Subgroups — C₂×C₅×C₃⋊D₆₀₉ #49141691

Order 36540.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₆₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₆₀₉	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₆₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₆₀₉	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₂₉	D₃	1	4	yes	complemented
8	C₂×C₅×C₃⋊D₈₇	—	7	1	no	maximal, Hall
9	C₂×C₅×D₂₀₃	—	9	1	no	Hall
10	C₃⋊D₆₀₉	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₃²×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₉	C₂×D₃	1	4	yes	complemented
13	C₅×C₃⋊D₈₇	—	7	2	no	—
14	C₂×C₃²×C₅×C₂₉	D₇	1	1	yes	characteristic, complemented
15	C₂×D₆₀₉	—	3	4	no	—
16	C₅×D₂₀₃	—	9	2	no	—
17	C₂×C₅×C₇×C₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₃²×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₈₇	—	21	4	no	—
20	C₃²×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₃⋊D₂₁	—	29	1	no	maximal, Hall
22	C₂×C₃×C₇×C₂₉	C₅×D₃	1	4	yes	complemented
23	D₆₀₉	—	3	8	no	—
24	C₂×C₃⋊D₈₇	—	7	1	no	Hall
25	C₅×C₇×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₂₉	D₂₁	1	4	yes	complemented
27	C₅×D₈₇	—	21	8	no	—
28	C₂×D₂₀₃	—	9	1	no	Hall
29	C₂×C₃²×C₅×C₇	D₂₉	1	1	yes	characteristic, complemented
30	C₅×C₃⋊D₂₁	—	29	2	no	—
31	C₃×C₇×C₂₉	C₂×C₅×D₃	1	4	yes	complemented
32	C₂×C₅×D₂₉	—	63	1	no	Hall
33	C₂×C₃²×C₂₉	C₅×D₇	1	1	yes	characteristic, complemented
34	C₃⋊D₈₇	—	7	2	no	—
35	C₃×C₅×C₂₉	C₂×D₂₁	1	4	yes	complemented
36	C₂×C₅×D₂₁	—	87	4	no	—
37	C₂×C₇×C₂₉	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
38	D₂₀₃	—	9	2	no	—
39	C₂×D₈₇	—	21	4	no	—
40	C₃²×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₂₉	C₃⋊D₂₁	1	1	yes	characteristic, complemented
42	C₅×D₂₉	—	63	2	no	—
43	C₃²×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃⋊D₂₁	—	29	1	no	Hall
45	C₂×C₃×C₅×C₇	D₈₇	1	4	yes	complemented
46	C₅×D₂₁	—	87	8	no	—
47	C₇×C₂₉	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅×C₃⋊D₃	—	203	1	no	Hall
49	C₂×C₃×C₂₉	C₅×D₂₁	1	4	yes	complemented
50	D₈₇	—	21	8	no	—
51	C₅×C₂₉	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
52	C₂×C₅×D₇	—	261	1	no	Hall
53	C₂×C₃²×C₇	C₅×D₂₉	1	1	yes	characteristic, complemented
54	C₃⋊D₂₁	—	29	2	no	—
55	C₂×D₂₉	—	63	1	no	Hall
56	C₃×C₅×C₇	C₂×D₈₇	1	4	yes	complemented
57	C₂×C₃²×C₅	D₂₀₃	1	1	yes	characteristic, complemented
58	C₅×C₃⋊D₃	—	203	2	no	—
59	C₃×C₂₉	C₂×C₅×D₂₁	1	4	yes	complemented
60	C₂×D₂₁	—	87	4	no	—
61	C₂×C₅×C₇	C₃⋊D₈₇	1	1	yes	characteristic, complemented
62	C₅×D₇	—	261	2	no	—
63	C₃²×C₇	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
64	C₂×C₅×D₃	—	609	4	no	—
65	C₂×C₂₉	C₅×C₃⋊D₂₁	1	1	yes	characteristic, complemented
66	D₂₉	—	63	2	no	—
67	C₃²×C₅	C₂×D₂₀₃	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×C₇	C₅×D₈₇	1	4	yes	complemented
69	D₂₁	—	87	8	no	—
70	C₂×C₃⋊D₃	—	203	1	no	Hall
71	C₅×C₇	C₂×C₃⋊D₈₇	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	D₆₀₉	1	4	yes	complemented
