Subgroups — C₂×C₁₇×D₂₈₅ #34084404

Order 19380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₂₈₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₉₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₅₇	—	5	1	no	maximal, Hall
6	C₁₇×D₉₅	—	3	2	no	—
7	C₂×C₅×C₁₇×C₁₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₇×C₁₉	D₅	1	1	yes	characteristic, complemented
9	C₁₇×D₅₇	—	5	2	no	—
10	C₅×C₁₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×D₁₉	—	15	1	no	Hall
12	C₂×D₂₈₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₇×D₁₅	—	19	1	no	maximal, Hall
14	C₃×C₁₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₇×C₁₉	D₁₅	1	1	yes	characteristic, complemented
16	C₁₇×D₁₉	—	15	2	no	—
17	C₂×C₃×C₅×C₁₉	C₂×C₁₇	1	1	yes	characteristic, complemented
18	D₂₈₅	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×C₃×C₅×C₁₇	D₁₉	1	1	yes	characteristic, complemented
20	C₁₇×D₁₅	—	19	2	no	—
21	C₂×D₉₅	—	3	1	no	Hall
22	C₂×D₅×C₁₇	—	57	1	no	Hall
23	C₁₇×C₁₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×C₁₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₅₇	—	5	1	no	Hall
27	C₂×D₃×C₁₇	—	95	1	no	Hall
28	C₂×C₅×C₁₉	D₃×C₁₇	1	1	yes	characteristic, complemented
29	D₉₅	—	3	2	no	—
30	C₂×C₅×C₁₇	D₅₇	1	1	yes	characteristic, complemented
31	D₅×C₁₇	—	57	2	no	—
32	C₂×C₃×C₁₉	D₅×C₁₇	1	1	yes	characteristic, complemented
33	D₅₇	—	5	2	no	—
34	C₂×C₃×C₁₇	D₉₅	1	1	yes	characteristic, complemented
35	D₃×C₁₇	—	95	2	no	—
36	C₅×C₁₉	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
37	C₅×C₁₇	C₂×D₅₇	1	1	yes	characteristic, complemented, Hall
38	C₂×D₁₉	—	15	1	no	Hall
39	C₂²×C₁₇	—	285	1	no	Hall
40	C₂×D₁₅	—	19	1	no	Hall
41	C₃×C₁₉	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₇	C₂×D₉₅	1	1	yes	characteristic, complemented, Hall
43	C₂×C₁₉	C₁₇×D₁₅	1	1	yes	characteristic, complemented
44	D₁₉	—	15	2	no	—
45	C₂×C₁₇	—	285	2	no	—
46	C₂×C₁₇	D₂₈₅	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₅	C₁₇×D₁₉	1	1	yes	characteristic, complemented
48	D₁₅	—	19	2	no	—
49	C₂×D₅	—	57	1	no	Hall
50	C₁₉	C₂×C₁₇×D₁₅	1	1	yes	characteristic, complemented, Sylow
51	C₁₇	C₂×D₂₈₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	C₂×C₁₇×D₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃	—	95	1	no	Hall
54	C₂×C₅	C₁₇×D₅₇	1	1	yes	characteristic, complemented
55	D₅	—	57	2	no	—
56	C₂×C₃	C₁₇×D₉₅	1	1	yes	characteristic, complemented
57	D₃	—	95	2	no	—
58	C₅	C₂×C₁₇×D₅₇	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	285	1	no	Sylow
60	C₃	C₂×C₁₇×D₉₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	285	2	no	—
62	C₂	C₁₇×D₂₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₂₈₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₁₉	C₂
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₂₈₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₇×C₁₉	C₂²	semidirect
7. C₂×C₅×C₁₇×C₁₉	D₃	semidirect
8. C₂×C₃×C₁₇×C₁₉	D₅	semidirect
10. C₅×C₁₇×C₁₉	C₂×D₃	semidirect
12. C₂×D₂₈₅	C₁₇	direct (N × H)
14. C₃×C₁₇×C₁₉	C₂×D₅	semidirect
15. C₂×C₁₇×C₁₉	D₁₅	semidirect
17. C₂×C₃×C₅×C₁₉	C₂×C₁₇	semidirect
18. D₂₈₅	C₂×C₁₇	direct (N × H)
19. C₂×C₃×C₅×C₁₇	D₁₉	semidirect
23. C₁₇×C₁₉	C₂×D₁₅	semidirect
24. C₃×C₅×C₁₉	C₂²×C₁₇	semidirect
25. C₃×C₅×C₁₇	C₂×D₁₉	semidirect
28. C₂×C₅×C₁₉	D₃×C₁₇	semidirect
30. C₂×C₅×C₁₇	D₅₇	semidirect
32. C₂×C₃×C₁₉	D₅×C₁₇	semidirect
34. C₂×C₃×C₁₇	D₉₅	semidirect
36. C₅×C₁₉	C₂×D₃×C₁₇	semidirect
37. C₅×C₁₇	C₂×D₅₇	semidirect
41. C₃×C₁₉	C₂×D₅×C₁₇	semidirect
42. C₃×C₁₇	C₂×D₉₅	semidirect
43. C₂×C₁₉	C₁₇×D₁₅	semidirect
46. C₂×C₁₇	D₂₈₅	direct (N × H)
47. C₂×C₃×C₅	C₁₇×D₁₉	semidirect
50. C₁₉	C₂×C₁₇×D₁₅	semidirect
51. C₁₇	C₂×D₂₈₅	direct (N × H)
52. C₃×C₅	C₂×C₁₇×D₁₉	semidirect
54. C₂×C₅	C₁₇×D₅₇	semidirect
56. C₂×C₃	C₁₇×D₉₅	semidirect
58. C₅	C₂×C₁₇×D₅₇	semidirect
60. C₃	C₂×C₁₇×D₉₅	semidirect
62. C₂	C₁₇×D₂₈₅	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×D₂₈₅	2
C₂×C₃×C₅×C₁₇×C₁₉	2
C₂×C₁₇×D₉₅	3
C₂×C₁₇×D₅₇	5
C₂×D₂₈₅	17
C₂×C₁₇×D₁₅	19

Subgroups — C2×C17×D285 #34084404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×D₂₈₅ #34084404