Subgroups — C₅×D₁₅×D₁₇ #19099803

Order 5100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅²×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₅×D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅×D₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×D₃×D₁₇	—	5	1	no	maximal
8	C₅×D₈₅	—	3	1	no	—
9	C₅×D₅×C₁₇	—	3	1	no	—
10	C₅²×D₁₇	D₃	1	1	yes	characteristic, complemented
11	D₂₅₅	C₂×C₅	1	1	yes	characteristic, complemented
12	C₁₇×D₁₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₅₁	—	5	1	no	—
14	C₅×D₃×C₁₇	—	5	1	no	—
15	C₃×C₅×D₁₇	—	2	2	no	—
16	C₃×C₅×D₁₇	D₅	1	1	yes	characteristic, complemented
17	C₃×C₅×D₁₇	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₁₇	—	15	1	no	—
20	D₅×D₁₇	—	3	1	no	—
21	C₂×C₅×D₁₅	—	17	1	no	maximal, Hall
22	C₃×C₅×C₁₇	—	2	2	no	—
23	C₃×C₅×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented
25	D₃×D₁₇	—	5	1	no	Hall
26	C₂×C₅×C₁₇	—	15	1	no	—
27	D₈₅	—	3	1	no	—
28	C₅×D₁₇	—	2	2	no	—
29	C₅×D₁₇	—	15	1	no	—
30	C₅×D₁₇	C₅×D₃	1	1	yes	characteristic, complemented
31	C₅×D₁₇	D₁₅	1	1	yes	characteristic, direct product factor
32	D₅×C₁₇	—	3	1	no	—
33	C₂×C₃×C₅²	—	17	1	no	—
34	C₅×D₁₅	—	17	1	no	—
35	C₅×D₁₅	D₁₇	1	1	yes	characteristic, direct product factor
36	D₅₁	—	5	1	no	—
37	C₃×D₁₇	C₅×D₅	1	1	yes	characteristic, complemented
38	D₃×C₁₇	—	5	1	no	—
39	C₂×C₅×D₅	—	51	1	no	Hall
40	C₅×C₁₇	—	2	2	no	—
41	C₅×C₁₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented
42	C₅×C₁₇	C₂×D₁₅	1	1	yes	characteristic, complemented
43	C₃×C₅²	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₁₇	—	15	1	no	Hall
45	C₂×D₁₅	—	17	1	no	—
46	C₂×C₅×D₃	—	85	1	no	—
47	C₃×C₁₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅²	—	17	1	no	—
49	C₅×D₅	—	3	1	no	—
50	C₅×D₅	—	51	1	no	—
51	C₂×C₁₇	—	15	1	no	—
52	D₁₇	—	15	1	no	—
53	D₁₇	C₅×D₁₅	1	1	yes	characteristic, direct product factor
54	C₂×C₃×C₅	—	17	1	no	—
55	C₂×C₃×C₅	—	17	1	no	—
56	C₂×C₃×C₅	—	34	2	no	—
57	D₁₅	—	17	1	no	—
58	D₁₅	C₅×D₁₇	1	1	yes	characteristic, direct product factor
59	C₅×D₃	—	5	1	no	—
60	C₅×D₃	—	85	1	no	—
61	C₅²	D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₅	—	255	1	no	—
63	C₂×D₅	—	51	1	no	—
64	C₁₇	C₂×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₁₇	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented
68	C₂×D₃	—	85	1	no	Hall
69	C₂×C₅	—	15	1	no	—
70	C₂×C₅	—	17	1	no	—
71	C₂×C₅	—	17	1	no	—
72	C₂×C₅	—	34	2	no	—
73	C₂×C₅	—	255	1	no	—
74	D₅	—	3	1	no	—
75	D₅	—	51	1	no	—
76	C₂×C₃	—	17	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	85	1	no	—
79	C₅	—	2	2	no	—
80	C₅	C₅×D₃×D₁₇	1	1	yes	characteristic, complemented
81	C₅	D₁₅×D₁₇	1	1	yes	characteristic, direct product factor
82	C₂²	—	255	1	no	Sylow
83	C₃	C₅×D₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	15	1	no	—
85	C₂	—	17	1	no	—
86	C₂	—	255	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₅×D₁₇
commutator, hypocenter	C₃×C₅×C₁₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₇	C₂²
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₂₅₅	C₂	semidirect
2. C₅×C₁₇×D₁₅	C₂	semidirect
3. C₃×C₅²×D₁₇	C₂	semidirect
5. C₃×C₅²×C₁₇	C₂²	semidirect
6. D₁₅×D₁₇	C₅	direct (N × H)
10. C₅²×D₁₇	D₃	semidirect
11. D₂₅₅	C₂×C₅	semidirect
12. C₁₇×D₁₅	C₂×C₅	semidirect
16. C₃×C₅×D₁₇	D₅	semidirect
17. C₃×C₅×D₁₇	C₂×C₅	semidirect
18. C₅²×C₁₇	C₂×D₃	semidirect
23. C₃×C₅×C₁₇	C₂×D₅	semidirect
24. C₃×C₅×C₁₇	C₂²×C₅	semidirect
30. C₅×D₁₇	C₅×D₃	semidirect
31. C₅×D₁₇	D₁₅	direct (N × H)
35. C₅×D₁₅	D₁₇	direct (N × H)
37. C₃×D₁₇	C₅×D₅	semidirect
41. C₅×C₁₇	C₂×C₅×D₃	semidirect
42. C₅×C₁₇	C₂×D₁₅	semidirect
43. C₃×C₅²	C₂×D₁₇	semidirect
47. C₃×C₁₇	C₂×C₅×D₅	semidirect
53. D₁₇	C₅×D₁₅	direct (N × H)
58. D₁₅	C₅×D₁₇	direct (N × H)
61. C₅²	D₃×D₁₇	semidirect
64. C₁₇	C₂×C₅×D₁₅	semidirect
66. C₃×C₅	D₅×D₁₇	semidirect
67. C₃×C₅	C₂×C₅×D₁₇	semidirect
80. C₅	C₅×D₃×D₁₇	semidirect
81. C₅	D₁₅×D₁₇	direct (N × H)
83. C₃	C₅×D₅×D₁₇	semidirect

Subgroups — C5×D15×D17 #19099803

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₁₅×D₁₇ #19099803