Subgroups — C₅×C₇×C₂₉×C₂²⋊C₉ #49141306

Order 36540.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₇×C₂₉	C₃	1	1	yes	maximal, characteristic
2	C₅×C₇×C₉×C₂₉	—	4	1	no	maximal, Hall
3	C₇×C₂₉×C₂²⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×C₇×C₂₉	—	3	1	no	—
5	C₅×C₂₉×C₂²⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₅×C₇×C₂₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₇×C₂₉	A₄	1	1	yes	characteristic
8	C₂²×C₃×C₇×C₂₉	C₃×C₅	1	1	yes	characteristic
9	C₂×C₅×C₇×C₂₉	—	3	1	no	—
10	C₇×C₉×C₂₉	—	4	1	no	Hall
11	C₂²×C₃×C₅×C₂₉	C₃×C₇	1	1	yes	characteristic
12	C₅×C₉×C₂₉	—	4	1	no	Hall
13	C₅×C₇×C₂²⋊C₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₂₉	—	3	1	no	—
15	C₂₉×C₂²⋊C₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇×C₂₉	C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₅×C₂₉	—	3	1	no	—
18	C₂²×C₇×C₂₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×C₂₉	C₅×A₄	1	1	yes	characteristic
20	C₂²×C₅×C₂₉	C₇×C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₂₉	C₇×A₄	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₇	C₃×C₂₉	1	1	yes	characteristic
23	C₂×C₇×C₂₉	—	3	1	no	—
24	C₂²×C₃×C₂₉	C₃×C₅×C₇	1	1	yes	characteristic
25	C₅×C₇×C₉	—	4	1	no	Hall
26	C₂×C₅×C₂₉	—	3	1	no	—
27	C₉×C₂₉	—	4	1	no	Hall
28	C₇×C₂²⋊C₉	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₅×C₇	—	3	1	no	—
30	C₇×C₂₉	C₅×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₂²⋊C₉	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₃×C₂₉	—	3	1	no	—
33	C₅×C₂₉	C₇×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂²×C₅×C₇	C₉×C₂₉	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₂₉	C₅×C₇×C₉	1	1	yes	characteristic, complemented, Hall
36	C₃×C₅×C₇	A₄×C₂₉	1	1	yes	characteristic
37	C₃×C₂₉	C₅×C₇×A₄	1	1	yes	characteristic
38	C₂²×C₃×C₇	C₃×C₅×C₂₉	1	1	yes	characteristic
39	C₂×C₅×C₇	—	3	1	no	—
40	C₇×C₉	—	4	1	no	Hall
41	C₂²×C₃×C₅	C₃×C₇×C₂₉	1	1	yes	characteristic
42	C₂×C₂₉	—	3	1	no	—
43	C₅×C₉	—	4	1	no	Hall
44	C₂×C₃×C₇	—	3	1	no	—
45	C₂²⋊C₉	C₅×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
46	C₅×C₇	C₂₉×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Hall
47	C₂×C₃×C₅	—	3	1	no	—
48	C₂₉	C₅×C₇×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²×C₇	C₅×C₉×C₂₉	1	1	yes	characteristic, complemented, Hall
50	C₃×C₇	C₅×A₄×C₂₉	1	1	yes	characteristic
51	C₂²×C₅	C₇×C₉×C₂₉	1	1	yes	characteristic, complemented, Hall
52	C₃×C₅	C₇×A₄×C₂₉	1	1	yes	characteristic
53	C₂×C₇	—	3	1	no	—
54	C₂²×C₃	C₃×C₅×C₇×C₂₉	1	1	yes	characteristic
55	C₂×C₅	—	3	1	no	—
56	C₉	—	4	1	no	Sylow
57	C₇	C₅×C₂₉×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₃	—	3	1	no	—
59	C₅	C₇×C₂₉×C₂²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
60	C₂²	C₅×C₇×C₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
61	C₃	C₅×C₇×A₄×C₂₉	1	1	yes	characteristic
62	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₇×C₂₉	A₄
commutator, hypocenter	C₂²	C₅×C₇×C₉×C₂₉
Frattini	C₃	C₅×C₇×A₄×C₂₉
Fitting, socle, prime radical	C₂²×C₃×C₅×C₇×C₂₉	C₃
cosocle	C₂²×C₃	C₃×C₅×C₇×C₂₉
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₅×C₇×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₂₉×C₂²⋊C₉	C₅	direct (N × H)
5. C₅×C₂₉×C₂²⋊C₉	C₇	direct (N × H)
6. C₂²×C₅×C₇×C₂₉	C₉	semidirect
13. C₅×C₇×C₂²⋊C₉	C₂₉	direct (N × H)
15. C₂₉×C₂²⋊C₉	C₅×C₇	direct (N × H)
16. C₅×C₇×C₂₉	C₂²⋊C₉	direct (N × H)
18. C₂²×C₇×C₂₉	C₅×C₉	semidirect
20. C₂²×C₅×C₂₉	C₇×C₉	semidirect
28. C₇×C₂²⋊C₉	C₅×C₂₉	direct (N × H)
30. C₇×C₂₉	C₅×C₂²⋊C₉	direct (N × H)
31. C₅×C₂²⋊C₉	C₇×C₂₉	direct (N × H)
33. C₅×C₂₉	C₇×C₂²⋊C₉	direct (N × H)
34. C₂²×C₅×C₇	C₉×C₂₉	semidirect
35. C₂²×C₂₉	C₅×C₇×C₉	semidirect
45. C₂²⋊C₉	C₅×C₇×C₂₉	direct (N × H)
46. C₅×C₇	C₂₉×C₂²⋊C₉	direct (N × H)
48. C₂₉	C₅×C₇×C₂²⋊C₉	direct (N × H)
49. C₂²×C₇	C₅×C₉×C₂₉	semidirect
51. C₂²×C₅	C₇×C₉×C₂₉	semidirect
57. C₇	C₅×C₂₉×C₂²⋊C₉	direct (N × H)
59. C₅	C₇×C₂₉×C₂²⋊C₉	direct (N × H)
60. C₂²	C₅×C₇×C₉×C₂₉	semidirect

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×C₂₉	3
C₅×C₇×C₉×C₂₉	4
C₇×C₂₉×C₂²⋊C₉	5
C₅×C₂₉×C₂²⋊C₉	7
C₅×C₇×C₂²⋊C₉	29

Subgroups — C5×C7×C29×C22⋊C9 #49141306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₂₉×C₂²⋊C₉ #49141306