Subgroups — D₅×C₃⋊D₃×C₈₉ #30630872

Order 16020.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₃×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₅×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₅×C₈₉	—	3	4	no	maximal
5	C₃²×C₅×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃⋊D₃×C₈₉	—	5	1	no	maximal, Hall
7	D₁₅×C₈₉	—	3	4	no	—
8	C₅×D₃×C₈₉	—	3	4	no	—
9	C₃×D₅×C₈₉	D₃	1	4	yes	complemented
10	C₂×D₅×C₈₉	—	9	1	no	Hall
11	C₂×C₃²×C₈₉	—	5	1	no	—
12	C₃⋊D₃×C₈₉	—	5	1	no	—
13	C₃⋊D₃×C₈₉	D₅	1	1	yes	characteristic, direct product factor
14	C₃×C₅×C₈₉	C₂×D₃	1	4	yes	complemented
15	C₂×D₃×C₈₉	—	15	4	no	—
16	C₂×C₅×C₈₉	—	9	1	no	—
17	D₅×C₈₉	—	9	1	no	—
18	D₅×C₈₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₈₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₈₉	—	5	4	no	—
21	D₃×C₈₉	—	3	4	no	—
22	D₃×C₈₉	—	15	4	no	—
23	C₅×C₈₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₈₉	—	45	1	no	Hall
25	C₃×C₈₉	D₃×D₅	1	4	yes	complemented
26	D₅×C₃⋊D₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₈₉	—	5	1	no	—
28	C₂×C₈₉	—	9	1	no	—
29	C₂×C₈₉	—	45	1	no	—
30	C₃⋊D₁₅	C₂×C₈₉	1	1	yes	characteristic, complemented
31	C₅×C₃⋊D₃	C₂×C₈₉	1	1	yes	characteristic, complemented
32	C₃²×D₅	C₂×C₈₉	1	1	yes	characteristic, complemented
33	C₈₉	D₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
34	D₃×D₅	—	3	4	no	—
35	C₃²×C₅	C₂²×C₈₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃⋊D₃	—	5	1	no	Hall
37	D₁₅	—	3	4	no	—
38	C₃×D₅	D₃×C₈₉	1	4	yes	complemented
39	C₅×D₃	—	3	4	no	—
40	C₂×D₅	—	9	1	no	Hall
41	C₂×C₃²	—	5	1	no	—
42	C₃⋊D₃	—	5	1	no	—
43	C₃⋊D₃	D₅×C₈₉	1	1	yes	characteristic, direct product factor
44	C₃×C₅	C₂×D₃×C₈₉	1	4	yes	complemented
45	C₂×D₃	—	15	4	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	9	1	no	—
48	D₅	C₃⋊D₃×C₈₉	1	1	yes	characteristic, direct product factor
49	C₃²	C₂×D₅×C₈₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	5	4	no	—
51	D₃	—	3	4	no	—
52	D₃	—	15	4	no	—
53	C₅	C₂×C₃⋊D₃×C₈₉	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	45	1	no	Sylow
55	C₃	D₃×D₅×C₈₉	1	4	yes	complemented
56	C₂	—	5	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₈₉	D₅×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₈₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₈₉	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₈₉

Complements

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

N	H ≅ G/N	type
1. C₈₉×C₃⋊D₁₅	C₂	semidirect
2. C₅×C₃⋊D₃×C₈₉	C₂	semidirect
3. C₃²×D₅×C₈₉	C₂	semidirect
5. C₃²×C₅×C₈₉	C₂²	semidirect
9. C₃×D₅×C₈₉	D₃	semidirect
13. C₃⋊D₃×C₈₉	D₅	direct (N × H)
14. C₃×C₅×C₈₉	C₂×D₃	semidirect
18. D₅×C₈₉	C₃⋊D₃	direct (N × H)
19. C₃²×C₈₉	C₂×D₅	semidirect
23. C₅×C₈₉	C₂×C₃⋊D₃	semidirect
25. C₃×C₈₉	D₃×D₅	semidirect
26. D₅×C₃⋊D₃	C₈₉	direct (N × H)
30. C₃⋊D₁₅	C₂×C₈₉	semidirect
31. C₅×C₃⋊D₃	C₂×C₈₉	semidirect
32. C₃²×D₅	C₂×C₈₉	semidirect
33. C₈₉	D₅×C₃⋊D₃	direct (N × H)
35. C₃²×C₅	C₂²×C₈₉	semidirect
38. C₃×D₅	D₃×C₈₉	semidirect
43. C₃⋊D₃	D₅×C₈₉	direct (N × H)
44. C₃×C₅	C₂×D₃×C₈₉	semidirect
48. D₅	C₃⋊D₃×C₈₉	direct (N × H)
49. C₃²	C₂×D₅×C₈₉	semidirect
53. C₅	C₂×C₃⋊D₃×C₈₉	semidirect
55. C₃	D₃×D₅×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×C₃⋊D₁₅	2
C₅×C₃⋊D₃×C₈₉	2
C₃²×D₅×C₈₉	2
D₃×D₅×C₈₉	3
C₂×C₃⋊D₃×C₈₉	5
D₅×C₃⋊D₃	89

Subgroups — D5×C3⋊D3×C89 #30630872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₃⋊D₃×C₈₉ #30630872