Subgroups — C₂²×C₃²×C₅×C₂₉⋊C₇ #49141499

Order 36540.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₂₉⋊C₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₂₉⋊C₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃²×C₂₉⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₂₉⋊C₇	C₂×C₃	1	12	yes	direct product factor
6	C₂²×C₃²×C₅×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂²×C₅×C₂₉⋊C₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃²×C₂₉⋊C₇	C₂×C₅	1	3	yes	direct product factor
9	C₃×C₅×C₂₉⋊C₇	C₂²×C₃	1	4	yes	direct product factor
10	C₂×C₃²×C₅×C₂₉	C₂×C₇	1	3	yes	complemented
11	C₂²×C₃×C₂₉⋊C₇	C₃×C₅	1	4	yes	direct product factor
12	C₂×C₅×C₂₉⋊C₇	C₂×C₃²	1	3	yes	direct product factor
13	C₃²×C₂₉⋊C₇	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₃×C₅×C₂₉	C₃×C₇	1	4	yes	complemented
15	C₃²×C₅×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃²×C₅×C₇	—	29	1	no	maximal, Hall
17	C₂×C₃×C₂₉⋊C₇	C₂×C₃×C₅	1	12	yes	direct product factor
18	C₂²×C₃²×C₂₉	C₅×C₇	1	1	yes	characteristic, complemented, Hall
19	C₅×C₂₉⋊C₇	C₂²×C₃²	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₅×C₂₉	C₂×C₃×C₇	1	12	yes	complemented
21	C₂²×C₂₉⋊C₇	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃²×C₅×C₇	—	29	3	no	—
23	C₃×C₂₉⋊C₇	C₂²×C₃×C₅	1	4	yes	direct product factor
24	C₂²×C₅×C₂₉	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃²×C₂₉	C₂×C₅×C₇	1	3	yes	complemented
26	C₃×C₅×C₂₉	C₂²×C₃×C₇	1	4	yes	complemented
27	C₂²×C₃×C₅×C₇	—	29	4	no	—
28	C₂×C₂₉⋊C₇	C₂×C₃²×C₅	1	3	yes	direct product factor
29	C₂²×C₃×C₂₉	C₃×C₅×C₇	1	4	yes	complemented
30	C₃²×C₅×C₇	—	29	1	no	Hall
31	C₂×C₅×C₂₉	C₂×C₃²×C₇	1	3	yes	complemented
32	C₃²×C₂₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃²×C₇	—	29	1	no	Hall
34	C₂×C₃×C₅×C₇	—	29	12	no	—
35	C₂₉⋊C₇	C₂²×C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
36	C₂²×C₃²×C₅	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₃×C₂₉	C₂×C₃×C₅×C₇	1	12	yes	complemented
38	C₅×C₂₉	C₂²×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₅×C₇	—	29	1	no	Hall
40	C₂×C₃²×C₇	—	29	3	no	—
41	C₂²×C₂₉	C₃²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
42	C₃×C₅×C₇	—	29	4	no	—
43	C₂×C₃²×C₅	C₂×C₂₉⋊C₇	1	3	yes	direct product factor
44	C₃×C₂₉	C₂²×C₃×C₅×C₇	1	4	yes	complemented
45	C₂²×C₃×C₇	—	29	4	no	—
46	C₂×C₅×C₇	—	29	3	no	—
47	C₃²×C₇	—	29	1	no	Hall
48	C₂²×C₃×C₅	C₃×C₂₉⋊C₇	1	4	yes	direct product factor
49	C₂×C₂₉	C₂×C₃²×C₅×C₇	1	3	yes	complemented
50	C₃²×C₅	C₂²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₃×C₇	—	29	12	no	—
52	C₂²×C₃²	C₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
53	C₅×C₇	—	29	1	no	Hall
54	C₂×C₃×C₅	C₂×C₃×C₂₉⋊C₇	1	12	yes	direct product factor
55	C₂₉	C₂²×C₃²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₇	—	29	1	no	Hall
57	C₃×C₇	—	29	4	no	—
58	C₂²×C₅	C₃²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
59	C₂×C₃²	C₂×C₅×C₂₉⋊C₇	1	3	yes	direct product factor
60	C₃×C₅	C₂²×C₃×C₂₉⋊C₇	1	4	yes	direct product factor
