Subgroups — D₈₅⋊Q₈ #13062797

Order 1360.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₃₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#10621757	C₂	1	2	yes	maximal, complemented
5	#10621753	C₂	1	2	yes	maximal
6	C₂×D₈₅	C₂²	1	1	yes	characteristic
7	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic
8	Dic₈₅	C₂²	1	1	yes	characteristic
9	C₅×Dic₁₇	C₂²	1	2	yes	—
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	D₈₅	Q₈	1	2	yes	complemented
14	Q₈×C₁₇	—	5	1	no	—
15	C₄×D₁₇	—	5	1	no	—
16	C₄×D₁₇	—	5	2	no	—
17	Dic₃₄	—	5	2	no	—
18	Dic₃₄	D₅	1	1	yes	characteristic, complemented
19	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
20	Q₈×D₅	—	17	1	no	maximal, Hall
21	C₂×D₁₇	—	5	1	no	—
22	C₄×C₁₇	—	5	2	no	—
23	C₄×C₁₇	C₂×D₅	1	1	yes	characteristic
24	Dic₁₇	—	5	1	no	—
25	Dic₁₇	C₂×D₅	1	2	yes	—
26	C₅×Q₈	—	17	1	no	—
27	C₄×D₅	—	17	1	no	—
28	C₄×D₅	—	17	2	no	—
29	Dic₁₀	—	17	2	no	—
30	Dic₁₀	D₁₇	1	1	yes	characteristic, complemented
31	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
32	D₁₇	—	5	2	no	—
33	C₂×D₅	—	17	1	no	—
34	C₄×C₅	—	17	2	no	—
35	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic
36	Dic₅	—	17	1	no	—
37	Dic₅	C₂×D₁₇	1	2	yes	—
38	C₁₇	Q₈×D₅	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	85	1	no	Sylow
40	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
41	D₅	—	17	2	no	—
42	Q₈	—	5	1	no	—
43	Q₈	—	17	1	no	—
44	Q₈	—	85	2	no	—
45	C₂×C₄	—	85	2	no	—
46	C₂×C₄	—	85	1	no	—
47	C₅	Q₈×D₁₇	1	1	yes	characteristic, complemented, Sylow
48	C₂²	—	85	1	no	—
49	C₄	—	5	2	no	—
50	C₄	—	17	2	no	—
51	C₄	—	85	1	no	—
52	C₄	D₅×D₁₇	1	1	yes	characteristic
53	C₂	—	85	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×D₈₅	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
2. C₁₇×Dic₁₀	C₂	semidirect
3. C₅×Dic₃₄	C₂	semidirect
4. #10621757	C₂	semidirect
13. D₈₅	Q₈	semidirect
18. Dic₃₄	D₅	semidirect
19. C₅×C₁₇	C₂×Q₈	semidirect
30. Dic₁₀	D₁₇	semidirect
38. C₁₇	Q₈×D₅	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
C₄×D₈₅	2
C₁₇×Dic₁₀	2
C₅×Dic₃₄	2
#10621757	2
#10621753	2
Q₈×D₁₇	5
Q₈×D₅	17

Subgroups — D85⋊Q8 #13062797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈₅⋊Q₈ #13062797