Subgroups — D₅×Dic₃₄ #13062794

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	C₄×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₃₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#10621757	C₂	1	2	yes	maximal, complemented
5	D₅×Dic₁₇	C₂	1	2	yes	maximal
6	C₂×D₅×C₁₇	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	2	yes	—
10	C₁₇×Dic₅	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₄	—	5	1	no	maximal, Hall
12	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
13	D₅×C₁₇	Q₈	1	2	yes	complemented
14	C₂×C₄×C₁₇	—	5	1	no	—
15	C₂×Dic₁₇	—	5	2	no	—
16	Dic₃₄	—	5	1	no	—
17	Dic₃₄	—	5	2	no	—
18	Dic₃₄	D₅	1	1	yes	characteristic, direct product factor
19	C₅×C₁₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
20	Q₈×D₅	—	17	1	no	maximal, Hall
21	C₂²×C₁₇	—	5	1	no	—
22	C₄×C₁₇	—	5	1	no	—
23	C₄×C₁₇	C₂×D₅	1	1	yes	characteristic
24	Dic₁₇	—	5	2	no	—
25	Dic₁₇	C₂×D₅	1	2	yes	—
26	C₅×Q₈	—	17	1	no	—
27	C₄×D₅	—	17	2	no	—
28	C₄×D₅	D₁₇	1	1	yes	characteristic
29	Dic₁₀	—	17	1	no	—
30	Dic₁₀	—	17	2	no	—
31	C₂×C₁₇	—	5	2	no	—
32	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
33	C₂×D₅	C₂×D₁₇	1	1	yes	characteristic
34	C₄×C₅	—	17	2	no	—
35	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic
36	Dic₅	—	17	2	no	—
37	Dic₅	C₂×D₁₇	1	1	yes	characteristic
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	Dic₃₄	1	2	yes	direct product factor
42	Q₈	—	17	1	no	—
43	Q₈	—	85	2	no	—
44	Q₈	—	85	1	no	—
45	C₂×C₄	—	5	1	no	—
46	C₂×C₄	—	85	2	no	—
47	C₅	C₂×Dic₃₄	1	1	yes	characteristic, complemented, Sylow
48	C₂²	—	5	1	no	—
49	C₄	—	5	1	no	—
50	C₄	—	17	2	no	—
51	C₄	—	85	2	no	—
52	C₄	D₅×D₁₇	1	1	yes	characteristic
53	C₂	—	5	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×D₅×C₁₇	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
3. C₅×Dic₃₄	C₂	semidirect
4. #10621757	C₂	semidirect
13. D₅×C₁₇	Q₈	semidirect
18. Dic₃₄	D₅	direct (N × H)
19. C₅×C₁₇	C₂×Q₈	semidirect
38. C₁₇	Q₈×D₅	semidirect
41. D₅	Dic₃₄	direct (N × H)
47. C₅	C₂×Dic₃₄	semidirect

Maximal subgroups

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

subgroup	index
Dic₁₇₀	2
C₄×D₅×C₁₇	2
C₅×Dic₃₄	2
#10621757	2
D₅×Dic₁₇	2
C₂×Dic₃₄	5
Q₈×D₅	17

Subgroups — D5×Dic34 #13062794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×Dic₃₄ #13062794