Subgroups — C₅×D₃×D₇×C₇₃ #44501414

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₂₁×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₇×C₇₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₇×C₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₇×C₇₃	—	3	1	no	—
8	C₅×D₇×C₇₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₇×C₇₃	—	3	1	no	—
10	C₂×C₅×D₃×C₇₃	—	7	1	no	maximal, Hall
11	D₂₁×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×D₇×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₃×C₇₃	—	7	1	no	—
16	C₅×D₃×C₇₃	D₇	1	1	yes	characteristic, direct product factor
17	C₂×C₃×C₅×C₇₃	—	7	1	no	—
18	C₂×D₇×C₇₃	—	3	1	no	Hall
19	C₃×C₇×C₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₅×C₇₃	—	21	1	no	Hall
21	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₇₃	—	3	1	no	—
23	D₇×C₇₃	—	3	1	no	—
24	D₇×C₇₃	C₅×D₃	1	1	yes	characteristic, direct product factor
25	C₂×D₃×C₇₃	—	7	1	no	Hall
26	C₂×C₅×C₇₃	—	3	1	no	—
27	C₂×C₅×C₇₃	—	7	1	no	—
28	C₂×C₅×C₇₃	—	21	1	no	—
29	C₇×C₇₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇₃	—	7	1	no	—
31	D₃×C₇₃	—	7	1	no	—
32	D₃×C₇₃	C₅×D₇	1	1	yes	characteristic, direct product factor
33	C₅×D₃×D₇	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₅×C₇₃	D₃×D₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂²×C₇₃	—	21	1	no	Hall
36	C₃×C₇₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₅×D₂₁	C₂×C₇₃	1	1	yes	characteristic, complemented
38	C₅×D₃×C₇	C₂×C₇₃	1	1	yes	characteristic, complemented
39	C₃×C₅×D₇	C₂×C₇₃	1	1	yes	characteristic, complemented
40	C₂×C₇₃	—	3	1	no	—
41	C₂×C₇₃	—	7	1	no	—
42	C₂×C₇₃	—	21	1	no	—
43	C₂×C₅×D₇	—	3	1	no	Hall
44	C₃×C₅×C₇	C₂²×C₇₃	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	C₅×C₇₃	1	1	yes	characteristic, direct product factor, Hall
46	C₇₃	C₅×D₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₅×C₇	—	3	1	no	—
48	C₅×D₇	—	3	1	no	—
49	C₅×D₇	D₃×C₇₃	1	1	yes	characteristic, direct product factor
50	C₂×C₅×D₃	—	7	1	no	Hall
51	D₂₁	C₂×C₅×C₇₃	1	1	yes	characteristic, complemented
52	C₃×D₇	C₂×C₅×C₇₃	1	1	yes	characteristic, complemented
53	D₃×C₇	C₂×C₅×C₇₃	1	1	yes	characteristic, complemented
54	C₅×C₇	C₂×D₃×C₇₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	7	1	no	—
56	C₅×D₃	—	7	1	no	—
57	C₅×D₃	D₇×C₇₃	1	1	yes	characteristic, direct product factor
58	C₂×D₇	—	3	1	no	Hall
59	C₃×C₇	C₂²×C₅×C₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	21	1	no	Hall
61	C₃×C₅	C₂×D₇×C₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	3	1	no	—
63	D₇	—	3	1	no	—
64	D₇	C₅×D₃×C₇₃	1	1	yes	characteristic, direct product factor
65	C₂×D₃	—	7	1	no	Hall
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	7	1	no	—
68	C₂×C₅	—	21	1	no	—
69	C₇	C₂×C₅×D₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	7	1	no	—
71	D₃	—	7	1	no	—
72	D₃	C₅×D₇×C₇₃	1	1	yes	characteristic, direct product factor
73	C₅	D₃×D₇×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	21	1	no	Sylow
75	C₃	C₂×C₅×D₇×C₇₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	7	1	no	—
78	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇₃	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₅×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₅×D₂₁×C₇₃	C₂	semidirect
2. C₅×D₃×C₇×C₇₃	C₂	semidirect
3. C₃×C₅×D₇×C₇₃	C₂	semidirect
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
6. D₃×D₇×C₇₃	C₅	direct (N × H)
8. C₅×D₇×C₇₃	D₃	direct (N × H)
11. D₂₁×C₇₃	C₂×C₅	semidirect
12. D₃×C₇×C₇₃	C₂×C₅	semidirect
13. C₃×D₇×C₇₃	C₂×C₅	semidirect
14. C₅×C₇×C₇₃	C₂×D₃	semidirect
16. C₅×D₃×C₇₃	D₇	direct (N × H)
19. C₃×C₇×C₇₃	C₂²×C₅	semidirect
21. C₃×C₅×C₇₃	C₂×D₇	semidirect
24. D₇×C₇₃	C₅×D₃	direct (N × H)
29. C₇×C₇₃	C₂×C₅×D₃	semidirect
32. D₃×C₇₃	C₅×D₇	direct (N × H)
33. C₅×D₃×D₇	C₇₃	direct (N × H)
34. C₅×C₇₃	D₃×D₇	direct (N × H)
36. C₃×C₇₃	C₂×C₅×D₇	semidirect
37. C₅×D₂₁	C₂×C₇₃	semidirect
38. C₅×D₃×C₇	C₂×C₇₃	semidirect
39. C₃×C₅×D₇	C₂×C₇₃	semidirect
44. C₃×C₅×C₇	C₂²×C₇₃	semidirect
45. D₃×D₇	C₅×C₇₃	direct (N × H)
46. C₇₃	C₅×D₃×D₇	direct (N × H)
49. C₅×D₇	D₃×C₇₃	direct (N × H)
51. D₂₁	C₂×C₅×C₇₃	semidirect
52. C₃×D₇	C₂×C₅×C₇₃	semidirect
53. D₃×C₇	C₂×C₅×C₇₃	semidirect
54. C₅×C₇	C₂×D₃×C₇₃	semidirect
57. C₅×D₃	D₇×C₇₃	direct (N × H)
59. C₃×C₇	C₂²×C₅×C₇₃	semidirect
61. C₃×C₅	C₂×D₇×C₇₃	semidirect
64. D₇	C₅×D₃×C₇₃	direct (N × H)
69. C₇	C₂×C₅×D₃×C₇₃	semidirect
72. D₃	C₅×D₇×C₇₃	direct (N × H)
73. C₅	D₃×D₇×C₇₃	direct (N × H)
75. C₃	C₂×C₅×D₇×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₂₁×C₇₃	2
C₅×D₃×C₇×C₇₃	2
C₃×C₅×D₇×C₇₃	2
C₂×C₅×D₇×C₇₃	3
D₃×D₇×C₇₃	5
C₂×C₅×D₃×C₇₃	7
C₅×D₃×D₇	73

Subgroups — C5×D3×D7×C73 #44501414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₇×C₇₃ #44501414