Subgroups — C₃×C₅²×D₇₃⋊C₃ #45659487

Order 32850.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×D₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₇₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×D₇₃⋊C₃	C₅	1	6	yes	maximal, direct product factor
5	C₅²×C₇₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅²×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×D₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₇₃⋊C₃	C₂×C₅	1	6	yes	complemented
9	C₅×D₇₃⋊C₃	C₃×C₅	1	18	yes	direct product factor
10	C₃×C₅×D₇₃	C₃×C₅	1	6	yes	complemented
11	C₅²×C₇₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₇₃⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇₃	C₂×C₃×C₅	1	6	yes	complemented
14	C₅×C₇₃⋊C₃	C₂×C₃×C₅	1	18	yes	complemented
15	C₅×D₇₃	C₃²×C₅	1	6	yes	complemented
16	C₃×C₇₃⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₅²	—	73	1	no	maximal, Hall
18	C₃×D₇₃	C₃×C₅²	1	1	yes	characteristic, complemented
19	D₇₃⋊C₃	C₃×C₅²	1	3	yes	direct product factor
20	C₅×C₇₃	C₂×C₃²×C₅	1	6	yes	complemented
21	C₃²×C₅²	—	73	1	no	Hall
22	C₃×C₇₃	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
23	C₇₃⋊C₃	C₂×C₃×C₅²	1	3	yes	complemented
24	C₂×C₃×C₅²	—	73	3	no	—
25	C₂×C₃×C₅²	—	73	1	no	—
26	D₇₃	C₃²×C₅²	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃²×C₅	—	73	6	no	—
28	C₃×C₅²	—	73	3	no	—
29	C₃×C₅²	D₇₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₇₃	C₂×C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅²	—	73	1	no	Hall
32	C₃²×C₅	—	73	6	no	—
33	C₂×C₃×C₅	—	73	18	no	—
34	C₂×C₃×C₅	—	73	6	no	—
35	C₅²	C₃×D₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃²	—	73	1	no	Hall
37	C₃×C₅	—	73	18	no	—
38	C₃×C₅	C₅×D₇₃⋊C₃	1	6	yes	direct product factor
39	C₂×C₅	—	73	6	no	—
40	C₃²	—	73	1	no	Sylow
41	C₂×C₃	—	73	3	no	—
42	C₂×C₃	—	73	1	no	—
43	C₅	C₃×C₅×D₇₃⋊C₃	1	6	yes	direct product factor
44	C₃	—	73	3	no	—
45	C₃	C₅²×D₇₃⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	—	73	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅²	D₇₃⋊C₃
commutator, cosocle, hypocenter	C₇₃	C₂×C₃²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₃	C₂×C₃
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₃×C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇₃⋊C₃	C₂	semidirect
2. C₃×C₅²×D₇₃	C₃	semidirect
3. C₅²×D₇₃⋊C₃	C₃	direct (N × H)
4. C₃×C₅×D₇₃⋊C₃	C₅	direct (N × H)
5. C₅²×C₇₃⋊C₃	C₂×C₃	semidirect
6. C₃×C₅²×C₇₃	C₂×C₃	semidirect
7. C₅²×D₇₃	C₃²	semidirect
8. C₃×C₅×C₇₃⋊C₃	C₂×C₅	semidirect
9. C₅×D₇₃⋊C₃	C₃×C₅	direct (N × H)
10. C₃×C₅×D₇₃	C₃×C₅	semidirect
11. C₅²×C₇₃	C₂×C₃²	semidirect
12. C₃×D₇₃⋊C₃	C₅²	direct (N × H)
13. C₃×C₅×C₇₃	C₂×C₃×C₅	semidirect
14. C₅×C₇₃⋊C₃	C₂×C₃×C₅	semidirect
15. C₅×D₇₃	C₃²×C₅	semidirect
16. C₃×C₇₃⋊C₃	C₂×C₅²	semidirect
18. C₃×D₇₃	C₃×C₅²	semidirect
19. D₇₃⋊C₃	C₃×C₅²	direct (N × H)
20. C₅×C₇₃	C₂×C₃²×C₅	semidirect
22. C₃×C₇₃	C₂×C₃×C₅²	semidirect
23. C₇₃⋊C₃	C₂×C₃×C₅²	semidirect
26. D₇₃	C₃²×C₅²	semidirect
29. C₃×C₅²	D₇₃⋊C₃	direct (N × H)
30. C₇₃	C₂×C₃²×C₅²	semidirect
35. C₅²	C₃×D₇₃⋊C₃	direct (N × H)
38. C₃×C₅	C₅×D₇₃⋊C₃	direct (N × H)
43. C₅	C₃×C₅×D₇₃⋊C₃	direct (N × H)
45. C₃	C₅²×D₇₃⋊C₃	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×C₅²×C₇₃⋊C₃	2
C₃×C₅²×D₇₃	3
C₅²×D₇₃⋊C₃	3
C₃×C₅×D₇₃⋊C₃	5
C₂×C₃²×C₅²	73

Subgroups — C3×C52×D73⋊C3 #45659487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×D₇₃⋊C₃ #45659487