Subgroups — D₄×D₅×C₁₇ #13062832

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₁₇	C₂	1	2	yes	maximal, complemented
2	C₅×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
4	C₁₇×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₁₇	C₂²	1	2	yes	complemented
7	C₂×D₅×C₁₇	—	2	4	no	—
8	C₂×D₅×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×D₅×C₁₇	C₂²	1	2	yes	complemented
10	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic, complemented
11	C₁₇×Dic₅	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₄×C₁₇	—	5	1	no	maximal, Hall
13	C₂×C₅×C₁₇	—	2	2	no	—
14	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
15	D₅×C₁₇	—	2	2	no	—
16	D₅×C₁₇	D₄	1	2	yes	direct product factor
17	C₂³×C₁₇	—	5	2	no	—
18	D₄×C₁₇	—	5	2	no	—
19	D₄×C₁₇	—	5	1	no	—
20	D₄×C₁₇	D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₄×C₁₇	—	5	1	no	—
22	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
23	D₄×D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₁₇	—	5	1	no	—
25	C₂²×C₁₇	—	5	2	no	—
26	C₂²×C₁₇	—	10	4	no	—
27	C₂²×C₁₇	C₂×D₅	1	2	yes	complemented
28	C₄×C₁₇	—	5	1	no	—
29	C₄×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
30	C₂²×D₅	C₂×C₁₇	1	2	yes	complemented
31	C₅×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
32	C₂²⋊D₅	C₂×C₁₇	1	2	yes	complemented
33	D₂₀	C₂×C₁₇	1	1	yes	characteristic, complemented
34	C₄×D₅	C₂×C₁₇	1	1	yes	characteristic, complemented
35	C₂×C₁₇	—	2	2	no	—
36	C₂×C₁₇	—	5	2	no	—
37	C₂×C₁₇	—	10	2	no	—
38	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
39	C₂²×C₅	C₂²×C₁₇	1	2	yes	complemented
40	C₂×D₅	—	2	4	no	—
41	C₂×D₅	C₂²×C₁₇	1	1	yes	characteristic
42	C₂×D₅	C₂²×C₁₇	1	2	yes	complemented
43	C₄×C₅	C₂²×C₁₇	1	1	yes	characteristic, complemented
44	Dic₅	C₂²×C₁₇	1	1	yes	characteristic, complemented
45	C₁₇	D₄×D₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×D₄	—	5	1	no	Sylow
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
49	D₅	—	2	2	no	—
50	D₅	D₄×C₁₇	1	2	yes	direct product factor
51	C₂³	—	5	2	no	—
52	D₄	—	5	2	no	—
53	D₄	—	5	1	no	—
54	D₄	D₅×C₁₇	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	5	1	no	—
56	C₅	C₂×D₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	5	1	no	—
58	C₂²	—	5	2	no	—
59	C₂²	—	10	4	no	—
60	C₂²	C₂×D₅×C₁₇	1	2	yes	complemented
61	C₄	—	5	1	no	—
62	C₄	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented
63	C₂	—	2	2	no	—
64	C₂	—	5	2	no	—
65	C₂	—	10	2	no	—
66	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×D₄×C₁₇	C₂
socle	C₂×C₅×C₁₇	C₂³
hypercenter	D₄×C₁₇	D₅
hypocenter	C₅	C₂×D₄×C₁₇
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₇ ◁ D₄×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅×C₁₇	C₂	semidirect
2. C₅×D₄×C₁₇	C₂	semidirect
3. C₁₇×C₂²⋊D₅	C₂	semidirect
4. C₁₇×D₂₀	C₂	semidirect
5. C₄×D₅×C₁₇	C₂	semidirect
6. C₂²×C₅×C₁₇	C₂²	semidirect
9. C₂×D₅×C₁₇	C₂²	semidirect
10. C₄×C₅×C₁₇	C₂²	semidirect
11. C₁₇×Dic₅	C₂²	semidirect
16. D₅×C₁₇	D₄	direct (N × H)
20. D₄×C₁₇	D₅	direct (N × H)
22. C₅×C₁₇	C₂×D₄	semidirect
23. D₄×D₅	C₁₇	direct (N × H)
27. C₂²×C₁₇	C₂×D₅	semidirect
29. C₄×C₁₇	C₂×D₅	semidirect
30. C₂²×D₅	C₂×C₁₇	semidirect
31. C₅×D₄	C₂×C₁₇	semidirect
32. C₂²⋊D₅	C₂×C₁₇	semidirect
33. D₂₀	C₂×C₁₇	semidirect
34. C₄×D₅	C₂×C₁₇	semidirect
39. C₂²×C₅	C₂²×C₁₇	semidirect
42. C₂×D₅	C₂²×C₁₇	semidirect
43. C₄×C₅	C₂²×C₁₇	semidirect
44. Dic₅	C₂²×C₁₇	semidirect
45. C₁₇	D₄×D₅	direct (N × H)
50. D₅	D₄×C₁₇	direct (N × H)
54. D₄	D₅×C₁₇	direct (N × H)
56. C₅	C₂×D₄×C₁₇	semidirect
60. C₂²	C₂×D₅×C₁₇	semidirect
62. C₄	C₂×D₅×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₁₇	2
C₅×D₄×C₁₇	2
C₁₇×C₂²⋊D₅	2
C₁₇×D₂₀	2
C₄×D₅×C₁₇	2
C₂×D₄×C₁₇	5
D₄×D₅	17

Subgroups — D4×D5×C17 #13062832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₅×C₁₇ #13062832