Subgroups — D₅×D₆₀₉ #27131801

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

Subgroups — D5×D609 #27131801

Conjugacy classes of subgroups

Complements

Subgroups — D₅×D₆₀₉ #27131801