Subgroups — D₃×C₇×D₅×C₇₃ #44501434

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₅×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₅×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₅×C₇₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₇×C₇₃	—	5	1	no	maximal, Hall
7	C₇×D₅×C₇₃	—	3	1	no	—
8	C₇×D₅×C₇₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₇×C₇₃	—	3	1	no	—
10	D₃×D₅×C₇₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₃×C₇×C₇₃	—	5	1	no	—
12	D₃×C₇×C₇₃	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₃×C₇×C₇₃	—	5	1	no	—
14	C₅×C₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₅×C₇₃	C₂×C₇	1	1	yes	characteristic, complemented
16	C₅×D₃×C₇₃	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×D₅×C₇₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂²×C₇×C₇₃	—	15	1	no	Hall
19	C₃×C₇×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₇₃	—	3	1	no	Hall
21	C₃×C₅×C₇₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₇₃	—	3	1	no	—
23	C₂×C₇×C₇₃	—	5	1	no	—
24	C₂×C₇×C₇₃	—	15	1	no	—
25	C₂×D₃×C₇₃	—	5	1	no	Hall
26	C₂×C₅×C₇₃	—	3	1	no	—
27	D₅×C₇₃	—	3	1	no	—
28	D₅×C₇₃	D₃×C₇	1	1	yes	characteristic, direct product factor
29	C₇×C₇₃	D₃×D₅	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₇₃	—	5	1	no	—
31	D₃×C₇₃	—	5	1	no	—
32	D₃×C₇₃	C₇×D₅	1	1	yes	characteristic, direct product factor
33	D₃×C₇×D₅	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₅×C₇₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₇₃	—	15	1	no	Hall
36	C₃×C₇₃	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
37	C₇×D₁₅	C₂×C₇₃	1	1	yes	characteristic, complemented
38	C₅×D₃×C₇	C₂×C₇₃	1	1	yes	characteristic, complemented
39	C₃×C₇×D₅	C₂×C₇₃	1	1	yes	characteristic, complemented
40	C₂×C₇₃	—	3	1	no	—
41	C₂×C₇₃	—	5	1	no	—
42	C₂×C₇₃	—	15	1	no	—
43	C₂×C₇×D₅	—	3	1	no	Hall
44	C₃×C₅×C₇	C₂²×C₇₃	1	1	yes	characteristic, complemented, Hall
45	C₂×D₃×C₇	—	5	1	no	Hall
46	C₇₃	D₃×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₅×C₇	—	3	1	no	—
48	C₇×D₅	—	3	1	no	—
49	C₇×D₅	D₃×C₇₃	1	1	yes	characteristic, direct product factor
50	D₃×D₅	C₇×C₇₃	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₃×C₇	—	5	1	no	—
52	D₃×C₇	—	5	1	no	—
53	D₃×C₇	D₅×C₇₃	1	1	yes	characteristic, direct product factor
54	C₅×C₇	C₂×D₃×C₇₃	1	1	yes	characteristic, complemented, Hall
55	D₁₅	C₂×C₇×C₇₃	1	1	yes	characteristic, complemented
56	C₃×D₅	C₂×C₇×C₇₃	1	1	yes	characteristic, complemented
57	C₅×D₃	C₂×C₇×C₇₃	1	1	yes	characteristic, complemented
58	C₂²×C₇	—	15	1	no	Hall
59	C₃×C₇	C₂×D₅×C₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	3	1	no	Hall
61	C₃×C₅	C₂²×C₇×C₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	3	1	no	—
63	C₂×C₇	—	5	1	no	—
64	C₂×C₇	—	15	1	no	—
65	C₂×D₃	—	5	1	no	Hall
66	C₂×C₅	—	3	1	no	—
67	D₅	—	3	1	no	—
68	D₅	D₃×C₇×C₇₃	1	1	yes	characteristic, direct product factor
69	C₇	D₃×D₅×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	5	1	no	—
71	D₃	—	5	1	no	—
72	D₃	C₇×D₅×C₇₃	1	1	yes	characteristic, direct product factor
73	C₅	C₂×D₃×C₇×C₇₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	15	1	no	Sylow
75	C₃	C₂×C₇×D₅×C₇₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	5	1	no	—
78	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₇₃	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₇×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₅×C₇₃	C₂	semidirect
2. C₅×D₃×C₇×C₇₃	C₂	semidirect
3. C₃×C₇×D₅×C₇₃	C₂	semidirect
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
8. C₇×D₅×C₇₃	D₃	direct (N × H)
10. D₃×D₅×C₇₃	C₇	direct (N × H)
12. D₃×C₇×C₇₃	D₅	direct (N × H)
14. C₅×C₇×C₇₃	C₂×D₃	semidirect
15. D₁₅×C₇₃	C₂×C₇	semidirect
16. C₅×D₃×C₇₃	C₂×C₇	semidirect
17. C₃×D₅×C₇₃	C₂×C₇	semidirect
19. C₃×C₇×C₇₃	C₂×D₅	semidirect
21. C₃×C₅×C₇₃	C₂²×C₇	semidirect
28. D₅×C₇₃	D₃×C₇	direct (N × H)
29. C₇×C₇₃	D₃×D₅	direct (N × H)
32. D₃×C₇₃	C₇×D₅	direct (N × H)
33. D₃×C₇×D₅	C₇₃	direct (N × H)
34. C₅×C₇₃	C₂×D₃×C₇	semidirect
36. C₃×C₇₃	C₂×C₇×D₅	semidirect
37. C₇×D₁₅	C₂×C₇₃	semidirect
38. C₅×D₃×C₇	C₂×C₇₃	semidirect
39. C₃×C₇×D₅	C₂×C₇₃	semidirect
44. C₃×C₅×C₇	C₂²×C₇₃	semidirect
46. C₇₃	D₃×C₇×D₅	direct (N × H)
49. C₇×D₅	D₃×C₇₃	direct (N × H)
50. D₃×D₅	C₇×C₇₃	direct (N × H)
53. D₃×C₇	D₅×C₇₃	direct (N × H)
54. C₅×C₇	C₂×D₃×C₇₃	semidirect
55. D₁₅	C₂×C₇×C₇₃	semidirect
56. C₃×D₅	C₂×C₇×C₇₃	semidirect
57. C₅×D₃	C₂×C₇×C₇₃	semidirect
59. C₃×C₇	C₂×D₅×C₇₃	semidirect
61. C₃×C₅	C₂²×C₇×C₇₃	semidirect
68. D₅	D₃×C₇×C₇₃	direct (N × H)
69. C₇	D₃×D₅×C₇₃	direct (N × H)
72. D₃	C₇×D₅×C₇₃	direct (N × H)
73. C₅	C₂×D₃×C₇×C₇₃	semidirect
75. C₃	C₂×C₇×D₅×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₅×C₇₃	2
C₅×D₃×C₇×C₇₃	2
C₃×C₇×D₅×C₇₃	2
C₂×C₇×D₅×C₇₃	3
C₂×D₃×C₇×C₇₃	5
D₃×D₅×C₇₃	7
D₃×C₇×D₅	73

Subgroups — D3×C7×D5×C73 #44501434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₅×C₇₃ #44501434