Subgroups — C₂×C₅²×C₇×D₁₇ #26045469

Order 11900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×D₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₇×D₁₇	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₇	C₂×C₅	1	6	yes	complemented
7	C₅×C₇×D₁₇	C₂×C₅	1	12	yes	direct product factor
8	C₂×C₅²×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
9	C₅²×D₁₇	C₂×C₇	1	2	yes	direct product factor
10	C₂²×C₅²×C₇	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₂²×C₅	1	6	yes	complemented
12	C₂×C₇×D₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₅²×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅²×C₇	—	17	2	no	—
15	C₂×C₅²×C₇	D₁₇	1	1	yes	characteristic, direct product factor
16	C₂×C₅×D₁₇	C₅×C₇	1	6	yes	direct product factor
17	C₂×C₇×C₁₇	C₂×C₅²	1	1	yes	characteristic, complemented
18	C₇×D₁₇	C₂×C₅²	1	2	yes	direct product factor
19	C₅²×C₇	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₇	C₂×C₅×C₇	1	6	yes	complemented
21	C₅×D₁₇	C₂×C₅×C₇	1	12	yes	direct product factor
22	C₂²×C₅×C₇	—	17	6	no	—
23	C₇×C₁₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₅²	—	17	1	no	Hall
25	C₅×C₁₇	C₂²×C₅×C₇	1	6	yes	complemented
26	C₂×C₅×C₇	—	17	12	no	—
27	C₂×C₅×C₇	C₅×D₁₇	1	6	yes	direct product factor
28	C₂×D₁₇	C₅²×C₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅²	—	17	2	no	—
30	C₂×C₅²	C₇×D₁₇	1	1	yes	characteristic, direct product factor
31	C₅×C₇	C₂×C₅×D₁₇	1	6	yes	direct product factor
32	C₂×C₁₇	C₂×C₅²×C₇	1	1	yes	characteristic, complemented
33	D₁₇	C₂×C₅²×C₇	1	2	yes	direct product factor
34	C₂²×C₇	—	17	1	no	Hall
35	C₅²	C₂×C₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₅	—	17	6	no	—
37	C₁₇	C₂²×C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₇	—	17	2	no	—
39	C₂×C₇	C₅²×D₁₇	1	1	yes	characteristic, direct product factor
40	C₂×C₅	—	17	12	no	—
41	C₂×C₅	C₅×C₇×D₁₇	1	6	yes	direct product factor
42	C₇	C₂×C₅²×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₅	C₂×C₅×C₇×D₁₇	1	6	yes	direct product factor
44	C₂²	—	17	1	no	Sylow
45	C₂	—	17	2	no	—
46	C₂	C₅²×C₇×D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₅²×C₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×D₁₇	C₂	direct (N × H)
2. C₂×C₅²×C₇×C₁₇	C₂	semidirect
3. C₅²×C₇×C₁₇	C₂²	semidirect
4. C₂×C₅×C₇×D₁₇	C₅	direct (N × H)
5. C₂×C₅²×D₁₇	C₇	direct (N × H)
6. C₂×C₅×C₇×C₁₇	C₂×C₅	semidirect
7. C₅×C₇×D₁₇	C₂×C₅	direct (N × H)
8. C₂×C₅²×C₁₇	C₂×C₇	semidirect
9. C₅²×D₁₇	C₂×C₇	direct (N × H)
11. C₅×C₇×C₁₇	C₂²×C₅	semidirect
12. C₂×C₇×D₁₇	C₅²	direct (N × H)
13. C₅²×C₁₇	C₂²×C₇	semidirect
15. C₂×C₅²×C₇	D₁₇	direct (N × H)
16. C₂×C₅×D₁₇	C₅×C₇	direct (N × H)
17. C₂×C₇×C₁₇	C₂×C₅²	semidirect
18. C₇×D₁₇	C₂×C₅²	direct (N × H)
19. C₅²×C₇	C₂×D₁₇	direct (N × H)
20. C₂×C₅×C₁₇	C₂×C₅×C₇	semidirect
21. C₅×D₁₇	C₂×C₅×C₇	direct (N × H)
23. C₇×C₁₇	C₂²×C₅²	semidirect
25. C₅×C₁₇	C₂²×C₅×C₇	semidirect
27. C₂×C₅×C₇	C₅×D₁₇	direct (N × H)
28. C₂×D₁₇	C₅²×C₇	direct (N × H)
30. C₂×C₅²	C₇×D₁₇	direct (N × H)
31. C₅×C₇	C₂×C₅×D₁₇	direct (N × H)
32. C₂×C₁₇	C₂×C₅²×C₇	semidirect
33. D₁₇	C₂×C₅²×C₇	direct (N × H)
35. C₅²	C₂×C₇×D₁₇	direct (N × H)
37. C₁₇	C₂²×C₅²×C₇	semidirect
39. C₂×C₇	C₅²×D₁₇	direct (N × H)
41. C₂×C₅	C₅×C₇×D₁₇	direct (N × H)
42. C₇	C₂×C₅²×D₁₇	direct (N × H)
43. C₅	C₂×C₅×C₇×D₁₇	direct (N × H)
46. C₂	C₅²×C₇×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
C₅²×C₇×D₁₇	2
C₂×C₅²×C₇×C₁₇	2
C₂×C₅×C₇×D₁₇	5
C₂×C₅²×D₁₇	7
C₂²×C₅²×C₇	17

Subgroups — C2×C52×C7×D17 #26045469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×C₇×D₁₇ #26045469