Subgroups — C₅×D₂₁×D₇₃ #44501413

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₅₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₁×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₇×D₇₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×D₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₅₁₁	—	3	1	no	—
8	C₅×D₇×C₇₃	—	3	1	no	—
9	C₅×C₇×D₇₃	D₃	1	1	yes	characteristic, complemented
10	C₅×D₃×D₇₃	—	7	1	no	maximal, Hall
11	D₁₅₃₃	C₂×C₅	1	1	yes	characteristic, complemented
12	D₂₁×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	—	7	1	no	—
16	C₅×D₃×C₇₃	—	7	1	no	—
17	C₃×C₅×D₇₃	D₇	1	1	yes	characteristic, complemented
18	D₇×D₇₃	—	3	1	no	Hall
19	C₃×C₇×C₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₇₃	—	21	1	no	Hall
21	C₃×C₅×C₇₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₅₁₁	—	3	1	no	—
23	C₇×D₇₃	C₅×D₃	1	1	yes	characteristic, complemented
24	D₇×C₇₃	—	3	1	no	—
25	D₃×D₇₃	—	7	1	no	Hall
26	C₂×C₅×C₇₃	—	21	1	no	—
27	C₅×D₇₃	—	21	1	no	—
28	C₅×D₇₃	D₂₁	1	1	yes	characteristic, direct product factor
29	C₇×C₇₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
30	D₂₁₉	—	7	1	no	—
31	C₃×D₇₃	C₅×D₇	1	1	yes	characteristic, complemented
32	D₃×C₇₃	—	7	1	no	—
33	C₂×C₅×D₂₁	—	73	1	no	maximal, Hall
34	C₅×C₇₃	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
35	C₂×D₇₃	—	21	1	no	Hall
36	C₃×C₇₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₅×C₇	—	73	1	no	—
38	C₅×D₂₁	—	73	1	no	—
39	C₅×D₂₁	D₇₃	1	1	yes	characteristic, direct product factor
40	C₂×C₇₃	—	21	1	no	—
41	D₇₃	—	21	1	no	—
42	D₇₃	C₅×D₂₁	1	1	yes	characteristic, direct product factor
43	C₂×C₅×D₇	—	219	1	no	Hall
44	C₃×C₅×C₇	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
45	C₂×D₂₁	—	73	1	no	Hall
46	C₇₃	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₅×C₇	—	73	1	no	—
48	C₅×D₇	—	3	1	no	—
49	C₅×D₇	—	219	1	no	—
50	C₂×C₅×D₃	—	511	1	no	Hall
51	C₂×C₃×C₇	—	73	1	no	—
52	D₂₁	—	73	1	no	—
53	D₂₁	C₅×D₇₃	1	1	yes	characteristic, direct product factor
54	C₅×C₇	D₃×D₇₃	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	73	1	no	—
56	C₅×D₃	—	7	1	no	—
57	C₅×D₃	—	511	1	no	—
58	C₂×D₇	—	219	1	no	Hall
59	C₃×C₇	C₂×C₅×D₇₃	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	1533	1	no	Hall
61	C₃×C₅	D₇×D₇₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	73	1	no	—
63	D₇	—	3	1	no	—
64	D₇	—	219	1	no	—
65	C₂×D₃	—	511	1	no	Hall
66	C₂×C₅	—	21	1	no	—
67	C₂×C₅	—	73	1	no	—
68	C₂×C₅	—	1533	1	no	—
69	C₇	C₅×D₃×D₇₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	73	1	no	—
71	D₃	—	7	1	no	—
72	D₃	—	511	1	no	—
73	C₅	D₂₁×D₇₃	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	1533	1	no	Sylow
75	C₃	C₅×D₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	73	1	no	—
78	C₂	—	1533	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₂₁×D₇₃
commutator, cosocle, hypocenter	C₃×C₇×C₇₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₇₃	C₂²
LCS	G ▷ C₃×C₇×C₇₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅₃₃	C₂	semidirect
2. C₅×D₂₁×C₇₃	C₂	semidirect
3. C₃×C₅×C₇×D₇₃	C₂	semidirect
5. C₃×C₅×C₇×C₇₃	C₂²	semidirect
6. D₂₁×D₇₃	C₅	direct (N × H)
9. C₅×C₇×D₇₃	D₃	semidirect
11. D₁₅₃₃	C₂×C₅	semidirect
12. D₂₁×C₇₃	C₂×C₅	semidirect
13. C₃×C₇×D₇₃	C₂×C₅	semidirect
14. C₅×C₇×C₇₃	C₂×D₃	semidirect
17. C₃×C₅×D₇₃	D₇	semidirect
19. C₃×C₇×C₇₃	C₂²×C₅	semidirect
21. C₃×C₅×C₇₃	C₂×D₇	semidirect
23. C₇×D₇₃	C₅×D₃	semidirect
28. C₅×D₇₃	D₂₁	direct (N × H)
29. C₇×C₇₃	C₂×C₅×D₃	semidirect
31. C₃×D₇₃	C₅×D₇	semidirect
34. C₅×C₇₃	C₂×D₂₁	semidirect
36. C₃×C₇₃	C₂×C₅×D₇	semidirect
39. C₅×D₂₁	D₇₃	direct (N × H)
42. D₇₃	C₅×D₂₁	direct (N × H)
44. C₃×C₅×C₇	C₂×D₇₃	semidirect
46. C₇₃	C₂×C₅×D₂₁	semidirect
53. D₂₁	C₅×D₇₃	direct (N × H)
54. C₅×C₇	D₃×D₇₃	semidirect
59. C₃×C₇	C₂×C₅×D₇₃	semidirect
61. C₃×C₅	D₇×D₇₃	semidirect
69. C₇	C₅×D₃×D₇₃	semidirect
73. C₅	D₂₁×D₇₃	direct (N × H)
75. C₃	C₅×D₇×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₅₃₃	2
C₅×D₂₁×C₇₃	2
C₃×C₅×C₇×D₇₃	2
C₅×D₇×D₇₃	3
D₂₁×D₇₃	5
C₅×D₃×D₇₃	7
C₂×C₅×D₂₁	73

Subgroups — C5×D21×D73 #44501413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₂₁×D₇₃ #44501413