Subgroups — C₂×C₉×C₁₇×C₅⋊D₅ #29505831

Order 15300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

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

Maximal subgroups

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

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

Subgroups — C2×C9×C17×C5⋊D5 #29505831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₇×C₅⋊D₅ #29505831