73	C₅×D₃	—	609	8	no	—
74	C₂₉	C₂×C₅×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
75	C₂×D₇	—	261	1	no	Hall
76	C₃×C₇	C₂×C₅×D₈₇	1	4	yes	complemented
77	C₂²×C₅	—	1827	1	no	Hall
78	C₂×C₃²	C₅×D₂₀₃	1	1	yes	characteristic, complemented
79	C₃⋊D₃	—	203	2	no	—
80	C₃×C₅	C₂×D₆₀₉	1	4	yes	complemented
81	C₂×C₇	C₅×C₃⋊D₈₇	1	1	yes	characteristic, complemented
82	D₇	—	261	2	no	—
83	C₂×D₃	—	609	4	no	—
84	C₂×C₅	—	1827	2	no	—
85	C₂×C₅	C₃⋊D₆₀₉	1	1	yes	characteristic, direct product factor
86	C₃²	C₂×C₅×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₅×C₃⋊D₈₇	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₅×D₆₀₉	1	4	yes	complemented
89	D₃	—	609	8	no	—
90	C₅	C₂×C₃⋊D₆₀₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	1827	1	no	Sylow
92	C₃	C₂×C₅×D₆₀₉	1	4	yes	complemented
93	C₂	—	1827	2	no	—
94	C₂	C₅×C₃⋊D₆₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₆₀₉
commutator, cosocle, hypocenter	C₃²×C₇×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₃²×C₇×C₂₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₆₀₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₂₉	C₂	semidirect
4. C₃²×C₅×C₇×C₂₉	C₂²	semidirect
5. C₂×C₃⋊D₆₀₉	C₅	direct (N × H)
7. C₂×C₃×C₅×C₇×C₂₉	D₃	semidirect
10. C₃⋊D₆₀₉	C₂×C₅	direct (N × H)
11. C₂×C₃²×C₇×C₂₉	C₂×C₅	semidirect
12. C₃×C₅×C₇×C₂₉	C₂×D₃	semidirect
14. C₂×C₃²×C₅×C₂₉	D₇	semidirect
17. C₂×C₅×C₇×C₂₉	C₃⋊D₃	semidirect
18. C₃²×C₇×C₂₉	C₂²×C₅	semidirect
20. C₃²×C₅×C₂₉	C₂×D₇	semidirect
22. C₂×C₃×C₇×C₂₉	C₅×D₃	semidirect
25. C₅×C₇×C₂₉	C₂×C₃⋊D₃	semidirect
26. C₂×C₃×C₅×C₂₉	D₂₁	semidirect
29. C₂×C₃²×C₅×C₇	D₂₉	semidirect
31. C₃×C₇×C₂₉	C₂×C₅×D₃	semidirect
33. C₂×C₃²×C₂₉	C₅×D₇	semidirect
35. C₃×C₅×C₂₉	C₂×D₂₁	semidirect
37. C₂×C₇×C₂₉	C₅×C₃⋊D₃	semidirect
40. C₃²×C₅×C₇	C₂×D₂₉	semidirect
41. C₂×C₅×C₂₉	C₃⋊D₂₁	semidirect
43. C₃²×C₂₉	C₂×C₅×D₇	semidirect
45. C₂×C₃×C₅×C₇	D₈₇	semidirect
47. C₇×C₂₉	C₂×C₅×C₃⋊D₃	semidirect
49. C₂×C₃×C₂₉	C₅×D₂₁	semidirect
51. C₅×C₂₉	C₂×C₃⋊D₂₁	semidirect
53. C₂×C₃²×C₇	C₅×D₂₉	semidirect
56. C₃×C₅×C₇	C₂×D₈₇	semidirect
57. C₂×C₃²×C₅	D₂₀₃	semidirect
59. C₃×C₂₉	C₂×C₅×D₂₁	semidirect
61. C₂×C₅×C₇	C₃⋊D₈₇	semidirect
63. C₃²×C₇	C₂×C₅×D₂₉	semidirect
65. C₂×C₂₉	C₅×C₃⋊D₂₁	semidirect
67. C₃²×C₅	C₂×D₂₀₃	semidirect
68. C₂×C₃×C₇	C₅×D₈₇	semidirect
71. C₅×C₇	C₂×C₃⋊D₈₇	semidirect
72. C₂×C₃×C₅	D₆₀₉	semidirect
74. C₂₉	C₂×C₅×C₃⋊D₂₁	semidirect
76. C₃×C₇	C₂×C₅×D₈₇	semidirect
78. C₂×C₃²	C₅×D₂₀₃	semidirect
80. C₃×C₅	C₂×D₆₀₉	semidirect
81. C₂×C₇	C₅×C₃⋊D₈₇	semidirect
85. C₂×C₅	C₃⋊D₆₀₉	direct (N × H)
86. C₃²	C₂×C₅×D₂₀₃	semidirect
87. C₇	C₂×C₅×C₃⋊D₈₇	semidirect
88. C₂×C₃	C₅×D₆₀₉	semidirect
90. C₅	C₂×C₃⋊D₆₀₉	direct (N × H)
92. C₃	C₂×C₅×D₆₀₉	semidirect
94. C₂	C₅×C₃⋊D₆₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₃⋊D₆₀₉	2
C₂×C₃²×C₅×C₇×C₂₉	2
C₂×C₅×D₆₀₉	3
C₂×C₃⋊D₆₀₉	5
C₂×C₅×C₃⋊D₈₇	7
C₂×C₅×C₃⋊D₂₁	29

Subgroups — C2×C5×C3⋊D609 #49141691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₃⋊D₆₀₉ #49141691