Subgroups — Q₈×D₅×C₁₇ #13062834

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₁₇	C₂²×D₅
commutator, cosocle	C₂×C₅	C₂³×C₁₇
Frattini	C₂	C₂²×D₅×C₁₇
Fitting	C₅×Q₈×C₁₇	C₂
socle	C₂×C₅×C₁₇	C₂³
prime radical	C₂×D₅×C₁₇	C₂²
hypercenter	Q₈×C₁₇	D₅
hypocenter	C₅	C₂×Q₈×C₁₇
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₇ ◁ Q₈×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×Q₈×C₁₇	C₂	semidirect
3. C₁₇×Dic₁₀	C₂	semidirect
9. D₅×C₁₇	Q₈	direct (N × H)
11. Q₈×C₁₇	D₅	direct (N × H)
13. C₅×C₁₇	C₂×Q₈	semidirect
14. Q₈×D₅	C₁₇	direct (N × H)
18. C₅×Q₈	C₂×C₁₇	semidirect
20. Dic₁₀	C₂×C₁₇	semidirect
26. C₁₇	Q₈×D₅	direct (N × H)
29. D₅	Q₈×C₁₇	direct (N × H)
31. Q₈	D₅×C₁₇	direct (N × H)
33. C₅	C₂×Q₈×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×Q₈×C₁₇	2
C₄×D₅×C₁₇	2
C₁₇×Dic₁₀	2
C₂×Q₈×C₁₇	5
Q₈×D₅	17

Subgroups — Q8×D5×C17 #13062834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×D₅×C₁₇ #13062834