Subgroups — C₂×C₁₇×C₅⋊D₄₅ #29505837

Order 15300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅⋊D₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₃⋊(C₅⋊D₅)	—	3	1	no	maximal
4	C₅²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₄₅	—	5	6	no	maximal
6	C₁₇×C₃⋊(C₅⋊D₅)	—	3	2	no	—
7	C₂×C₃×C₅²×C₁₇	D₃	1	1	yes	characteristic
8	C₂×C₁₇×C₅⋊D₅	—	9	1	no	Hall
9	C₂×C₅×C₉×C₁₇	D₅	1	6	yes	complemented
10	C₁₇×D₄₅	—	5	12	no	—
11	C₃×C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic
12	C₂×C₁₇×D₁₅	—	15	6	no	—
13	C₂×C₅⋊D₄₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅²×C₁₇	D₉	1	1	yes	characteristic, complemented
15	C₁₇×C₅⋊D₅	—	9	2	no	—
16	C₅×C₉×C₁₇	C₂×D₅	1	6	yes	complemented
17	C₂×C₁₇×D₉	—	25	1	no	Hall
18	C₂×C₃×C₅×C₁₇	D₁₅	1	6	yes	—
19	C₁₇×D₁₅	—	15	12	no	—
20	C₂×C₅²×C₉	C₂×C₁₇	1	1	yes	characteristic, complemented
21	C₅⋊D₄₅	C₂×C₁₇	1	2	yes	direct product factor
22	C₅²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₇	—	45	6	no	—
24	C₂×C₉×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented
25	C₁₇×D₉	—	25	2	no	—
26	C₂×C₃⋊(C₅⋊D₅)	—	3	1	no	—
27	C₃×C₅×C₁₇	C₂×D₁₅	1	6	yes	—
28	C₅²×C₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₂×D₃×C₁₇	—	75	1	no	—
30	C₂×D₄₅	—	5	6	no	—
31	C₂×C₅×C₁₇	D₄₅	1	6	yes	complemented
32	D₅×C₁₇	—	45	12	no	—
33	C₉×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅²	D₃×C₁₇	1	1	yes	characteristic
35	C₃⋊(C₅⋊D₅)	—	3	2	no	—
36	C₂×C₃×C₁₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
37	D₃×C₁₇	—	75	2	no	—
38	C₂×C₅⋊D₅	—	9	1	no	Hall
39	C₂×C₅×C₉	D₅×C₁₇	1	6	yes	complemented
40	D₄₅	—	5	12	no	—
41	C₅×C₁₇	C₂×D₄₅	1	6	yes	complemented
42	C₃×C₅²	C₂×D₃×C₁₇	1	1	yes	characteristic
43	C₂²×C₁₇	—	225	1	no	Hall
44	C₂×D₁₅	—	15	6	no	—
45	C₃×C₁₇	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
46	C₂×C₅²	C₁₇×D₉	1	1	yes	characteristic, complemented
47	C₅⋊D₅	—	9	2	no	—
48	C₅×C₉	C₂×D₅×C₁₇	1	6	yes	complemented
49	C₂×D₉	—	25	1	no	Hall
50	C₂×C₁₇	—	225	2	no	—
51	C₂×C₁₇	C₅⋊D₄₅	1	1	yes	characteristic, direct product factor
52	C₂×C₃×C₅	C₁₇×D₁₅	1	6	yes	—
53	D₁₅	—	15	12	no	—
54	C₅²	C₂×C₁₇×D₉	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₅	—	45	6	no	—
56	C₂×C₉	C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented
57	D₉	—	25	2	no	—
58	C₁₇	C₂×C₅⋊D₄₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₅	C₂×C₁₇×D₁₅	1	6	yes	—
60	C₂×D₃	—	75	1	no	—
61	C₂×C₅	C₁₇×D₄₅	1	6	yes	complemented
62	D₅	—	45	12	no	—
63	C₉	C₂×C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₁₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
65	D₃	—	75	2	no	—
66	C₅	C₂×C₁₇×D₄₅	1	6	yes	complemented
67	C₂²	—	225	1	no	Sylow
68	C₃	C₂×C₁₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
69	C₂	—	225	2	no	—
70	C₂	C₁₇×C₅⋊D₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₅⋊D₄₅
commutator, cosocle, hypocenter	C₅²×C₉	C₂²×C₁₇
Frattini	C₃	C₂×C₁₇×C₃⋊(C₅⋊D₅)
Fitting	C₂×C₅²×C₉×C₁₇	C₂
socle	C₂×C₃×C₅²×C₁₇	D₃
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅⋊D₄₅	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₁₇	C₂	semidirect
4. C₅²×C₉×C₁₇	C₂²	semidirect
9. C₂×C₅×C₉×C₁₇	D₅	semidirect
13. C₂×C₅⋊D₄₅	C₁₇	direct (N × H)
14. C₂×C₅²×C₁₇	D₉	semidirect
16. C₅×C₉×C₁₇	C₂×D₅	semidirect
20. C₂×C₅²×C₉	C₂×C₁₇	semidirect
21. C₅⋊D₄₅	C₂×C₁₇	direct (N × H)
22. C₅²×C₁₇	C₂×D₉	semidirect
24. C₂×C₉×C₁₇	C₅⋊D₅	semidirect
28. C₅²×C₉	C₂²×C₁₇	semidirect
31. C₂×C₅×C₁₇	D₄₅	semidirect
33. C₉×C₁₇	C₂×C₅⋊D₅	semidirect
39. C₂×C₅×C₉	D₅×C₁₇	semidirect
41. C₅×C₁₇	C₂×D₄₅	semidirect
46. C₂×C₅²	C₁₇×D₉	semidirect
48. C₅×C₉	C₂×D₅×C₁₇	semidirect
51. C₂×C₁₇	C₅⋊D₄₅	direct (N × H)
54. C₅²	C₂×C₁₇×D₉	semidirect
56. C₂×C₉	C₁₇×C₅⋊D₅	semidirect
58. C₁₇	C₂×C₅⋊D₄₅	direct (N × H)
61. C₂×C₅	C₁₇×D₄₅	semidirect
63. C₉	C₂×C₁₇×C₅⋊D₅	semidirect
66. C₅	C₂×C₁₇×D₄₅	semidirect
70. C₂	C₁₇×C₅⋊D₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₅⋊D₄₅	2
C₂×C₅²×C₉×C₁₇	2
C₂×C₁₇×C₃⋊(C₅⋊D₅)	3
C₂×C₁₇×D₄₅	5
C₂×C₅⋊D₄₅	17

Subgroups — C2×C17×C5⋊D45 #29505837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₅⋊D₄₅ #29505837