61	C₂×C₇	—	29	3	no	—
62	C₂²×C₃	C₃×C₅×C₂₉⋊C₇	1	4	yes	direct product factor
63	C₂×C₅	C₂×C₃²×C₂₉⋊C₇	1	3	yes	direct product factor
64	C₃²	C₂²×C₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₇	—	29	1	no	Sylow
66	C₂×C₃	C₂×C₃×C₅×C₂₉⋊C₇	1	12	yes	direct product factor
67	C₅	C₂²×C₃²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²	C₃²×C₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
69	C₃	C₂²×C₃×C₅×C₂₉⋊C₇	1	4	yes	direct product factor
70	C₂	C₂×C₃²×C₅×C₂₉⋊C₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃²×C₅	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₂²×C₃²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂²×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₅×C₂₉⋊C₇	C₂	direct (N × H)
2. C₂²×C₃×C₅×C₂₉⋊C₇	C₃	direct (N × H)
3. C₃²×C₅×C₂₉⋊C₇	C₂²	direct (N × H)
4. C₂²×C₃²×C₂₉⋊C₇	C₅	direct (N × H)
5. C₂×C₃×C₅×C₂₉⋊C₇	C₂×C₃	direct (N × H)
6. C₂²×C₃²×C₅×C₂₉	C₇	semidirect
7. C₂²×C₅×C₂₉⋊C₇	C₃²	direct (N × H)
8. C₂×C₃²×C₂₉⋊C₇	C₂×C₅	direct (N × H)
9. C₃×C₅×C₂₉⋊C₇	C₂²×C₃	direct (N × H)
10. C₂×C₃²×C₅×C₂₉	C₂×C₇	semidirect
11. C₂²×C₃×C₂₉⋊C₇	C₃×C₅	direct (N × H)
12. C₂×C₅×C₂₉⋊C₇	C₂×C₃²	direct (N × H)
13. C₃²×C₂₉⋊C₇	C₂²×C₅	direct (N × H)
14. C₂²×C₃×C₅×C₂₉	C₃×C₇	semidirect
15. C₃²×C₅×C₂₉	C₂²×C₇	semidirect
17. C₂×C₃×C₂₉⋊C₇	C₂×C₃×C₅	direct (N × H)
18. C₂²×C₃²×C₂₉	C₅×C₇	semidirect
19. C₅×C₂₉⋊C₇	C₂²×C₃²	direct (N × H)
20. C₂×C₃×C₅×C₂₉	C₂×C₃×C₇	semidirect
21. C₂²×C₂₉⋊C₇	C₃²×C₅	direct (N × H)
23. C₃×C₂₉⋊C₇	C₂²×C₃×C₅	direct (N × H)
24. C₂²×C₅×C₂₉	C₃²×C₇	semidirect
25. C₂×C₃²×C₂₉	C₂×C₅×C₇	semidirect
26. C₃×C₅×C₂₉	C₂²×C₃×C₇	semidirect
28. C₂×C₂₉⋊C₇	C₂×C₃²×C₅	direct (N × H)
29. C₂²×C₃×C₂₉	C₃×C₅×C₇	semidirect
31. C₂×C₅×C₂₉	C₂×C₃²×C₇	semidirect
32. C₃²×C₂₉	C₂²×C₅×C₇	semidirect
35. C₂₉⋊C₇	C₂²×C₃²×C₅	direct (N × H)
36. C₂²×C₃²×C₅	C₂₉⋊C₇	direct (N × H)
37. C₂×C₃×C₂₉	C₂×C₃×C₅×C₇	semidirect
38. C₅×C₂₉	C₂²×C₃²×C₇	semidirect
41. C₂²×C₂₉	C₃²×C₅×C₇	semidirect
43. C₂×C₃²×C₅	C₂×C₂₉⋊C₇	direct (N × H)
44. C₃×C₂₉	C₂²×C₃×C₅×C₇	semidirect
48. C₂²×C₃×C₅	C₃×C₂₉⋊C₇	direct (N × H)
49. C₂×C₂₉	C₂×C₃²×C₅×C₇	semidirect
50. C₃²×C₅	C₂²×C₂₉⋊C₇	direct (N × H)
52. C₂²×C₃²	C₅×C₂₉⋊C₇	direct (N × H)
54. C₂×C₃×C₅	C₂×C₃×C₂₉⋊C₇	direct (N × H)
55. C₂₉	C₂²×C₃²×C₅×C₇	semidirect
58. C₂²×C₅	C₃²×C₂₉⋊C₇	direct (N × H)
59. C₂×C₃²	C₂×C₅×C₂₉⋊C₇	direct (N × H)
60. C₃×C₅	C₂²×C₃×C₂₉⋊C₇	direct (N × H)
62. C₂²×C₃	C₃×C₅×C₂₉⋊C₇	direct (N × H)
63. C₂×C₅	C₂×C₃²×C₂₉⋊C₇	direct (N × H)
64. C₃²	C₂²×C₅×C₂₉⋊C₇	direct (N × H)
66. C₂×C₃	C₂×C₃×C₅×C₂₉⋊C₇	direct (N × H)
67. C₅	C₂²×C₃²×C₂₉⋊C₇	direct (N × H)
68. C₂²	C₃²×C₅×C₂₉⋊C₇	direct (N × H)
69. C₃	C₂²×C₃×C₅×C₂₉⋊C₇	direct (N × H)
70. C₂	C₂×C₃²×C₅×C₂₉⋊C₇	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×C₃²×C₅×C₂₉⋊C₇	2
C₂²×C₃×C₅×C₂₉⋊C₇	3
C₂²×C₃²×C₂₉⋊C₇	5
C₂²×C₃²×C₅×C₂₉	7
C₂²×C₃²×C₅×C₇	29

Subgroups — C22×C32×C5×C29⋊C7 #49141499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×C₅×C₂₉⋊C₇ #49141499