Subgroups — C₂×C₇×D₁₅×C₈₉ #49153231

Order 37380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₅×C₈₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₅×C₈₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₇×C₈₉	—	5	1	no	maximal, Hall
6	C₇×D₅×C₈₉	—	3	2	no	—
7	C₂×C₅×C₇×C₈₉	D₃	1	1	yes	characteristic, complemented
8	C₂×D₁₅×C₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₇×C₈₉	—	5	2	no	—
10	C₂×C₃×C₇×C₈₉	D₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₈₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	D₁₅×C₈₉	C₂×C₇	1	2	yes	direct product factor
13	C₂×C₃×C₅×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂²×C₇×C₈₉	—	15	1	no	Hall
15	C₃×C₇×C₈₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅×C₈₉	—	3	1	no	Hall
17	C₃×C₅×C₈₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₈₉	—	15	2	no	—
19	C₂×C₇×C₈₉	D₁₅	1	1	yes	characteristic, direct product factor
20	C₂×D₃×C₈₉	—	5	1	no	Hall
21	C₂×C₅×C₈₉	D₃×C₇	1	1	yes	characteristic, complemented
22	D₅×C₈₉	—	3	2	no	—
23	C₇×C₈₉	C₂×D₁₅	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₈₉	C₇×D₅	1	1	yes	characteristic, complemented
25	D₃×C₈₉	—	5	2	no	—
26	C₅×C₈₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₇×D₁₅	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₈₉	—	15	1	no	Hall
29	C₃×C₈₉	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅×C₇	C₂×C₈₉	1	1	yes	characteristic, complemented
31	C₇×D₁₅	C₂×C₈₉	1	2	yes	direct product factor
32	C₂×C₈₉	—	15	2	no	—
33	C₂×C₈₉	C₇×D₁₅	1	1	yes	characteristic, direct product factor
34	C₂×C₇×D₅	—	3	1	no	Hall
35	C₃×C₅×C₇	C₂²×C₈₉	1	1	yes	characteristic, complemented, Hall
36	C₈₉	C₂×C₇×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×D₃×C₇	—	5	1	no	Hall
38	C₂×C₅×C₇	D₃×C₈₉	1	1	yes	characteristic, complemented
39	C₇×D₅	—	3	2	no	—
40	C₂×D₁₅	C₇×C₈₉	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₃×C₇	D₅×C₈₉	1	1	yes	characteristic, complemented
42	D₃×C₇	—	5	2	no	—
43	C₅×C₇	C₂×D₃×C₈₉	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	C₂×C₇×C₈₉	1	1	yes	characteristic, complemented
45	D₁₅	C₂×C₇×C₈₉	1	2	yes	direct product factor
46	C₂²×C₇	—	15	1	no	Hall
47	C₃×C₇	C₂×D₅×C₈₉	1	1	yes	characteristic, complemented, Hall
48	C₂×D₅	—	3	1	no	Hall
49	C₃×C₅	C₂²×C₇×C₈₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	—	15	2	no	—
51	C₂×C₇	D₁₅×C₈₉	1	1	yes	characteristic, direct product factor
52	C₂×D₃	—	5	1	no	Hall
53	C₂×C₅	D₃×C₇×C₈₉	1	1	yes	characteristic, complemented
54	D₅	—	3	2	no	—
55	C₇	C₂×D₁₅×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	C₇×D₅×C₈₉	1	1	yes	characteristic, complemented
57	D₃	—	5	2	no	—
58	C₅	C₂×D₃×C₇×C₈₉	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	15	1	no	Sylow
60	C₃	C₂×C₇×D₅×C₈₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	15	2	no	—
62	C₂	C₇×D₁₅×C₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₈₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₇×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₈₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₇×C₈₉

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₅×C₈₉	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₈₉	C₂	semidirect
4. C₃×C₅×C₇×C₈₉	C₂²	semidirect
7. C₂×C₅×C₇×C₈₉	D₃	semidirect
8. C₂×D₁₅×C₈₉	C₇	direct (N × H)
10. C₂×C₃×C₇×C₈₉	D₅	semidirect
11. C₅×C₇×C₈₉	C₂×D₃	semidirect
12. D₁₅×C₈₉	C₂×C₇	direct (N × H)
13. C₂×C₃×C₅×C₈₉	C₂×C₇	semidirect
15. C₃×C₇×C₈₉	C₂×D₅	semidirect
17. C₃×C₅×C₈₉	C₂²×C₇	semidirect
19. C₂×C₇×C₈₉	D₁₅	direct (N × H)
21. C₂×C₅×C₈₉	D₃×C₇	semidirect
23. C₇×C₈₉	C₂×D₁₅	direct (N × H)
24. C₂×C₃×C₈₉	C₇×D₅	semidirect
26. C₅×C₈₉	C₂×D₃×C₇	semidirect
27. C₂×C₇×D₁₅	C₈₉	direct (N × H)
29. C₃×C₈₉	C₂×C₇×D₅	semidirect
30. C₂×C₃×C₅×C₇	C₂×C₈₉	semidirect
31. C₇×D₁₅	C₂×C₈₉	direct (N × H)
33. C₂×C₈₉	C₇×D₁₅	direct (N × H)
35. C₃×C₅×C₇	C₂²×C₈₉	semidirect
36. C₈₉	C₂×C₇×D₁₅	direct (N × H)
38. C₂×C₅×C₇	D₃×C₈₉	semidirect
40. C₂×D₁₅	C₇×C₈₉	direct (N × H)
41. C₂×C₃×C₇	D₅×C₈₉	semidirect
43. C₅×C₇	C₂×D₃×C₈₉	semidirect
44. C₂×C₃×C₅	C₂×C₇×C₈₉	semidirect
45. D₁₅	C₂×C₇×C₈₉	direct (N × H)
47. C₃×C₇	C₂×D₅×C₈₉	semidirect
49. C₃×C₅	C₂²×C₇×C₈₉	semidirect
51. C₂×C₇	D₁₅×C₈₉	direct (N × H)
53. C₂×C₅	D₃×C₇×C₈₉	semidirect
55. C₇	C₂×D₁₅×C₈₉	direct (N × H)
56. C₂×C₃	C₇×D₅×C₈₉	semidirect
58. C₅	C₂×D₃×C₇×C₈₉	semidirect
60. C₃	C₂×C₇×D₅×C₈₉	semidirect
62. C₂	C₇×D₁₅×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
C₇×D₁₅×C₈₉	2
C₂×C₃×C₅×C₇×C₈₉	2
C₂×C₇×D₅×C₈₉	3
C₂×D₃×C₇×C₈₉	5
C₂×D₁₅×C₈₉	7
C₂×C₇×D₁₅	89

Subgroups — C2×C7×D15×C89 #49153231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₅×C₈₉ #49153231