Subgroups — C₅×D₁₇×D₆₅ #36348488

Order 22100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₇×D₆₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₅×D₁₃×D₁₇	—	5	1	no	maximal
7	D₁₁₀₅	C₂×C₅	1	1	yes	characteristic, complemented
8	C₁₇×D₆₅	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₂₂₁	—	5	1	no	—
10	C₅×C₁₇×D₁₃	—	5	1	no	—
11	C₅×C₁₃×D₁₇	—	2	2	no	—
12	C₅×C₁₃×D₁₇	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×D₁₇	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₅×D₁₇	—	13	1	no	maximal, Hall
15	C₂×C₅×D₆₅	—	17	1	no	maximal, Hall
16	C₅×C₁₃×C₁₇	—	2	2	no	—
17	C₅×C₁₃×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
18	C₅×C₁₃×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented
19	D₁₃×D₁₇	—	5	1	no	Hall
20	C₅×D₈₅	—	13	1	no	—
21	C₅×D₅×C₁₇	—	13	1	no	—
22	C₅²×D₁₇	D₁₃	1	1	yes	characteristic, complemented
23	C₂×C₅²×C₁₃	—	17	1	no	—
24	C₅×D₆₅	—	17	1	no	—
25	C₅×D₆₅	D₁₇	1	1	yes	characteristic, direct product factor
26	D₂₂₁	—	5	1	no	—
27	C₁₃×D₁₇	C₅×D₅	1	1	yes	characteristic, complemented
28	C₁₇×D₁₃	—	5	1	no	—
29	C₅²×C₁₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×D₁₇	—	65	1	no	—
31	D₅×D₁₇	—	13	1	no	—
32	C₅²×C₁₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×D₆₅	—	17	1	no	—
34	C₂×C₅×D₁₃	—	85	1	no	—
35	C₁₃×C₁₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₇	—	65	1	no	—
37	D₈₅	—	13	1	no	—
38	C₅×D₁₇	—	2	2	no	—
39	C₅×D₁₇	—	65	1	no	—
40	C₅×D₁₇	C₅×D₁₃	1	1	yes	characteristic, complemented
41	C₅×D₁₇	D₆₅	1	1	yes	characteristic, direct product factor
42	D₅×C₁₇	—	13	1	no	—
43	C₂×C₅×C₁₃	—	17	1	no	—
44	C₂×C₅×C₁₃	—	17	1	no	—
45	C₂×C₅×C₁₃	—	34	2	no	—
46	D₆₅	—	17	1	no	—
47	D₆₅	C₅×D₁₇	1	1	yes	characteristic, direct product factor
48	C₅×D₁₃	—	5	1	no	—
49	C₅×D₁₃	—	85	1	no	—
50	C₂×C₅×D₅	—	221	1	no	Hall
51	C₅×C₁₇	—	2	2	no	—
52	C₅×C₁₇	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented
53	C₅×C₁₇	C₂×D₆₅	1	1	yes	characteristic, complemented
54	C₂×D₁₇	—	65	1	no	Hall
55	C₅×C₁₃	—	2	2	no	—
56	C₅×C₁₃	D₅×D₁₇	1	1	yes	characteristic, complemented
57	C₅×C₁₃	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented
58	C₂×D₁₃	—	85	1	no	Hall
59	C₂×C₅²	—	17	1	no	—
60	C₅×D₅	—	13	1	no	—
61	C₅×D₅	—	221	1	no	—
62	C₂×C₁₇	—	65	1	no	—
63	D₁₇	—	65	1	no	—
64	D₁₇	C₅×D₆₅	1	1	yes	characteristic, direct product factor
65	C₂×C₁₃	—	17	1	no	—
66	D₁₃	—	5	1	no	—
67	D₁₃	—	85	1	no	—
68	C₅²	D₁₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₅	—	1105	1	no	—
70	C₂×D₅	—	221	1	no	—
71	C₁₇	C₂×C₅×D₆₅	1	1	yes	characteristic, complemented, Sylow
72	C₁₃	C₅×D₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	17	1	no	—
74	C₂×C₅	—	17	1	no	—
75	C₂×C₅	—	34	2	no	—
76	C₂×C₅	—	65	1	no	—
77	C₂×C₅	—	1105	1	no	—
78	D₅	—	13	1	no	—
79	D₅	—	221	1	no	—
80	C₅	—	2	2	no	—
81	C₅	C₅×D₁₃×D₁₇	1	1	yes	characteristic, complemented
82	C₅	D₁₇×D₆₅	1	1	yes	characteristic, direct product factor
83	C₂²	—	1105	1	no	Sylow
84	C₂	—	17	1	no	—
85	C₂	—	65	1	no	—
86	C₂	—	1105	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₇×D₆₅
commutator, cosocle, hypocenter	C₅×C₁₃×C₁₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₇	C₂²
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₃×D₁₇	C₂	semidirect
2. C₅×C₁₇×D₆₅	C₂	semidirect
3. C₅×D₁₁₀₅	C₂	semidirect
4. C₅²×C₁₃×C₁₇	C₂²	semidirect
5. D₁₇×D₆₅	C₅	direct (N × H)
7. D₁₁₀₅	C₂×C₅	semidirect
8. C₁₇×D₆₅	C₂×C₅	semidirect
12. C₅×C₁₃×D₁₇	D₅	semidirect
13. C₅×C₁₃×D₁₇	C₂×C₅	semidirect
17. C₅×C₁₃×C₁₇	C₂×D₅	semidirect
18. C₅×C₁₃×C₁₇	C₂²×C₅	semidirect
22. C₅²×D₁₇	D₁₃	semidirect
25. C₅×D₆₅	D₁₇	direct (N × H)
27. C₁₃×D₁₇	C₅×D₅	semidirect
29. C₅²×C₁₇	C₂×D₁₃	semidirect
32. C₅²×C₁₃	C₂×D₁₇	semidirect
35. C₁₃×C₁₇	C₂×C₅×D₅	semidirect
40. C₅×D₁₇	C₅×D₁₃	semidirect
41. C₅×D₁₇	D₆₅	direct (N × H)
47. D₆₅	C₅×D₁₇	direct (N × H)
52. C₅×C₁₇	C₂×C₅×D₁₃	semidirect
53. C₅×C₁₇	C₂×D₆₅	semidirect
56. C₅×C₁₃	D₅×D₁₇	semidirect
57. C₅×C₁₃	C₂×C₅×D₁₇	semidirect
64. D₁₇	C₅×D₆₅	direct (N × H)
68. C₅²	D₁₃×D₁₇	semidirect
71. C₁₇	C₂×C₅×D₆₅	semidirect
72. C₁₃	C₅×D₅×D₁₇	semidirect
81. C₅	C₅×D₁₃×D₁₇	semidirect
82. C₅	D₁₇×D₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₁₃×D₁₇	2
C₅×C₁₇×D₆₅	2
C₅×D₁₁₀₅	2
D₁₇×D₆₅	5
C₅×D₁₃×D₁₇	5
C₅×D₅×D₁₇	13
C₂×C₅×D₆₅	17

Subgroups — C5×D17×D65 #36348488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₇×D₆₅ #36348488