Subgroups — C₂×C₁₇×D₂₀ #13062830

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₁₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×D₂₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
5	C₂×D₅×C₁₇	—	2	4	no	—
6	C₂×D₅×C₁₇	C₂²	1	4	yes	complemented
7	C₄×C₅×C₁₇	C₂²	1	2	yes	complemented
8	C₂×D₄×C₁₇	—	5	1	no	maximal, Hall
9	C₂×C₅×C₁₇	D₄	1	2	yes	complemented
10	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
11	D₅×C₁₇	—	2	4	no	—
12	C₂³×C₁₇	—	5	2	no	—
13	D₄×C₁₇	—	5	4	no	—
14	C₂×C₄×C₁₇	D₅	1	1	yes	characteristic, complemented
15	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
16	C₂×D₂₀	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₁₇	—	5	4	no	—
18	C₂²×C₁₇	—	10	4	no	—
19	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
20	C₄×C₁₇	C₂×D₅	1	2	yes	complemented
21	C₂²×D₅	C₂×C₁₇	1	2	yes	complemented
22	C₂×C₄×C₅	C₂×C₁₇	1	1	yes	characteristic, complemented
23	D₂₀	C₂×C₁₇	1	4	yes	direct product factor
24	C₂×C₁₇	—	10	4	no	—
25	C₂×C₁₇	D₂₀	1	2	yes	direct product factor
26	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
27	C₂²×C₅	C₂²×C₁₇	1	1	yes	characteristic
28	C₂×D₅	—	2	4	no	—
29	C₂×D₅	C₂²×C₁₇	1	4	yes	complemented
30	C₄×C₅	C₂²×C₁₇	1	2	yes	complemented
31	C₁₇	C₂×D₂₀	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×D₄	—	5	1	no	Sylow
33	C₂×C₅	D₄×C₁₇	1	2	yes	complemented
34	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
35	D₅	—	2	4	no	—
36	C₂³	—	5	2	no	—
37	D₄	—	5	4	no	—
38	C₂×C₄	D₅×C₁₇	1	1	yes	characteristic, complemented
39	C₅	C₂×D₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
40	C₂²	—	5	4	no	—
41	C₂²	—	10	4	no	—
42	C₂²	C₂×D₅×C₁₇	1	1	yes	characteristic
43	C₄	C₂×D₅×C₁₇	1	2	yes	complemented
44	C₂	—	10	4	no	—
45	C₂	C₁₇×D₂₀	1	2	yes	direct product factor
46	C₂	C₂²×D₅×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₇	C₂×D₅
commutator, cosocle	C₂×C₅	C₂³×C₁₇
Frattini	C₂	C₂²×D₅×C₁₇
Fitting	C₂×C₄×C₅×C₁₇	C₂
socle	C₂²×C₅×C₁₇	C₂²
hypercenter	C₂×C₄×C₁₇	D₅
hypocenter	C₅	C₂×D₄×C₁₇
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅×C₁₇	C₂	semidirect
2. C₂×C₄×C₅×C₁₇	C₂	semidirect
3. C₁₇×D₂₀	C₂	direct (N × H)
6. C₂×D₅×C₁₇	C₂²	semidirect
7. C₄×C₅×C₁₇	C₂²	semidirect
9. C₂×C₅×C₁₇	D₄	semidirect
14. C₂×C₄×C₁₇	D₅	semidirect
15. C₅×C₁₇	C₂×D₄	semidirect
16. C₂×D₂₀	C₁₇	direct (N × H)
20. C₄×C₁₇	C₂×D₅	semidirect
21. C₂²×D₅	C₂×C₁₇	semidirect
22. C₂×C₄×C₅	C₂×C₁₇	semidirect
23. D₂₀	C₂×C₁₇	direct (N × H)
25. C₂×C₁₇	D₂₀	direct (N × H)
29. C₂×D₅	C₂²×C₁₇	semidirect
30. C₄×C₅	C₂²×C₁₇	semidirect
31. C₁₇	C₂×D₂₀	direct (N × H)
33. C₂×C₅	D₄×C₁₇	semidirect
38. C₂×C₄	D₅×C₁₇	semidirect
39. C₅	C₂×D₄×C₁₇	semidirect
43. C₄	C₂×D₅×C₁₇	semidirect
45. C₂	C₁₇×D₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₁₇	2
C₂×C₄×C₅×C₁₇	2
C₁₇×D₂₀	2
C₂×D₄×C₁₇	5
C₂×D₂₀	17

Subgroups — C2×C17×D20 #13062830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×D₂₀ #13062830