Subgroups — D₁₇×Dic₁₀ #13062791

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₇₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#10621757	C₂	1	2	yes	maximal, complemented
5	Dic₅×D₁₇	C₂	1	2	yes	maximal
6	C₂×C₅×D₁₇	C₂²	1	1	yes	characteristic
7	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic
8	Dic₈₅	C₂²	1	2	yes	—
9	C₅×Dic₁₇	C₂²	1	1	yes	characteristic
10	C₁₇×Dic₅	C₂²	1	2	yes	—
11	Q₈×D₁₇	—	5	1	no	maximal, Hall
12	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
13	C₅×D₁₇	Q₈	1	2	yes	complemented
14	Q₈×C₁₇	—	5	1	no	—
15	C₄×D₁₇	—	5	2	no	—
16	C₄×D₁₇	D₅	1	1	yes	characteristic
17	Dic₃₄	—	5	1	no	—
18	Dic₃₄	—	5	2	no	—
19	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
20	C₂×Dic₁₀	—	17	1	no	maximal, Hall
21	C₂×D₁₇	C₂×D₅	1	1	yes	characteristic
22	C₄×C₁₇	—	5	2	no	—
23	C₄×C₁₇	C₂×D₅	1	1	yes	characteristic
24	Dic₁₇	—	5	2	no	—
25	Dic₁₇	C₂×D₅	1	1	yes	characteristic
26	C₂×C₄×C₅	—	17	1	no	—
27	C₂×Dic₅	—	17	2	no	—
28	Dic₁₀	—	17	1	no	—
29	Dic₁₀	—	17	2	no	—
30	Dic₁₀	D₁₇	1	1	yes	characteristic, direct product factor
31	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
32	D₁₇	Dic₁₀	1	2	yes	direct product factor
33	C₂²×C₅	—	17	1	no	—
34	C₄×C₅	—	17	1	no	—
35	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic
36	Dic₅	—	17	2	no	—
37	Dic₅	C₂×D₁₇	1	2	yes	—
38	C₁₇	C₂×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	85	1	no	Sylow
40	C₂×C₅	—	17	2	no	—
41	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
42	Q₈	—	5	1	no	—
43	Q₈	—	85	2	no	—
44	Q₈	—	85	1	no	—
45	C₂×C₄	—	17	1	no	—
46	C₂×C₄	—	85	2	no	—
47	C₅	Q₈×D₁₇	1	1	yes	characteristic, complemented, Sylow
48	C₂²	—	17	1	no	—
49	C₄	—	5	2	no	—
50	C₄	—	17	1	no	—
51	C₄	—	85	2	no	—
52	C₄	D₅×D₁₇	1	1	yes	characteristic
53	C₂	—	17	2	no	—
54	C₂	C₂×D₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₅×D₁₇
commutator, socle, cosocle	C₂×C₅×C₁₇	C₂³
Fitting	C₄×C₅×C₁₇	C₂²
prime radical	C₂×C₅×D₁₇	C₂²
hypercenter	C₄	D₅×D₁₇
hypocenter	C₅×C₁₇	C₂×Q₈
LCS	G ▷ C₂×C₅×C₁₇ ▷ C₅×C₁₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. Dic₁₇₀	C₂	semidirect
2. C₁₇×Dic₁₀	C₂	semidirect
4. #10621757	C₂	semidirect
13. C₅×D₁₇	Q₈	semidirect
19. C₅×C₁₇	C₂×Q₈	semidirect
30. Dic₁₀	D₁₇	direct (N × H)
32. D₁₇	Dic₁₀	direct (N × H)
38. C₁₇	C₂×Dic₁₀	semidirect
47. C₅	Q₈×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
Dic₁₇₀	2
C₁₇×Dic₁₀	2
C₄×C₅×D₁₇	2
#10621757	2
Dic₅×D₁₇	2
Q₈×D₁₇	5
C₂×Dic₁₀	17

Subgroups — D17×Dic10 #13062791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×Dic₁₀ #13062791