Subgroups — C₂²×C₃×D₃₅ #11719879

Order 840.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×C₇	C₂²	1	3	yes	complemented
5	C₃×D₃₅	C₂²	1	4	yes	direct product factor
6	C₂²×C₃×D₇	—	5	1	no	maximal, Hall
7	C₂²×C₅×C₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×D₃₅	C₂×C₃	1	6	yes	direct product factor
9	C₂²×C₃×D₅	—	7	1	no	maximal, Hall
10	C₃×C₅×C₇	C₂³	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₃×C₇	D₅	1	1	yes	characteristic, complemented
12	C₂×C₃×D₇	—	5	6	no	—
13	C₂×C₅×C₇	C₂²×C₃	1	3	yes	complemented
14	D₃₅	C₂²×C₃	1	4	yes	direct product factor
15	C₂²×C₃×C₅	D₇	1	1	yes	characteristic, complemented
16	C₂×C₃×D₅	—	7	6	no	—
17	C₂²×D₇	—	5	1	no	Hall
18	C₂×C₃×C₇	C₂×D₅	1	3	yes	complemented
19	C₃×D₇	—	5	4	no	—
20	C₂²×D₅	—	7	1	no	Hall
21	C₅×C₇	C₂³×C₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅	C₂×D₇	1	3	yes	complemented
23	C₃×D₅	—	7	4	no	—
24	C₂²×C₇	C₃×D₅	1	1	yes	characteristic, complemented
25	C₂×D₇	—	5	6	no	—
26	C₂³×C₃	—	35	1	no	Hall
27	C₃×C₇	C₂²×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₅	C₃×D₇	1	1	yes	characteristic, complemented
29	C₂×D₅	—	7	6	no	—
30	C₃×C₅	C₂²×D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₇	C₂×C₃×D₅	1	3	yes	complemented
32	D₇	—	5	4	no	—
33	C₂²×C₃	—	35	6	no	—
34	C₂²×C₃	D₃₅	1	1	yes	characteristic, direct product factor
35	C₂×C₅	C₂×C₃×D₇	1	3	yes	complemented
36	D₅	—	7	4	no	—
37	C₂³	—	35	1	no	Sylow
38	C₇	C₂²×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃	—	35	4	no	—
40	C₂×C₃	C₂×D₃₅	1	3	yes	direct product factor
41	C₅	C₂²×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	35	6	no	—
43	C₂²	C₃×D₃₅	1	1	yes	characteristic, direct product factor
44	C₃	C₂²×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	35	4	no	—
46	C₂	C₂×C₃×D₃₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₇	C₂	semidirect
2. C₂×C₃×D₃₅	C₂	direct (N × H)
3. C₂²×D₃₅	C₃	direct (N × H)
4. C₂×C₃×C₅×C₇	C₂²	semidirect
5. C₃×D₃₅	C₂²	direct (N × H)
7. C₂²×C₅×C₇	C₂×C₃	semidirect
8. C₂×D₃₅	C₂×C₃	direct (N × H)
10. C₃×C₅×C₇	C₂³	semidirect
11. C₂²×C₃×C₇	D₅	semidirect
13. C₂×C₅×C₇	C₂²×C₃	semidirect
14. D₃₅	C₂²×C₃	direct (N × H)
15. C₂²×C₃×C₅	D₇	semidirect
18. C₂×C₃×C₇	C₂×D₅	semidirect
21. C₅×C₇	C₂³×C₃	semidirect
22. C₂×C₃×C₅	C₂×D₇	semidirect
24. C₂²×C₇	C₃×D₅	semidirect
27. C₃×C₇	C₂²×D₅	semidirect
28. C₂²×C₅	C₃×D₇	semidirect
30. C₃×C₅	C₂²×D₇	semidirect
31. C₂×C₇	C₂×C₃×D₅	semidirect
34. C₂²×C₃	D₃₅	direct (N × H)
35. C₂×C₅	C₂×C₃×D₇	semidirect
38. C₇	C₂²×C₃×D₅	semidirect
40. C₂×C₃	C₂×D₃₅	direct (N × H)
41. C₅	C₂²×C₃×D₇	semidirect
43. C₂²	C₃×D₃₅	direct (N × H)
44. C₃	C₂²×D₃₅	direct (N × H)
46. C₂	C₂×C₃×D₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₇	2
C₂×C₃×D₃₅	2
C₂²×D₃₅	3
C₂²×C₃×D₇	5
C₂²×C₃×D₅	7

Subgroups — C22×C3×D35 #11719879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₃₅ #11719879