Subgroups — C₂²×C₅×C₂₃×C₄₁ #34038199

Order 18860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₄₁	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₂₃×C₄₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₂₃×C₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₄₁	C₂×C₅	1	3	yes	direct product factor
5	C₂₃×C₄₁	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₅×C₄₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₂₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₄₁	C₂×C₂₃	1	3	yes	direct product factor
9	C₂×C₅×C₂₃	C₂×C₄₁	1	3	yes	direct product factor
10	C₅×C₄₁	C₂²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₄₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₂₃	C₂²×C₄₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₂₃	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₄₁	C₂×C₅×C₂₃	1	3	yes	direct product factor
15	C₂×C₂₃	C₂×C₅×C₄₁	1	3	yes	direct product factor
16	C₄₁	C₂²×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₃	C₂²×C₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₅	C₂₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₂×C₂₃×C₄₁	1	3	yes	direct product factor
20	C₅	C₂²×C₂₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²	C₅×C₂₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₂₃×C₄₁	1	3	yes	direct product factor

	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. C₂×C₅×C₂₃×C₄₁	C₂	direct (N × H)
2. C₅×C₂₃×C₄₁	C₂²	direct (N × H)
3. C₂²×C₂₃×C₄₁	C₅	direct (N × H)
4. C₂×C₂₃×C₄₁	C₂×C₅	direct (N × H)
5. C₂₃×C₄₁	C₂²×C₅	direct (N × H)
6. C₂²×C₅×C₄₁	C₂₃	direct (N × H)
7. C₂²×C₅×C₂₃	C₄₁	direct (N × H)
8. C₂×C₅×C₄₁	C₂×C₂₃	direct (N × H)
9. C₂×C₅×C₂₃	C₂×C₄₁	direct (N × H)
10. C₅×C₄₁	C₂²×C₂₃	direct (N × H)
11. C₂²×C₄₁	C₅×C₂₃	direct (N × H)
12. C₅×C₂₃	C₂²×C₄₁	direct (N × H)
13. C₂²×C₂₃	C₅×C₄₁	direct (N × H)
14. C₂×C₄₁	C₂×C₅×C₂₃	direct (N × H)
15. C₂×C₂₃	C₂×C₅×C₄₁	direct (N × H)
16. C₄₁	C₂²×C₅×C₂₃	direct (N × H)
17. C₂₃	C₂²×C₅×C₄₁	direct (N × H)
18. C₂²×C₅	C₂₃×C₄₁	direct (N × H)
19. C₂×C₅	C₂×C₂₃×C₄₁	direct (N × H)
20. C₅	C₂²×C₂₃×C₄₁	direct (N × H)
21. C₂²	C₅×C₂₃×C₄₁	direct (N × H)
22. C₂	C₂×C₅×C₂₃×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₂₃×C₄₁	2
C₂²×C₂₃×C₄₁	5
C₂²×C₅×C₄₁	23
C₂²×C₅×C₂₃	41

Subgroups — C22×C5×C23×C41 #34038199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₂₃×C₄₁ #34038199