Subgroups — C₇₃×D₁₅⋊D₇ #44501446

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×D₂₁×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃₅×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₇×C₇₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₇×C₇₃	—	5	1	no	maximal, Hall
7	D₃₅×C₇₃	D₃	1	1	yes	characteristic, complemented
8	C₇×D₅×C₇₃	—	3	1	no	—
9	C₅×D₇×C₇₃	—	3	1	no	—
10	D₃×D₅×C₇₃	—	7	1	no	maximal, Hall
11	D₂₁×C₇₃	D₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₇₃	—	5	1	no	—
13	C₃×D₇×C₇₃	—	5	1	no	—
14	C₅×C₇×C₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₅×C₇₃	D₇	1	1	yes	characteristic, complemented
16	C₅×D₃×C₇₃	—	7	1	no	—
17	C₃×D₅×C₇₃	—	7	1	no	—
18	C₂×D₇×C₇₃	—	15	1	no	Hall
19	C₃×C₇×C₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₇₃	—	21	1	no	Hall
21	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₇₃	—	15	1	no	—
23	D₇×C₇₃	—	3	1	no	—
24	D₇×C₇₃	—	5	1	no	—
25	C₂×D₃×C₇₃	—	35	1	no	Hall
26	C₂×C₅×C₇₃	—	21	1	no	—
27	D₅×C₇₃	—	3	1	no	—
28	D₅×C₇₃	—	7	1	no	—
29	C₇×C₇₃	D₃×D₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇₃	—	35	1	no	—
31	D₃×C₇₃	—	5	1	no	—
32	D₃×C₇₃	—	7	1	no	—
33	D₁₅⋊D₇	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₅×C₇₃	D₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₇₃	—	105	1	no	Hall
36	C₃×C₇₃	D₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₇×D₁₅	C₂×C₇₃	1	1	yes	characteristic, complemented
38	C₅×D₂₁	C₂×C₇₃	1	1	yes	characteristic, complemented
39	C₃×D₃₅	C₂×C₇₃	1	1	yes	characteristic, complemented
40	C₂×C₇₃	—	15	1	no	—
41	C₂×C₇₃	—	21	1	no	—
42	C₂×C₇₃	—	35	1	no	—
43	D₅×D₇	—	3	1	no	Hall
44	C₃×C₅×C₇	C₂²×C₇₃	1	1	yes	characteristic, complemented, Hall
45	D₃×D₇	—	5	1	no	Hall
46	C₇₃	D₁₅⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
47	D₃₅	D₃×C₇₃	1	1	yes	characteristic, complemented
48	C₅×D₇	—	3	1	no	—
49	C₇×D₅	—	3	1	no	—
50	D₃×D₅	—	7	1	no	Hall
51	D₂₁	D₅×C₇₃	1	1	yes	characteristic, complemented
52	C₃×D₇	—	5	1	no	—
53	D₃×C₇	—	5	1	no	—
54	C₅×C₇	C₂×D₃×C₇₃	1	1	yes	characteristic, complemented, Hall
55	D₁₅	D₇×C₇₃	1	1	yes	characteristic, complemented
56	C₃×D₅	—	7	1	no	—
57	C₅×D₃	—	7	1	no	—
58	C₂×D₇	—	15	1	no	Hall
59	C₃×C₇	C₂×D₅×C₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	21	1	no	Hall
61	C₃×C₅	C₂×D₇×C₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	15	1	no	—
63	D₇	—	3	1	no	—
64	D₇	—	5	1	no	—
65	C₂×D₃	—	35	1	no	Hall
66	C₂×C₅	—	21	1	no	—
67	D₅	—	3	1	no	—
68	D₅	—	7	1	no	—
69	C₇	D₃×D₅×C₇₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	35	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	7	1	no	—
73	C₅	D₃×D₇×C₇₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	105	1	no	Sylow
75	C₃	D₅×D₇×C₇₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	21	1	no	—
78	C₂	—	35	1	no	—

	subgroup	G/H
center, hypercenter	C₇₃	D₁₅⋊D₇
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ 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×D₂₁×C₇₃	C₂	semidirect
3. C₃×D₃₅×C₇₃	C₂	semidirect
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
7. D₃₅×C₇₃	D₃	semidirect
11. D₂₁×C₇₃	D₅	semidirect
14. C₅×C₇×C₇₃	C₂×D₃	semidirect
15. D₁₅×C₇₃	D₇	semidirect
19. C₃×C₇×C₇₃	C₂×D₅	semidirect
21. C₃×C₅×C₇₃	C₂×D₇	semidirect
29. C₇×C₇₃	D₃×D₅	semidirect
33. D₁₅⋊D₇	C₇₃	direct (N × H)
34. C₅×C₇₃	D₃×D₇	semidirect
36. C₃×C₇₃	D₅×D₇	semidirect
37. C₇×D₁₅	C₂×C₇₃	semidirect
38. C₅×D₂₁	C₂×C₇₃	semidirect
39. C₃×D₃₅	C₂×C₇₃	semidirect
44. C₃×C₅×C₇	C₂²×C₇₃	semidirect
46. C₇₃	D₁₅⋊D₇	direct (N × H)
47. D₃₅	D₃×C₇₃	semidirect
51. D₂₁	D₅×C₇₃	semidirect
54. C₅×C₇	C₂×D₃×C₇₃	semidirect
55. D₁₅	D₇×C₇₃	semidirect
59. C₃×C₇	C₂×D₅×C₇₃	semidirect
61. C₃×C₅	C₂×D₇×C₇₃	semidirect
69. C₇	D₃×D₅×C₇₃	semidirect
73. C₅	D₃×D₇×C₇₃	semidirect
75. C₃	D₅×D₇×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×D₂₁×C₇₃	2
C₃×D₃₅×C₇₃	2
D₅×D₇×C₇₃	3
D₃×D₇×C₇₃	5
D₃×D₅×C₇₃	7
D₁₅⋊D₇	73

Subgroups — C73×D15⋊D7 #44501446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×D₁₅⋊D₇ #44501446