Subgroups — C₂×C₁₇×Dic₁₀ #13062828

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×Dic₅	C₂	1	2	yes	maximal
3	C₁₇×Dic₁₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
5	C₄×C₅×C₁₇	C₂²	1	2	yes	—
6	C₁₇×Dic₅	C₂²	1	4	yes	—
7	C₂×Q₈×C₁₇	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₇	Q₈	1	2	yes	complemented
9	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
10	Q₈×C₁₇	—	5	4	no	—
11	C₂×C₄×C₁₇	—	5	2	no	—
12	C₂×C₄×C₁₇	D₅	1	1	yes	characteristic
13	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
14	C₂×Dic₁₀	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
16	C₄×C₁₇	—	5	4	no	—
17	C₄×C₁₇	C₂×D₅	1	2	yes	—
18	C₂×C₄×C₅	C₂×C₁₇	1	1	yes	characteristic
19	C₂×Dic₅	C₂×C₁₇	1	2	yes	—
20	Dic₁₀	C₂×C₁₇	1	4	yes	direct product factor
21	C₂×C₁₇	Dic₁₀	1	2	yes	direct product factor
22	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
23	C₂²×C₅	C₂²×C₁₇	1	1	yes	characteristic
24	C₄×C₅	C₂²×C₁₇	1	2	yes	—
25	Dic₅	C₂²×C₁₇	1	4	yes	—
26	C₁₇	C₂×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×Q₈	—	5	1	no	Sylow
28	C₂×C₅	Q₈×C₁₇	1	2	yes	complemented
29	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
30	Q₈	—	5	4	no	—
31	C₂×C₄	—	5	2	no	—
32	C₂×C₄	D₅×C₁₇	1	1	yes	characteristic
33	C₅	C₂×Q₈×C₁₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	C₂×D₅×C₁₇	1	1	yes	characteristic
35	C₄	—	5	4	no	—
36	C₄	C₂×D₅×C₁₇	1	2	yes	—
37	C₂	C₁₇×Dic₁₀	1	2	yes	direct product factor
38	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, prime radical	C₂²×C₅×C₁₇	C₂²
hypercenter	C₂×C₄×C₁₇	D₅
hypocenter	C₅	C₂×Q₈×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
3. C₁₇×Dic₁₀	C₂	direct (N × H)
8. C₂×C₅×C₁₇	Q₈	semidirect
13. C₅×C₁₇	C₂×Q₈	semidirect
14. C₂×Dic₁₀	C₁₇	direct (N × H)
20. Dic₁₀	C₂×C₁₇	direct (N × H)
21. C₂×C₁₇	Dic₁₀	direct (N × H)
26. C₁₇	C₂×Dic₁₀	direct (N × H)
28. C₂×C₅	Q₈×C₁₇	semidirect
33. C₅	C₂×Q₈×C₁₇	semidirect
37. C₂	C₁₇×Dic₁₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₇	2
C₂×C₁₇×Dic₅	2
C₁₇×Dic₁₀	2
C₂×Q₈×C₁₇	5
C₂×Dic₁₀	17

Subgroups — C2×C17×Dic10 #13062828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×Dic₁₀ #13062828