Subgroups — D₅×D₁₆₀₅ #44545688

Order 32100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₆₀₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₅⋊D₅₃₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₃₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₆₀₅	—	5	1	no	maximal
7	D₅×D₃₂₁	—	5	1	no	maximal
8	C₅⋊D₅₃₅	—	3	1	no	—
9	C₅×D₅₃₅	—	3	1	no	—
10	C₅×D₅×C₁₀₇	D₃	1	1	yes	characteristic, complemented
11	D₁₆₀₅	—	5	1	no	—
12	D₁₆₀₅	—	5	1	no	—
13	D₁₆₀₅	—	10	2	no	—
14	D₁₆₀₅	D₅	1	1	yes	characteristic, direct product factor
15	C₅×D₃₂₁	—	5	1	no	—
16	C₃×D₅×C₁₀₇	D₅	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×C₁₀₇	—	5	1	no	—
18	C₅²×C₁₀₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₅₃₅	—	15	1	no	—
20	D₅×D₁₀₇	—	15	1	no	—
21	C₃×C₅×C₁₀₇	—	2	2	no	—
22	C₃×C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented
24	C₂×D₃₂₁	—	25	1	no	Hall
25	C₂×C₅×C₁₀₇	—	5	1	no	—
26	D₅₃₅	—	3	1	no	—
27	D₅₃₅	—	15	1	no	—
28	D₅₃₅	—	15	1	no	—
29	D₅₃₅	—	30	2	no	—
30	C₅×D₁₀₇	—	15	1	no	—
31	D₅×C₁₀₇	D₁₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₁₀₇	—	5	1	no	—
33	D₃₂₁	—	5	1	no	—
34	D₃₂₁	—	25	1	no	—
35	C₅×C₁₀₇	—	2	2	no	—
36	C₅×C₁₀₇	D₃×D₅	1	1	yes	characteristic, complemented
37	C₅×C₁₀₇	C₂×D₁₅	1	1	yes	characteristic, complemented
38	C₂×D₁₀₇	—	75	1	no	Hall
39	C₃×C₁₀₇	D₅²	1	1	yes	characteristic, complemented, Hall
40	D₅×D₁₅	—	107	1	no	maximal, Hall
41	C₂×C₁₀₇	—	5	1	no	—
42	D₁₀₇	—	15	1	no	—
43	D₁₀₇	—	75	1	no	—
44	C₃⋊(C₅⋊D₅)	—	107	1	no	—
45	C₅×D₁₅	—	107	1	no	—
46	C₃×C₅×D₅	D₁₀₇	1	1	yes	characteristic, complemented
47	C₁₀₇	D₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
48	D₅²	—	321	1	no	Hall
49	C₃×C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₅	—	535	1	no	—
51	D₃×D₅	—	535	1	no	—
52	C₅⋊D₅	—	321	1	no	—
53	C₅×D₅	—	321	1	no	—
54	C₅×D₅	D₃₂₁	1	1	yes	characteristic, complemented
55	C₂×C₃×C₅	—	5	1	no	—
56	D₁₅	—	535	1	no	—
57	D₁₅	—	535	1	no	—
58	D₁₅	—	1070	2	no	—
59	D₁₅	—	107	1	no	—
60	C₃×D₅	D₅₃₅	1	1	yes	characteristic, complemented
61	C₅×D₃	—	535	1	no	—
62	C₅²	C₂×D₃₂₁	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	1605	1	no	—
64	C₂×D₅	—	1605	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₁₀₇	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₅₃₅	1	1	yes	characteristic, complemented
68	C₂×D₃	—	2675	1	no	Hall
69	C₂×C₅	—	5	1	no	—
70	C₂×C₅	—	1605	1	no	—
71	D₅	—	321	1	no	—
72	D₅	—	1605	1	no	—
73	D₅	—	1605	1	no	—
74	D₅	—	3210	2	no	—
75	D₅	D₁₆₀₅	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	5	1	no	—
77	D₃	—	535	1	no	—
78	D₃	—	2675	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₅×D₃₂₁	1	1	yes	characteristic, complemented
81	C₅	C₂×D₁₆₀₅	1	1	yes	characteristic, complemented
82	C₂²	—	8025	1	no	Sylow
83	C₃	D₅×D₅₃₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	1605	1	no	—
86	C₂	—	8025	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₁₀₇	C₂²
LCS	G ▷ C₃×C₅²×C₁₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅×C₁₀₇	C₂	semidirect
2. C₅×D₁₆₀₅	C₂	semidirect
3. C₃⋊(C₅⋊D₅₃₅)	C₂	semidirect
5. C₃×C₅²×C₁₀₇	C₂²	semidirect
10. C₅×D₅×C₁₀₇	D₃	semidirect
14. D₁₆₀₅	D₅	direct (N × H)
16. C₃×D₅×C₁₀₇	D₅	semidirect
18. C₅²×C₁₀₇	C₂×D₃	semidirect
22. C₃×C₅×C₁₀₇	C₂×D₅	semidirect
23. C₃×C₅×C₁₀₇	C₂×D₅	semidirect
31. D₅×C₁₀₇	D₁₅	semidirect
36. C₅×C₁₀₇	D₃×D₅	semidirect
37. C₅×C₁₀₇	C₂×D₁₅	semidirect
39. C₃×C₁₀₇	D₅²	semidirect
46. C₃×C₅×D₅	D₁₀₇	semidirect
47. C₁₀₇	D₅×D₁₅	semidirect
49. C₃×C₅²	C₂×D₁₀₇	semidirect
54. C₅×D₅	D₃₂₁	semidirect
60. C₃×D₅	D₅₃₅	semidirect
62. C₅²	C₂×D₃₂₁	semidirect
66. C₃×C₅	D₅×D₁₀₇	semidirect
67. C₃×C₅	C₂×D₅₃₅	semidirect
75. D₅	D₁₆₀₅	direct (N × H)
80. C₅	D₅×D₃₂₁	semidirect
81. C₅	C₂×D₁₆₀₅	semidirect
83. C₃	D₅×D₅₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₅×C₁₀₇	2
C₅×D₁₆₀₅	2
C₃⋊(C₅⋊D₅₃₅)	2
D₅×D₅₃₅	3
C₂×D₁₆₀₅	5
D₅×D₃₂₁	5
D₅×D₁₅	107

Subgroups — D5×D1605 #44545688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₆₀₅ #44545688