Subgroups — C₂×C₅×C₂²⋊D₁₇ #13062827

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂²⋊D₁₇	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×C₁₇	—	2	2	no	—
6	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
7	C₂²×C₅×C₁₇	C₂²	1	2	yes	complemented
8	C₂×C₅×D₁₇	—	2	2	no	—
9	C₂×C₅×D₁₇	C₂²	1	2	yes	complemented
10	C₅×Dic₁₇	C₂²	1	2	yes	complemented
11	C₂×C₂²⋊D₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₁₇	—	2	2	no	—
13	C₂×C₅×C₁₇	D₄	1	2	yes	complemented
14	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
15	C₅×D₁₇	—	2	2	no	—
16	C₂³×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂²×D₁₇	C₂×C₅	1	1	yes	characteristic, complemented
18	C₂²⋊D₁₇	C₂×C₅	1	4	yes	direct product factor
19	C₂×Dic₁₇	C₂×C₅	1	1	yes	characteristic, complemented
20	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×D₄	—	17	1	no	maximal, Hall
22	C₂²×C₁₇	—	2	2	no	—
23	C₂²×C₁₇	C₂²×C₅	1	1	yes	characteristic
24	C₂²×C₁₇	C₂²×C₅	1	2	yes	complemented
25	C₂×D₁₇	—	2	2	no	—
26	C₂×D₁₇	C₂²×C₅	1	2	yes	complemented
27	Dic₁₇	C₂²×C₅	1	2	yes	complemented
28	C₂³×C₅	—	17	1	no	—
29	C₂³×C₅	D₁₇	1	1	yes	characteristic, complemented
30	C₅×D₄	—	17	4	no	—
31	C₂×C₄×C₅	—	17	1	no	—
32	C₂×C₁₇	—	2	2	no	—
33	C₂×C₁₇	C₅×D₄	1	2	yes	complemented
34	C₂×C₁₇	C₂³×C₅	1	1	yes	characteristic
35	D₁₇	—	2	2	no	—
36	C₂²×C₅	—	2	2	no	—
37	C₂²×C₅	—	17	2	no	—
38	C₂²×C₅	—	34	2	no	—
39	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
40	C₂²×C₅	C₂×D₁₇	1	2	yes	complemented
41	C₄×C₅	—	17	2	no	—
42	C₁₇	C₂×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₄	—	17	1	no	Sylow
44	C₂×C₅	—	2	2	no	—
45	C₂×C₅	—	34	2	no	—
46	C₂×C₅	C₂²⋊D₁₇	1	2	yes	direct product factor
47	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
48	C₂³	—	17	1	no	—
49	C₂³	C₅×D₁₇	1	1	yes	characteristic, complemented
50	D₄	—	17	4	no	—
51	C₂×C₄	—	17	1	no	—
52	C₅	C₂×C₂²⋊D₁₇	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²	—	2	2	no	—
54	C₂²	—	17	2	no	—
55	C₂²	—	34	2	no	—
56	C₂²	C₂×C₅×D₁₇	1	1	yes	characteristic
57	C₂²	C₂×C₅×D₁₇	1	2	yes	complemented
58	C₄	—	17	2	no	—
59	C₂	—	2	2	no	—
60	C₂	—	34	2	no	—
61	C₂	C₅×C₂²⋊D₁₇	1	2	yes	direct product factor
62	C₂	C₂²×C₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₁₇
commutator, cosocle	C₂×C₁₇	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₁₇
Fitting	C₂³×C₅×C₁₇	C₂
socle	C₂²×C₅×C₁₇	C₂²
hypercenter	C₂³×C₅	D₁₇
hypocenter	C₁₇	C₂×C₅×D₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×C₁₇	C₂	semidirect
2. C₂²×C₅×D₁₇	C₂	semidirect
3. C₅×C₂²⋊D₁₇	C₂	direct (N × H)
4. C₂×C₅×Dic₁₇	C₂	semidirect
7. C₂²×C₅×C₁₇	C₂²	semidirect
9. C₂×C₅×D₁₇	C₂²	semidirect
10. C₅×Dic₁₇	C₂²	semidirect
11. C₂×C₂²⋊D₁₇	C₅	direct (N × H)
13. C₂×C₅×C₁₇	D₄	semidirect
16. C₂³×C₁₇	C₂×C₅	semidirect
17. C₂²×D₁₇	C₂×C₅	semidirect
18. C₂²⋊D₁₇	C₂×C₅	direct (N × H)
19. C₂×Dic₁₇	C₂×C₅	semidirect
20. C₅×C₁₇	C₂×D₄	semidirect
24. C₂²×C₁₇	C₂²×C₅	semidirect
26. C₂×D₁₇	C₂²×C₅	semidirect
27. Dic₁₇	C₂²×C₅	semidirect
29. C₂³×C₅	D₁₇	semidirect
33. C₂×C₁₇	C₅×D₄	semidirect
40. C₂²×C₅	C₂×D₁₇	semidirect
42. C₁₇	C₂×C₅×D₄	semidirect
46. C₂×C₅	C₂²⋊D₁₇	direct (N × H)
49. C₂³	C₅×D₁₇	semidirect
52. C₅	C₂×C₂²⋊D₁₇	direct (N × H)
57. C₂²	C₂×C₅×D₁₇	semidirect
61. C₂	C₅×C₂²⋊D₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₁₇	2
C₂²×C₅×D₁₇	2
C₅×C₂²⋊D₁₇	2
C₂×C₅×Dic₁₇	2
C₂×C₂²⋊D₁₇	5
C₂×C₅×D₄	17

Subgroups — C2×C5×C22⋊D17 #13062827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂²⋊D₁₇ #13062827