Subgroups — D₃×C₅⋊D₃₅ #14523658

Order 2100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₃₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₃₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₃₅	—	5	6	no	maximal
7	C₂×C₅²×C₇	—	3	1	no	—
8	C₅⋊D₃₅	—	3	1	no	—
9	C₅⋊D₃₅	D₃	1	1	yes	characteristic, direct product factor
10	D₃×C₅⋊D₅	—	7	1	no	maximal, Hall
11	D₁₀₅	—	5	6	no	—
12	C₅×D₃×C₇	D₅	1	6	yes	complemented
13	C₃×D₃₅	—	5	6	no	—
14	C₅²×C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₃⋊(C₅⋊D₅)	—	7	1	no	—
16	C₅²×D₃	D₇	1	1	yes	characteristic, complemented
17	C₃×C₅⋊D₅	—	7	1	no	—
18	C₂×D₃₅	—	15	6	no	—
19	C₃×C₅×C₇	C₂×D₅	1	6	yes	complemented
20	C₂×C₅⋊D₅	—	21	1	no	Hall
21	D₃×D₇	—	25	1	no	Hall
22	C₃×C₅²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₇	—	3	6	no	—
24	D₃₅	—	5	6	no	—
25	D₃₅	—	15	6	no	—
26	D₃×D₅	—	35	6	no	—
27	C₂×C₅²	—	3	1	no	—
28	C₅⋊D₅	—	7	1	no	—
29	C₅⋊D₅	—	21	1	no	—
30	D₂₁	—	25	1	no	—
31	C₃×D₇	—	25	1	no	—
32	D₃×C₇	C₅⋊D₅	1	1	yes	characteristic, complemented
33	C₅×C₇	D₃×D₅	1	6	yes	complemented
34	D₁₅	—	35	6	no	—
35	C₃×D₅	—	35	6	no	—
36	C₅×D₃	D₃₅	1	6	yes	complemented
37	C₂×D₇	—	75	1	no	Hall
38	C₅²	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
40	C₂×D₅	—	105	6	no	—
41	C₃×C₅	C₂×D₃₅	1	6	yes	complemented
42	C₂×C₇	—	3	1	no	—
43	D₇	—	25	1	no	—
44	D₇	—	75	1	no	—
45	C₂×D₃	—	175	1	no	Hall
46	C₂×C₅	—	3	6	no	—
47	D₅	—	35	6	no	—
48	D₅	—	105	6	no	—
49	C₇	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	175	1	no	—
51	D₃	—	175	1	no	—
52	D₃	C₅⋊D₃₅	1	1	yes	characteristic, direct product factor
53	C₅	D₃×D₃₅	1	6	yes	complemented
54	C₂²	—	525	1	no	Sylow
55	C₃	C₂×C₅⋊D₃₅	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	525	1	no	—
58	C₂	—	175	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₇	C₂²
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₃₅)	C₂	semidirect
2. C₅²×D₃×C₇	C₂	semidirect
3. C₃×C₅⋊D₃₅	C₂	semidirect
5. C₃×C₅²×C₇	C₂²	semidirect
9. C₅⋊D₃₅	D₃	direct (N × H)
12. C₅×D₃×C₇	D₅	semidirect
14. C₅²×C₇	C₂×D₃	semidirect
16. C₅²×D₃	D₇	semidirect
19. C₃×C₅×C₇	C₂×D₅	semidirect
22. C₃×C₅²	C₂×D₇	semidirect
32. D₃×C₇	C₅⋊D₅	semidirect
33. C₅×C₇	D₃×D₅	semidirect
36. C₅×D₃	D₃₅	semidirect
38. C₅²	D₃×D₇	semidirect
39. C₃×C₇	C₂×C₅⋊D₅	semidirect
41. C₃×C₅	C₂×D₃₅	semidirect
49. C₇	D₃×C₅⋊D₅	semidirect
52. D₃	C₅⋊D₃₅	direct (N × H)
53. C₅	D₃×D₃₅	semidirect
55. C₃	C₂×C₅⋊D₃₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₅⋊D₃₅)	2
C₅²×D₃×C₇	2
C₃×C₅⋊D₃₅	2
C₂×C₅⋊D₃₅	3
D₃×D₃₅	5
D₃×C₅⋊D₅	7

Subgroups — D3×C5⋊D35 #14523658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₅⋊D₃₅ #14523658