16	C₃²×C₄×C₅	—	89	1	no	maximal, Hall
17	C₂×C₈₉	C₂×C₃²×C₅	1	1	yes	characteristic
18	C₂×C₃²×C₅	D₈₉	1	1	yes	characteristic
19	C₈₉	C₃²×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₄×C₅	—	89	4	no	—
21	C₃²×C₅	Dic₈₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃²×C₄	—	89	1	no	Hall
23	C₂×C₃×C₅	C₃×D₈₉	1	4	yes	—
24	C₄×C₅	—	89	1	no	Hall
25	C₂×C₃²	C₅×D₈₉	1	1	yes	characteristic
26	C₃×C₅	C₃×Dic₈₉	1	4	yes	direct product factor
27	C₃×C₄	—	89	4	no	—
28	C₂×C₅	C₃²×D₈₉	1	1	yes	characteristic
29	C₃²	C₅×Dic₈₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₃×C₅×D₈₉	1	4	yes	—
31	C₅	C₃²×Dic₈₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	—	89	1	no	Sylow
33	C₃	C₃×C₅×Dic₈₉	1	4	yes	direct product factor
34	C₂	C₃²×C₅×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	D₈₉
commutator, hypocenter	C₈₉	C₃²×C₄×C₅
Frattini	C₂	C₃²×C₅×D₈₉
Fitting, socle, prime radical	C₂×C₃²×C₅×C₈₉	C₂
cosocle	C₂×C₈₉	C₂×C₃²×C₅
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×Dic₈₉	C₃	direct (N × H)
3. C₃²×C₅×C₈₉	C₄	semidirect
4. C₃²×Dic₈₉	C₅	direct (N × H)
6. C₅×Dic₈₉	C₃²	direct (N × H)
8. C₃×C₅×C₈₉	C₃×C₄	semidirect
9. C₃×Dic₈₉	C₃×C₅	direct (N × H)
11. C₃²×C₈₉	C₄×C₅	semidirect
13. C₅×C₈₉	C₃²×C₄	semidirect
14. Dic₈₉	C₃²×C₅	direct (N × H)
15. C₃×C₈₉	C₃×C₄×C₅	semidirect
19. C₈₉	C₃²×C₄×C₅	semidirect
21. C₃²×C₅	Dic₈₉	direct (N × H)
26. C₃×C₅	C₃×Dic₈₉	direct (N × H)
29. C₃²	C₅×Dic₈₉	direct (N × H)
31. C₅	C₃²×Dic₈₉	direct (N × H)
33. C₃	C₃×C₅×Dic₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅×C₈₉	2
C₃×C₅×Dic₈₉	3
C₃²×Dic₈₉	5
C₃²×C₄×C₅	89

Subgroups — C32×C5×Dic89 #30630833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×Dic₈₉ #30630833