Subgroups — C₂×C₁₇×C₂²⋊D₅ #13062837

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×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₂²⋊D₅	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₇×Dic₅	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×D₅×C₁₇	—	2	2	no	—
9	C₂×D₅×C₁₇	C₂²	1	2	yes	complemented
10	C₁₇×Dic₅	C₂²	1	2	yes	complemented
11	C₂×D₄×C₁₇	—	5	1	no	maximal, 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	D₅×C₁₇	—	2	2	no	—
16	C₂³×C₁₇	—	5	1	no	—
17	C₂³×C₁₇	D₅	1	1	yes	characteristic, complemented
18	D₄×C₁₇	—	5	4	no	—
19	C₂×C₄×C₁₇	—	5	1	no	—
20	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂²⋊D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₁₇	—	2	2	no	—
23	C₂²×C₁₇	—	5	2	no	—
24	C₂²×C₁₇	—	10	2	no	—
25	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
26	C₂²×C₁₇	C₂×D₅	1	2	yes	complemented
27	C₄×C₁₇	—	5	2	no	—
28	C₂³×C₅	C₂×C₁₇	1	1	yes	characteristic, complemented
29	C₂²×D₅	C₂×C₁₇	1	1	yes	characteristic, complemented
30	C₂²⋊D₅	C₂×C₁₇	1	4	yes	direct product factor
31	C₂×Dic₅	C₂×C₁₇	1	1	yes	characteristic, complemented
32	C₂×C₁₇	—	2	2	no	—
33	C₂×C₁₇	—	10	2	no	—
34	C₂×C₁₇	C₂²⋊D₅	1	2	yes	direct product factor
35	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
36	C₂²×C₅	—	2	2	no	—
37	C₂²×C₅	C₂²×C₁₇	1	1	yes	characteristic
38	C₂²×C₅	C₂²×C₁₇	1	2	yes	complemented
39	C₂×D₅	—	2	2	no	—
40	C₂×D₅	C₂²×C₁₇	1	2	yes	complemented
41	Dic₅	C₂²×C₁₇	1	2	yes	complemented
42	C₁₇	C₂×C₂²⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×D₄	—	5	1	no	Sylow
44	C₂×C₅	—	2	2	no	—
45	C₂×C₅	D₄×C₁₇	1	2	yes	complemented
46	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
47	D₅	—	2	2	no	—
48	C₂³	—	5	1	no	—
49	C₂³	D₅×C₁₇	1	1	yes	characteristic, complemented
50	D₄	—	5	4	no	—
51	C₂×C₄	—	5	1	no	—
52	C₅	C₂×D₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	2	2	no	—
54	C₂²	—	5	2	no	—
55	C₂²	—	10	2	no	—
56	C₂²	C₂×D₅×C₁₇	1	1	yes	characteristic
57	C₂²	C₂×D₅×C₁₇	1	2	yes	complemented
58	C₄	—	5	2	no	—
59	C₂	—	2	2	no	—
60	C₂	—	10	2	no	—
61	C₂	C₁₇×C₂²⋊D₅	1	2	yes	direct product factor
62	C₂	C₂²×D₅×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₇	C₂×D₅
commutator, cosocle	C₂×C₅	C₂³×C₁₇
Frattini	C₂	C₂²×D₅×C₁₇
Fitting	C₂³×C₅×C₁₇	C₂
socle	C₂²×C₅×C₁₇	C₂²
hypercenter	C₂³×C₁₇	D₅
hypocenter	C₅	C₂×D₄×C₁₇
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×C₁₇	C₂	semidirect
2. C₂²×D₅×C₁₇	C₂	semidirect
3. C₁₇×C₂²⋊D₅	C₂	direct (N × H)
4. C₂×C₁₇×Dic₅	C₂	semidirect
7. C₂²×C₅×C₁₇	C₂²	semidirect
9. C₂×D₅×C₁₇	C₂²	semidirect
10. C₁₇×Dic₅	C₂²	semidirect
13. C₂×C₅×C₁₇	D₄	semidirect
17. C₂³×C₁₇	D₅	semidirect
20. C₅×C₁₇	C₂×D₄	semidirect
21. C₂×C₂²⋊D₅	C₁₇	direct (N × H)
26. C₂²×C₁₇	C₂×D₅	semidirect
28. C₂³×C₅	C₂×C₁₇	semidirect
29. C₂²×D₅	C₂×C₁₇	semidirect
30. C₂²⋊D₅	C₂×C₁₇	direct (N × H)
31. C₂×Dic₅	C₂×C₁₇	semidirect
34. C₂×C₁₇	C₂²⋊D₅	direct (N × H)
38. C₂²×C₅	C₂²×C₁₇	semidirect
40. C₂×D₅	C₂²×C₁₇	semidirect
41. Dic₅	C₂²×C₁₇	semidirect
42. C₁₇	C₂×C₂²⋊D₅	direct (N × H)
45. C₂×C₅	D₄×C₁₇	semidirect
49. C₂³	D₅×C₁₇	semidirect
52. C₅	C₂×D₄×C₁₇	semidirect
57. C₂²	C₂×D₅×C₁₇	semidirect
61. C₂	C₁₇×C₂²⋊D₅	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×D₅×C₁₇	2
C₁₇×C₂²⋊D₅	2
C₂×C₁₇×Dic₅	2
C₂×D₄×C₁₇	5
C₂×C₂²⋊D₅	17

Subgroups — C2×C17×C22⋊D5 #13062837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₂²⋊D₅ #13062837