Subgroups — C₅×D₃×C₁₃×C₇₃ #43249694

Order 28470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×C₁₃×C₇₃	—	3	1	no	maximal, Hall
3	D₃×C₁₃×C₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₇₃	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₃×C₇₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₇₃	—	3	1	no	Hall
8	C₃×C₅×C₇₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₇₃	C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₇₃	—	3	1	no	Hall
11	D₃×C₇₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₅×D₃×C₁₃	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₇₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇₃	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₃	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇₃	—	3	1	no	Hall
17	C₂×C₅×C₁₃	—	3	1	no	Hall
18	D₃×C₁₃	C₅×C₇₃	1	1	yes	characteristic, direct product factor, Hall
19	C₇₃	C₅×D₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₅×C₁₃	D₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₃	C₂×C₅×C₇₃	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	C₁₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₃	—	3	1	no	Hall
24	C₃×C₅	C₂×C₁₃×C₇₃	1	1	yes	characteristic, complemented, Hall
25	C₁₃	C₅×D₃×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	—	3	1	no	Hall
27	D₃	C₅×C₁₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
28	C₅	D₃×C₁₃×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₅×C₁₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃×C₇₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₁₃×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₇₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₁₃×C₇₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×C₇₃	C₂	semidirect
3. D₃×C₁₃×C₇₃	C₅	direct (N × H)
4. C₅×C₁₃×C₇₃	D₃	direct (N × H)
5. C₃×C₁₃×C₇₃	C₂×C₅	semidirect
6. C₅×D₃×C₇₃	C₁₃	direct (N × H)
8. C₃×C₅×C₇₃	C₂×C₁₃	semidirect
9. C₁₃×C₇₃	C₅×D₃	direct (N × H)
11. D₃×C₇₃	C₅×C₁₃	direct (N × H)
12. C₅×D₃×C₁₃	C₇₃	direct (N × H)
13. C₅×C₇₃	D₃×C₁₃	direct (N × H)
14. C₃×C₇₃	C₂×C₅×C₁₃	semidirect
15. C₃×C₅×C₁₃	C₂×C₇₃	semidirect
18. D₃×C₁₃	C₅×C₇₃	direct (N × H)
19. C₇₃	C₅×D₃×C₁₃	direct (N × H)
20. C₅×C₁₃	D₃×C₇₃	direct (N × H)
21. C₃×C₁₃	C₂×C₅×C₇₃	semidirect
22. C₅×D₃	C₁₃×C₇₃	direct (N × H)
24. C₃×C₅	C₂×C₁₃×C₇₃	semidirect
25. C₁₃	C₅×D₃×C₇₃	direct (N × H)
27. D₃	C₅×C₁₃×C₇₃	direct (N × H)
28. C₅	D₃×C₁₃×C₇₃	direct (N × H)
29. C₃	C₂×C₅×C₁₃×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₃×C₇₃	2
C₂×C₅×C₁₃×C₇₃	3
D₃×C₁₃×C₇₃	5
C₅×D₃×C₇₃	13
C₅×D₃×C₁₃	73

Subgroups — C5×D3×C13×C73 #43249694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₃×C₇₃ #43249694