Subgroups — C₂×C₃×C₅²×C₇₃ #24926537

Order 10950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₇₃	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₇₃	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₇₃	C₂×C₅	1	6	yes	direct product factor
6	C₂×C₅×C₇₃	C₃×C₅	1	6	yes	direct product factor
7	C₂×C₃×C₇₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇₃	C₂×C₃×C₅	1	6	yes	direct product factor
9	C₃×C₇₃	C₂×C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₅²	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇₃	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅²	C₂×C₇₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇₃	C₂×C₃×C₅²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₅²	C₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₅	C₅×C₇₃	1	6	yes	direct product factor
16	C₅²	C₂×C₃×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₂×C₅×C₇₃	1	6	yes	direct product factor
18	C₂×C₅	C₃×C₅×C₇₃	1	6	yes	direct product factor
19	C₂×C₃	C₅²×C₇₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅	C₂×C₃×C₅×C₇₃	1	6	yes	direct product factor
21	C₃	C₂×C₅²×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₅²×C₇₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇₃	C₂	direct (N × H)
2. C₂×C₅²×C₇₃	C₃	direct (N × H)
3. C₂×C₃×C₅×C₇₃	C₅	direct (N × H)
4. C₅²×C₇₃	C₂×C₃	direct (N × H)
5. C₃×C₅×C₇₃	C₂×C₅	direct (N × H)
6. C₂×C₅×C₇₃	C₃×C₅	direct (N × H)
7. C₂×C₃×C₇₃	C₅²	direct (N × H)
8. C₅×C₇₃	C₂×C₃×C₅	direct (N × H)
9. C₃×C₇₃	C₂×C₅²	direct (N × H)
10. C₂×C₃×C₅²	C₇₃	direct (N × H)
11. C₂×C₇₃	C₃×C₅²	direct (N × H)
12. C₃×C₅²	C₂×C₇₃	direct (N × H)
13. C₇₃	C₂×C₃×C₅²	direct (N × H)
14. C₂×C₅²	C₃×C₇₃	direct (N × H)
15. C₂×C₃×C₅	C₅×C₇₃	direct (N × H)
16. C₅²	C₂×C₃×C₇₃	direct (N × H)
17. C₃×C₅	C₂×C₅×C₇₃	direct (N × H)
18. C₂×C₅	C₃×C₅×C₇₃	direct (N × H)
19. C₂×C₃	C₅²×C₇₃	direct (N × H)
20. C₅	C₂×C₃×C₅×C₇₃	direct (N × H)
21. C₃	C₂×C₅²×C₇₃	direct (N × H)
22. C₂	C₃×C₅²×C₇₃	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	2
C₂×C₅²×C₇₃	3
C₂×C₃×C₅×C₇₃	5
C₂×C₃×C₅²	73

Subgroups — C2×C3×C52×C73 #24926537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅²×C₇₃ #24926537