Subgroups — D₃₅×D₈₇ #27131805

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₀₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₉×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₉×D₃₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₇×D₈₇	—	5	1	no	maximal, Hall
7	D₁₀₁₅	—	3	1	no	—
8	C₂₉×D₃₅	D₃	1	1	yes	characteristic, complemented
9	C₅×C₇×D₂₉	—	3	1	no	—
10	D₅×D₈₇	—	7	1	no	maximal, Hall
11	D₆₀₉	—	5	1	no	—
12	C₇×D₈₇	D₅	1	1	yes	characteristic, complemented
13	C₃×D₇×C₂₉	—	5	1	no	—
14	C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₄₃₅	—	7	1	no	—
16	C₅×D₈₇	D₇	1	1	yes	characteristic, complemented
17	C₃×D₅×C₂₉	—	7	1	no	—
18	D₇×D₂₉	—	15	1	no	Hall
19	C₃×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₂₉	—	21	1	no	Hall
21	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₃×D₃₅	—	29	1	no	maximal, Hall
23	D₂₀₃	—	15	1	no	—
24	C₇×D₂₉	—	3	1	no	—
25	D₇×C₂₉	—	5	1	no	—
26	C₂×D₈₇	—	35	1	no	Hall
27	D₁₄₅	—	21	1	no	—
28	C₅×D₂₉	—	3	1	no	—
29	D₅×C₂₉	—	7	1	no	—
30	D₁₀₅	—	29	1	no	—
31	C₅×D₃×C₇	—	29	1	no	—
32	C₃×D₃₅	D₂₉	1	1	yes	characteristic, complemented
33	C₇×C₂₉	D₃×D₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₂₉	—	35	1	no	—
35	D₈₇	—	35	1	no	—
36	D₈₇	D₃₅	1	1	yes	characteristic, direct product factor
37	C₅×C₂₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃₅	—	87	1	no	Hall
39	C₂×D₂₉	—	105	1	no	Hall
40	C₃×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
42	D₃×D₇	—	145	1	no	Hall
43	C₂×C₅×C₇	—	87	1	no	—
44	D₃₅	—	87	1	no	—
45	D₃₅	D₈₇	1	1	yes	characteristic, direct product factor
46	D₃×D₅	—	203	1	no	Hall
47	C₂×C₂₉	—	35	1	no	—
48	D₂₉	—	3	1	no	—
49	D₂₉	—	105	1	no	—
50	D₂₁	—	145	1	no	—
51	C₃×D₇	—	5	1	no	—
52	D₃×C₇	—	29	1	no	—
53	C₅×C₇	C₂×D₈₇	1	1	yes	characteristic, complemented, Hall
54	D₁₅	—	203	1	no	—
55	C₃×D₅	—	7	1	no	—
56	C₅×D₃	—	29	1	no	—
57	C₂₉	D₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₇	—	435	1	no	Hall
59	C₃×C₇	D₅×D₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	609	1	no	Hall
61	C₃×C₅	D₇×D₂₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	87	1	no	—
63	D₇	—	5	1	no	—
64	D₇	—	435	1	no	—
65	C₂×D₃	—	1015	1	no	Hall
66	C₂×C₅	—	87	1	no	—
67	D₅	—	7	1	no	—
68	D₅	—	609	1	no	—
69	C₇	D₅×D₈₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	35	1	no	—
71	D₃	—	29	1	no	—
72	D₃	—	1015	1	no	—
73	C₅	D₇×D₈₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	3045	1	no	Sylow
75	C₃	D₂₉×D₃₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	35	1	no	—
77	C₂	—	87	1	no	—
78	C₂	—	3045	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₃₀₄₅	C₂	semidirect
2. C₅×C₇×D₈₇	C₂	semidirect
3. C₃×C₂₉×D₃₅	C₂	semidirect
5. C₃×C₅×C₇×C₂₉	C₂²	semidirect
8. C₂₉×D₃₅	D₃	semidirect
12. C₇×D₈₇	D₅	semidirect
14. C₅×C₇×C₂₉	C₂×D₃	semidirect
16. C₅×D₈₇	D₇	semidirect
19. C₃×C₇×C₂₉	C₂×D₅	semidirect
21. C₃×C₅×C₂₉	C₂×D₇	semidirect
32. C₃×D₃₅	D₂₉	semidirect
33. C₇×C₂₉	D₃×D₅	semidirect
36. D₈₇	D₃₅	direct (N × H)
37. C₅×C₂₉	D₃×D₇	semidirect
40. C₃×C₅×C₇	C₂×D₂₉	semidirect
41. C₃×C₂₉	C₂×D₃₅	semidirect
45. D₃₅	D₈₇	direct (N × H)
53. C₅×C₇	C₂×D₈₇	semidirect
57. C₂₉	D₃×D₃₅	semidirect
59. C₃×C₇	D₅×D₂₉	semidirect
61. C₃×C₅	D₇×D₂₉	semidirect
69. C₇	D₅×D₈₇	semidirect
73. C₅	D₇×D₈₇	semidirect
75. C₃	D₂₉×D₃₅	semidirect

Subgroups — D35×D87 #27131805

Conjugacy classes of subgroups

Complements

Subgroups — D₃₅×D₈₇ #27131805