Subgroups — C₃×D₃₅×D₇₃ #44501405

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₅₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃₅×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₅×D₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×D₇₃	—	5	1	no	maximal, Hall
7	D₂₅₅₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃₅×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₇×D₇₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅×D₇₃	—	7	1	no	maximal, Hall
11	C₃×D₅₁₁	—	5	1	no	—
12	C₃×D₇×C₇₃	—	5	1	no	—
13	C₃×C₇×D₇₃	D₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×D₃₆₅	—	7	1	no	—
16	C₃×D₅×C₇₃	—	7	1	no	—
17	C₃×C₅×D₇₃	D₇	1	1	yes	characteristic, complemented
18	D₇×D₇₃	—	5	1	no	Hall
19	C₃×C₇×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₇₃	—	7	1	no	Hall
21	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₅₁₁	—	5	1	no	—
23	C₇×D₇₃	C₃×D₅	1	1	yes	characteristic, complemented
24	D₇×C₇₃	—	5	1	no	—
25	C₂×C₃×D₇₃	—	35	1	no	Hall
26	D₃₆₅	—	7	1	no	—
27	C₅×D₇₃	C₃×D₇	1	1	yes	characteristic, complemented
28	D₅×C₇₃	—	7	1	no	—
29	C₇×C₇₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇₃	—	35	1	no	—
31	C₃×D₇₃	—	35	1	no	—
32	C₃×D₇₃	D₃₅	1	1	yes	characteristic, direct product factor
33	C₂×C₃×D₃₅	—	73	1	no	maximal, Hall
34	C₅×C₇₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₃	—	35	1	no	Hall
36	C₃×C₇₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₇	—	73	1	no	—
38	C₃×D₃₅	—	73	1	no	—
39	C₃×D₃₅	D₇₃	1	1	yes	characteristic, direct product factor
40	C₂×C₇₃	—	35	1	no	—
41	D₇₃	—	35	1	no	—
42	D₇₃	C₃×D₃₅	1	1	yes	characteristic, direct product factor
43	C₂×D₃₅	—	73	1	no	Hall
44	C₃×C₅×C₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×D₇	—	365	1	no	Hall
46	C₇₃	C₂×C₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅×C₇	—	73	1	no	—
48	D₃₅	—	73	1	no	—
49	D₃₅	C₃×D₇₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃×D₅	—	511	1	no	Hall
51	C₂×C₃×C₇	—	73	1	no	—
52	C₃×D₇	—	5	1	no	—
53	C₃×D₇	—	365	1	no	—
54	C₅×C₇	C₂×C₃×D₇₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	73	1	no	—
56	C₃×D₅	—	7	1	no	—
57	C₃×D₅	—	511	1	no	—
58	C₂×D₇	—	365	1	no	Hall
59	C₃×C₇	D₅×D₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	511	1	no	Hall
61	C₃×C₅	D₇×D₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	73	1	no	—
63	D₇	—	5	1	no	—
64	D₇	—	365	1	no	—
65	C₂²×C₃	—	2555	1	no	Hall
66	C₂×C₅	—	73	1	no	—
67	D₅	—	7	1	no	—
68	D₅	—	511	1	no	—
69	C₇	C₃×D₅×D₇₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	35	1	no	—
71	C₂×C₃	—	73	1	no	—
72	C₂×C₃	—	2555	1	no	—
73	C₅	C₃×D₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	2555	1	no	Sylow
75	C₃	D₃₅×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	35	1	no	—
77	C₂	—	73	1	no	—
78	C₂	—	2555	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃₅×D₇₃
commutator, cosocle, hypocenter	C₅×C₇×C₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₅×C₇×C₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₅₅₅	C₂	semidirect
2. C₃×D₃₅×C₇₃	C₂	semidirect
3. C₃×C₅×C₇×D₇₃	C₂	semidirect
4. D₃₅×D₇₃	C₃	direct (N × H)
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
7. D₂₅₅₅	C₂×C₃	semidirect
8. D₃₅×C₇₃	C₂×C₃	semidirect
9. C₅×C₇×D₇₃	C₂×C₃	semidirect
13. C₃×C₇×D₇₃	D₅	semidirect
14. C₅×C₇×C₇₃	C₂²×C₃	semidirect
17. C₃×C₅×D₇₃	D₇	semidirect
19. C₃×C₇×C₇₃	C₂×D₅	semidirect
21. C₃×C₅×C₇₃	C₂×D₇	semidirect
23. C₇×D₇₃	C₃×D₅	semidirect
27. C₅×D₇₃	C₃×D₇	semidirect
29. C₇×C₇₃	C₂×C₃×D₅	semidirect
32. C₃×D₇₃	D₃₅	direct (N × H)
34. C₅×C₇₃	C₂×C₃×D₇	semidirect
36. C₃×C₇₃	C₂×D₃₅	semidirect
39. C₃×D₃₅	D₇₃	direct (N × H)
42. D₇₃	C₃×D₃₅	direct (N × H)
44. C₃×C₅×C₇	C₂×D₇₃	semidirect
46. C₇₃	C₂×C₃×D₃₅	semidirect
49. D₃₅	C₃×D₇₃	direct (N × H)
54. C₅×C₇	C₂×C₃×D₇₃	semidirect
59. C₃×C₇	D₅×D₇₃	semidirect
61. C₃×C₅	D₇×D₇₃	semidirect
69. C₇	C₃×D₅×D₇₃	semidirect
73. C₅	C₃×D₇×D₇₃	semidirect
75. C₃	D₃₅×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₅₅₅	2
C₃×D₃₅×C₇₃	2
C₃×C₅×C₇×D₇₃	2
D₃₅×D₇₃	3
C₃×D₇×D₇₃	5
C₃×D₅×D₇₃	7
C₂×C₃×D₃₅	73

Subgroups — C3×D35×D73 #44501405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₅×D₇₃ #44501405