Subgroups — C₅×D₃×C₇×D₇₃ #44501411

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₂₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇×D₇₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇×D₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₇×D₇₃	—	3	1	no	—
8	C₅×C₇×D₇₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₇×C₇₃	—	3	1	no	—
10	C₅×D₃×D₇₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×D₂₁₉	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×C₇×D₇₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₂₁₉	C₂×C₇	1	1	yes	characteristic, complemented
16	C₅×D₃×C₇₃	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×C₅×D₇₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×D₇₃	—	3	1	no	Hall
19	C₃×C₇×C₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₇₃	—	3	1	no	Hall
21	C₃×C₅×C₇₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₇₃	—	3	1	no	—
23	C₇×D₇₃	—	3	1	no	—
24	C₇×D₇₃	C₅×D₃	1	1	yes	characteristic, direct product factor
25	D₃×D₇₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₇₃	—	3	1	no	—
27	C₅×D₇₃	—	3	1	no	—
28	C₅×D₇₃	D₃×C₇	1	1	yes	characteristic, direct product factor
29	C₇×C₇₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
30	D₂₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
31	C₃×D₇₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
32	D₃×C₇₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
33	C₂×C₅×D₃×C₇	—	73	1	no	maximal, Hall
34	C₅×C₇₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₃	—	3	1	no	Hall
36	C₃×C₇₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₇	—	73	1	no	—
38	C₅×D₃×C₇	—	73	1	no	—
39	C₅×D₃×C₇	D₇₃	1	1	yes	characteristic, direct product factor
40	C₂×C₇₃	—	3	1	no	—
41	D₇₃	—	3	1	no	—
42	D₇₃	C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
43	C₂²×C₅×C₇	—	219	1	no	Hall
44	C₃×C₅×C₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
45	C₂×D₃×C₇	—	73	1	no	Hall
46	C₇₃	C₂×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅×C₇	—	3	1	no	—
48	C₂×C₅×C₇	—	73	1	no	—
49	C₂×C₅×C₇	—	219	1	no	—
50	C₂×C₅×D₃	—	73	1	no	Hall
51	C₂×C₃×C₇	—	73	1	no	—
52	D₃×C₇	—	73	1	no	—
53	D₃×C₇	C₅×D₇₃	1	1	yes	characteristic, direct product factor
54	C₅×C₇	D₃×D₇₃	1	1	yes	characteristic, direct product factor, Hall
55	C₂×C₃×C₅	—	73	1	no	—
56	C₅×D₃	—	73	1	no	—
57	C₅×D₃	C₇×D₇₃	1	1	yes	characteristic, direct product factor
58	C₂²×C₇	—	219	1	no	Hall
59	C₃×C₇	C₂×C₅×D₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	219	1	no	Hall
61	C₃×C₅	C₂×C₇×D₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	3	1	no	—
63	C₂×C₇	—	73	1	no	—
64	C₂×C₇	—	219	1	no	—
65	C₂×D₃	—	73	1	no	Hall
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	73	1	no	—
68	C₂×C₅	—	219	1	no	—
69	C₇	C₅×D₃×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	73	1	no	—
71	D₃	—	73	1	no	—
72	D₃	C₅×C₇×D₇₃	1	1	yes	characteristic, direct product factor
73	C₅	D₃×C₇×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	219	1	no	Sylow
75	C₃	C₂×C₅×C₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	73	1	no	—
78	C₂	—	219	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	D₃×D₇₃
commutator, cosocle, hypocenter	C₃×C₇₃	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₃×C₇₃
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₂₁₉	C₂	semidirect
2. C₅×D₃×C₇×C₇₃	C₂	semidirect
3. C₃×C₅×C₇×D₇₃	C₂	semidirect
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
6. D₃×C₇×D₇₃	C₅	direct (N × H)
8. C₅×C₇×D₇₃	D₃	direct (N × H)
10. C₅×D₃×D₇₃	C₇	direct (N × H)
11. C₇×D₂₁₉	C₂×C₅	semidirect
12. D₃×C₇×C₇₃	C₂×C₅	semidirect
13. C₃×C₇×D₇₃	C₂×C₅	semidirect
14. C₅×C₇×C₇₃	C₂×D₃	semidirect
15. C₅×D₂₁₉	C₂×C₇	semidirect
16. C₅×D₃×C₇₃	C₂×C₇	semidirect
17. C₃×C₅×D₇₃	C₂×C₇	semidirect
19. C₃×C₇×C₇₃	C₂²×C₅	semidirect
21. C₃×C₅×C₇₃	C₂²×C₇	semidirect
24. C₇×D₇₃	C₅×D₃	direct (N × H)
25. D₃×D₇₃	C₅×C₇	direct (N × H)
28. C₅×D₇₃	D₃×C₇	direct (N × H)
29. C₇×C₇₃	C₂×C₅×D₃	semidirect
30. D₂₁₉	C₂×C₅×C₇	semidirect
31. C₃×D₇₃	C₂×C₅×C₇	semidirect
32. D₃×C₇₃	C₂×C₅×C₇	semidirect
34. C₅×C₇₃	C₂×D₃×C₇	semidirect
36. C₃×C₇₃	C₂²×C₅×C₇	semidirect
39. C₅×D₃×C₇	D₇₃	direct (N × H)
42. D₇₃	C₅×D₃×C₇	direct (N × H)
44. C₃×C₅×C₇	C₂×D₇₃	semidirect
46. C₇₃	C₂×C₅×D₃×C₇	semidirect
53. D₃×C₇	C₅×D₇₃	direct (N × H)
54. C₅×C₇	D₃×D₇₃	direct (N × H)
57. C₅×D₃	C₇×D₇₃	direct (N × H)
59. C₃×C₇	C₂×C₅×D₇₃	semidirect
61. C₃×C₅	C₂×C₇×D₇₃	semidirect
69. C₇	C₅×D₃×D₇₃	direct (N × H)
72. D₃	C₅×C₇×D₇₃	direct (N × H)
73. C₅	D₃×C₇×D₇₃	direct (N × H)
75. C₃	C₂×C₅×C₇×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×D₂₁₉	2
C₅×D₃×C₇×C₇₃	2
C₃×C₅×C₇×D₇₃	2
C₂×C₅×C₇×D₇₃	3
D₃×C₇×D₇₃	5
C₅×D₃×D₇₃	7
C₂×C₅×D₃×C₇	73

Subgroups — C5×D3×C7×D73 #44501411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₇×D₇₃ #44501411