Subgroups — C₂²×C₇×C₁₇×C₅²⋊C₃ #49088037

Order 35700.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₇×C₅²⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₇×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₇×C₅²⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅²×C₇×C₁₇	C₂×C₃	1	3	yes	complemented
5	C₂²×C₁₇×C₅²⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅²×C₇×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₇×C₅²⋊C₃	C₂×C₇	1	3	yes	direct product factor
8	C₂²×C₅×C₇×C₁₇	—	3	2	no	—
9	C₂²×C₇×C₅²⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₅²×C₁₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₃×C₇×C₁₇	—	25	1	no	maximal, Hall
12	C₁₇×C₅²⋊C₃	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅×C₇×C₁₇	—	3	6	no	—
14	C₂×C₇×C₅²⋊C₃	C₂×C₁₇	1	3	yes	direct product factor
15	C₂×C₅²×C₁₇	C₂×C₃×C₇	1	3	yes	complemented
16	C₂×C₃×C₇×C₁₇	—	25	3	no	—
17	C₂²×C₅²×C₇	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₅×C₇×C₁₇	—	3	2	no	—
19	C₇×C₅²⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₇×C₁₇	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₅²×C₁₇	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇×C₁₇	—	25	1	no	Hall
23	C₂×C₅²×C₇	C₂×C₃×C₁₇	1	3	yes	complemented
24	C₂²×C₅×C₁₇	—	3	2	no	—
25	C₂²×C₅²⋊C₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₇×C₁₇	C₂×C₅²⋊C₃	1	3	yes	direct product factor
27	C₂²×C₃×C₁₇	—	25	1	no	Hall
28	C₅²×C₇	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₁₇	—	3	6	no	—
30	C₂×C₅²⋊C₃	C₂×C₇×C₁₇	1	3	yes	direct product factor
31	C₂²×C₅×C₇	—	3	2	no	—
32	C₇×C₁₇	C₂²×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₁₇	—	25	3	no	—
34	C₂²×C₅²	C₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₅×C₁₇	—	3	2	no	—
36	C₂²×C₃×C₇	—	25	1	no	Hall
37	C₅²⋊C₃	C₂²×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₅×C₇	—	3	6	no	—
39	C₂²×C₁₇	C₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₁₇	—	25	1	no	Hall
41	C₂×C₅²	C₂×C₃×C₇×C₁₇	1	3	yes	complemented
42	C₂×C₃×C₇	—	25	3	no	—
43	C₅×C₇	—	3	2	no	—
44	C₂×C₁₇	C₂×C₇×C₅²⋊C₃	1	3	yes	direct product factor
45	C₂²×C₇	C₁₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
46	C₅²	C₂²×C₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₃×C₇	—	25	1	no	Hall
48	C₂²×C₅	—	3	2	no	—
49	C₁₇	C₂²×C₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₇	C₂×C₁₇×C₅²⋊C₃	1	3	yes	direct product factor
51	C₂²×C₃	—	25	1	no	Hall
52	C₂×C₅	—	3	6	no	—
53	C₇	C₂²×C₁₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃	—	25	3	no	—
55	C₅	—	3	2	no	—
56	C₂²	C₇×C₁₇×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₃	—	25	1	no	Sylow
58	C₂	C₂×C₇×C₁₇×C₅²⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₇×C₁₇	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₇×C₁₇	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₇×C₅²⋊C₃	C₂	direct (N × H)
2. C₂²×C₅²×C₇×C₁₇	C₃	semidirect
3. C₇×C₁₇×C₅²⋊C₃	C₂²	direct (N × H)
4. C₂×C₅²×C₇×C₁₇	C₂×C₃	semidirect
5. C₂²×C₁₇×C₅²⋊C₃	C₇	direct (N × H)
6. C₅²×C₇×C₁₇	C₂²×C₃	semidirect
7. C₂×C₁₇×C₅²⋊C₃	C₂×C₇	direct (N × H)
9. C₂²×C₇×C₅²⋊C₃	C₁₇	direct (N × H)
10. C₂²×C₅²×C₁₇	C₃×C₇	semidirect
12. C₁₇×C₅²⋊C₃	C₂²×C₇	direct (N × H)
14. C₂×C₇×C₅²⋊C₃	C₂×C₁₇	direct (N × H)
15. C₂×C₅²×C₁₇	C₂×C₃×C₇	semidirect
17. C₂²×C₅²×C₇	C₃×C₁₇	semidirect
19. C₇×C₅²⋊C₃	C₂²×C₁₇	direct (N × H)
20. C₂²×C₇×C₁₇	C₅²⋊C₃	direct (N × H)
21. C₅²×C₁₇	C₂²×C₃×C₇	semidirect
23. C₂×C₅²×C₇	C₂×C₃×C₁₇	semidirect
25. C₂²×C₅²⋊C₃	C₇×C₁₇	direct (N × H)
26. C₂×C₇×C₁₇	C₂×C₅²⋊C₃	direct (N × H)
28. C₅²×C₇	C₂²×C₃×C₁₇	semidirect
30. C₂×C₅²⋊C₃	C₂×C₇×C₁₇	direct (N × H)
32. C₇×C₁₇	C₂²×C₅²⋊C₃	direct (N × H)
34. C₂²×C₅²	C₃×C₇×C₁₇	semidirect
37. C₅²⋊C₃	C₂²×C₇×C₁₇	direct (N × H)
39. C₂²×C₁₇	C₇×C₅²⋊C₃	direct (N × H)
41. C₂×C₅²	C₂×C₃×C₇×C₁₇	semidirect
44. C₂×C₁₇	C₂×C₇×C₅²⋊C₃	direct (N × H)
45. C₂²×C₇	C₁₇×C₅²⋊C₃	direct (N × H)
46. C₅²	C₂²×C₃×C₇×C₁₇	semidirect
49. C₁₇	C₂²×C₇×C₅²⋊C₃	direct (N × H)
50. C₂×C₇	C₂×C₁₇×C₅²⋊C₃	direct (N × H)
53. C₇	C₂²×C₁₇×C₅²⋊C₃	direct (N × H)
56. C₂²	C₇×C₁₇×C₅²⋊C₃	direct (N × H)
58. C₂	C₂×C₇×C₁₇×C₅²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₁₇×C₅²⋊C₃	2
C₂²×C₅²×C₇×C₁₇	3
C₂²×C₁₇×C₅²⋊C₃	7
C₂²×C₇×C₅²⋊C₃	17
C₂²×C₃×C₇×C₁₇	25

Subgroups — C22×C7×C17×C52⋊C3 #49088037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₁₇×C₅²⋊C₃ #49088037