Subgroups — C₂×C₇×C₅⋊D₈₅ #26045461

Order 11900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₅⋊D₈₅	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×C₇×D₈₅	—	5	6	no	maximal
5	C₂×C₅⋊D₈₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₇	D₅	1	6	yes	complemented
7	C₇×D₈₅	—	5	12	no	—
8	C₂×C₅²×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
9	C₅⋊D₈₅	C₂×C₇	1	2	yes	direct product factor
10	C₂×C₇×C₅⋊D₅	—	17	1	no	maximal, Hall
11	C₅×C₇×C₁₇	C₂×D₅	1	6	yes	complemented
12	C₂×C₇×D₁₇	—	25	1	no	Hall
13	C₅²×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅²×C₇	D₁₇	1	1	yes	characteristic, complemented
15	C₇×C₅⋊D₅	—	17	2	no	—
16	C₂×D₈₅	—	5	6	no	—
17	C₂×C₇×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented
18	C₇×D₁₇	—	25	2	no	—
19	C₅²×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₁₇	C₇×D₅	1	6	yes	complemented
21	D₈₅	—	5	12	no	—
22	C₂×C₇×D₅	—	85	6	no	—
23	C₇×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅⋊D₅	—	17	1	no	Hall
25	C₅×C₁₇	C₂×C₇×D₅	1	6	yes	complemented
26	C₂×C₅×C₇	D₈₅	1	6	yes	complemented
27	C₇×D₅	—	85	12	no	—
28	C₂×D₁₇	—	25	1	no	Hall
29	C₂×C₅²	C₇×D₁₇	1	1	yes	characteristic, complemented
30	C₅⋊D₅	—	17	2	no	—
31	C₅×C₇	C₂×D₈₅	1	6	yes	complemented
32	C₂×C₁₇	C₇×C₅⋊D₅	1	1	yes	characteristic, complemented
33	D₁₇	—	25	2	no	—
34	C₂²×C₇	—	425	1	no	Hall
35	C₅²	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
36	C₂×D₅	—	85	6	no	—
37	C₁₇	C₂×C₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₇	—	425	2	no	—
39	C₂×C₇	C₅⋊D₈₅	1	1	yes	characteristic, direct product factor
40	C₂×C₅	C₇×D₈₅	1	6	yes	complemented
41	D₅	—	85	12	no	—
42	C₇	C₂×C₅⋊D₈₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₅	C₂×C₇×D₈₅	1	6	yes	complemented
44	C₂²	—	425	1	no	Sylow
45	C₂	—	425	2	no	—
46	C₂	C₇×C₅⋊D₈₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	C₅⋊D₈₅
commutator, cosocle, hypocenter	C₅²×C₁₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₇	C₂
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₅⋊D₈₅	C₂	direct (N × H)
2. C₂×C₅²×C₇×C₁₇	C₂	semidirect
3. C₅²×C₇×C₁₇	C₂²	semidirect
5. C₂×C₅⋊D₈₅	C₇	direct (N × H)
6. C₂×C₅×C₇×C₁₇	D₅	semidirect
8. C₂×C₅²×C₁₇	C₂×C₇	semidirect
9. C₅⋊D₈₅	C₂×C₇	direct (N × H)
11. C₅×C₇×C₁₇	C₂×D₅	semidirect
13. C₅²×C₁₇	C₂²×C₇	semidirect
14. C₂×C₅²×C₇	D₁₇	semidirect
17. C₂×C₇×C₁₇	C₅⋊D₅	semidirect
19. C₅²×C₇	C₂×D₁₇	semidirect
20. C₂×C₅×C₁₇	C₇×D₅	semidirect
23. C₇×C₁₇	C₂×C₅⋊D₅	semidirect
25. C₅×C₁₇	C₂×C₇×D₅	semidirect
26. C₂×C₅×C₇	D₈₅	semidirect
29. C₂×C₅²	C₇×D₁₇	semidirect
31. C₅×C₇	C₂×D₈₅	semidirect
32. C₂×C₁₇	C₇×C₅⋊D₅	semidirect
35. C₅²	C₂×C₇×D₁₇	semidirect
37. C₁₇	C₂×C₇×C₅⋊D₅	semidirect
39. C₂×C₇	C₅⋊D₈₅	direct (N × H)
40. C₂×C₅	C₇×D₈₅	semidirect
42. C₇	C₂×C₅⋊D₈₅	direct (N × H)
43. C₅	C₂×C₇×D₈₅	semidirect
46. C₂	C₇×C₅⋊D₈₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₅⋊D₈₅	2
C₂×C₅²×C₇×C₁₇	2
C₂×C₇×D₈₅	5
C₂×C₅⋊D₈₅	7
C₂×C₇×C₅⋊D₅	17

Subgroups — C2×C7×C5⋊D85 #26045461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₅⋊D₈₅ #26045461