Subgroups — C₂×C₅×D₄×C₁₇ #13062849

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	2	yes	maximal, complemented
2	C₅×D₄×C₁₇	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×C₁₇	—	2	4	no	—
5	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
6	C₂²×C₅×C₁₇	C₂²	1	4	yes	complemented
7	C₄×C₅×C₁₇	C₂²	1	2	yes	complemented
8	C₂×D₄×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₁₇	—	2	4	no	—
10	C₂×C₅×C₁₇	D₄	1	2	yes	direct product factor
11	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
12	C₂³×C₁₇	C₂×C₅	1	2	yes	complemented
13	D₄×C₁₇	C₂×C₅	1	4	yes	direct product factor
14	C₂×C₄×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
15	C₅×C₁₇	C₂×D₄	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×D₄	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₁₇	—	2	4	no	—
18	C₂²×C₁₇	C₂²×C₅	1	1	yes	characteristic
19	C₂²×C₁₇	C₂²×C₅	1	4	yes	complemented
20	C₄×C₁₇	C₂²×C₅	1	2	yes	complemented
21	C₂³×C₅	C₂×C₁₇	1	2	yes	complemented
22	C₅×D₄	C₂×C₁₇	1	4	yes	direct product factor
23	C₂×C₄×C₅	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₂×C₁₇	—	2	4	no	—
25	C₂×C₁₇	C₅×D₄	1	2	yes	direct product factor
26	C₂×C₁₇	C₂³×C₅	1	1	yes	characteristic
27	C₂²×C₅	—	2	4	no	—
28	C₂²×C₅	C₂²×C₁₇	1	1	yes	characteristic
29	C₂²×C₅	C₂²×C₁₇	1	4	yes	complemented
30	C₄×C₅	C₂²×C₁₇	1	2	yes	complemented
31	C₁₇	C₂×C₅×D₄	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×D₄	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₅	—	2	4	no	—
34	C₂×C₅	D₄×C₁₇	1	2	yes	direct product factor
35	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
36	C₂³	C₂×C₅×C₁₇	1	2	yes	complemented
37	D₄	C₂×C₅×C₁₇	1	4	yes	direct product factor
38	C₂×C₄	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
39	C₅	C₂×D₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	2	4	no	—
41	C₂²	C₂²×C₅×C₁₇	1	1	yes	characteristic
42	C₂²	C₂²×C₅×C₁₇	1	4	yes	complemented
43	C₄	C₂²×C₅×C₁₇	1	2	yes	complemented
44	C₂	—	2	4	no	—
45	C₂	C₅×D₄×C₁₇	1	2	yes	direct product factor
46	C₂	C₂³×C₅×C₁₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×C₁₇	C₂	semidirect
2. C₅×D₄×C₁₇	C₂	direct (N × H)
3. C₂×C₄×C₅×C₁₇	C₂	semidirect
6. C₂²×C₅×C₁₇	C₂²	semidirect
7. C₄×C₅×C₁₇	C₂²	semidirect
8. C₂×D₄×C₁₇	C₅	direct (N × H)
10. C₂×C₅×C₁₇	D₄	direct (N × H)
12. C₂³×C₁₇	C₂×C₅	semidirect
13. D₄×C₁₇	C₂×C₅	direct (N × H)
14. C₂×C₄×C₁₇	C₂×C₅	semidirect
15. C₅×C₁₇	C₂×D₄	direct (N × H)
16. C₂×C₅×D₄	C₁₇	direct (N × H)
19. C₂²×C₁₇	C₂²×C₅	semidirect
20. C₄×C₁₇	C₂²×C₅	semidirect
21. C₂³×C₅	C₂×C₁₇	semidirect
22. C₅×D₄	C₂×C₁₇	direct (N × H)
23. C₂×C₄×C₅	C₂×C₁₇	semidirect
25. C₂×C₁₇	C₅×D₄	direct (N × H)
29. C₂²×C₅	C₂²×C₁₇	semidirect
30. C₄×C₅	C₂²×C₁₇	semidirect
31. C₁₇	C₂×C₅×D₄	direct (N × H)
32. C₂×D₄	C₅×C₁₇	direct (N × H)
34. C₂×C₅	D₄×C₁₇	direct (N × H)
36. C₂³	C₂×C₅×C₁₇	semidirect
37. D₄	C₂×C₅×C₁₇	direct (N × H)
38. C₂×C₄	C₂×C₅×C₁₇	semidirect
39. C₅	C₂×D₄×C₁₇	direct (N × H)
42. C₂²	C₂²×C₅×C₁₇	semidirect
43. C₄	C₂²×C₅×C₁₇	semidirect
45. C₂	C₅×D₄×C₁₇	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
C₅×D₄×C₁₇	2
C₂×C₄×C₅×C₁₇	2
C₂×D₄×C₁₇	5
C₂×C₅×D₄	17

Subgroups — C2×C5×D4×C17 #13062849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₄×C₁₇ #13062849