Subgroups — C₂×C₅×C₇×D₈₇ #27131821

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₈₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×D₂₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×D₈₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×D₂₉	—	3	2	no	—
7	C₂×C₅×C₇×C₂₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₅×D₈₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₇×D₈₇	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
13	C₅×D₈₇	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₇×D₂₉	—	3	1	no	Hall
15	C₃×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×D₂₉	—	3	1	no	Hall
17	C₃×C₅×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×D₃×C₇	—	29	1	no	maximal, Hall
19	C₂×C₇×C₂₉	C₅×D₃	1	1	yes	characteristic, complemented
20	C₇×D₂₉	—	3	2	no	—
21	C₂×D₈₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₅×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented
23	C₅×D₂₉	—	3	2	no	—
24	C₂×C₃×C₅×C₇	D₂₉	1	1	yes	characteristic, complemented
25	C₅×D₃×C₇	—	29	2	no	—
26	C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
28	D₈₇	C₂×C₅×C₇	1	2	yes	direct product factor
29	C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₅×C₇	—	87	1	no	Hall
31	C₂×D₂₉	—	3	1	no	Hall
32	C₃×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₂₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃×C₇	—	29	1	no	Hall
35	C₂×C₅×C₇	—	87	2	no	—
36	C₂×C₅×C₇	D₈₇	1	1	yes	characteristic, direct product factor
37	C₂×C₅×D₃	—	29	1	no	Hall
38	C₂×C₂₉	C₅×D₃×C₇	1	1	yes	characteristic, complemented
39	D₂₉	—	3	2	no	—
40	C₂×C₃×C₇	C₅×D₂₉	1	1	yes	characteristic, complemented
41	D₃×C₇	—	29	2	no	—
42	C₅×C₇	C₂×D₈₇	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₅	C₇×D₂₉	1	1	yes	characteristic, complemented
44	C₅×D₃	—	29	2	no	—
45	C₂₉	C₂×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₇	—	87	1	no	Hall
47	C₃×C₇	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅	—	87	1	no	Hall
49	C₃×C₅	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇	—	87	2	no	—
51	C₂×C₇	C₅×D₈₇	1	1	yes	characteristic, direct product factor
52	C₂×D₃	—	29	1	no	Hall
53	C₂×C₅	—	87	2	no	—
54	C₂×C₅	C₇×D₈₇	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	C₅×C₇×D₂₉	1	1	yes	characteristic, complemented
57	D₃	—	29	2	no	—
58	C₅	C₂×C₇×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	87	1	no	Sylow
60	C₃	C₂×C₅×C₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	87	2	no	—
62	C₂	C₅×C₇×D₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₈₇
commutator, hypocenter	C₃×C₂₉	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₂×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₈₇	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇×C₂₉	C₂	semidirect
4. C₃×C₅×C₇×C₂₉	C₂²	semidirect
5. C₂×C₇×D₈₇	C₅	direct (N × H)
7. C₂×C₅×C₇×C₂₉	D₃	semidirect
8. C₂×C₅×D₈₇	C₇	direct (N × H)
9. C₂×C₃×C₇×C₂₉	C₂×C₅	semidirect
10. C₇×D₈₇	C₂×C₅	direct (N × H)
11. C₅×C₇×C₂₉	C₂×D₃	semidirect
12. C₂×C₃×C₅×C₂₉	C₂×C₇	semidirect
13. C₅×D₈₇	C₂×C₇	direct (N × H)
15. C₃×C₇×C₂₉	C₂²×C₅	semidirect
17. C₃×C₅×C₂₉	C₂²×C₇	semidirect
19. C₂×C₇×C₂₉	C₅×D₃	semidirect
21. C₂×D₈₇	C₅×C₇	direct (N × H)
22. C₂×C₅×C₂₉	D₃×C₇	semidirect
24. C₂×C₃×C₅×C₇	D₂₉	semidirect
26. C₇×C₂₉	C₂×C₅×D₃	semidirect
27. C₂×C₃×C₂₉	C₂×C₅×C₇	semidirect
28. D₈₇	C₂×C₅×C₇	direct (N × H)
29. C₅×C₂₉	C₂×D₃×C₇	semidirect
32. C₃×C₅×C₇	C₂×D₂₉	semidirect
33. C₃×C₂₉	C₂²×C₅×C₇	semidirect
36. C₂×C₅×C₇	D₈₇	direct (N × H)
38. C₂×C₂₉	C₅×D₃×C₇	semidirect
40. C₂×C₃×C₇	C₅×D₂₉	semidirect
42. C₅×C₇	C₂×D₈₇	direct (N × H)
43. C₂×C₃×C₅	C₇×D₂₉	semidirect
45. C₂₉	C₂×C₅×D₃×C₇	semidirect
47. C₃×C₇	C₂×C₅×D₂₉	semidirect
49. C₃×C₅	C₂×C₇×D₂₉	semidirect
51. C₂×C₇	C₅×D₈₇	direct (N × H)
54. C₂×C₅	C₇×D₈₇	direct (N × H)
55. C₇	C₂×C₅×D₈₇	direct (N × H)
56. C₂×C₃	C₅×C₇×D₂₉	semidirect
58. C₅	C₂×C₇×D₈₇	direct (N × H)
60. C₃	C₂×C₅×C₇×D₂₉	semidirect
62. C₂	C₅×C₇×D₈₇	direct (N × H)

Subgroups — C2×C5×C7×D87 #27131821

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×D₈₇ #27131821