Subgroups — C₂×C₅×C₂₃×D₄₃ #34089928

Order 19780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×D₄₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×D₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₃×C₄₃	C₂×C₅	1	1	yes	characteristic, complemented
6	C₂₃×D₄₃	C₂×C₅	1	2	yes	direct product factor
7	C₂₃×C₄₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×D₄₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₂₃	—	43	1	no	maximal, Hall
10	C₂×C₅×C₄₃	C₂×C₂₃	1	1	yes	characteristic, complemented
11	C₅×D₄₃	C₂×C₂₃	1	2	yes	direct product factor
12	C₂×C₅×C₂₃	—	43	2	no	—
13	C₂×C₅×C₂₃	D₄₃	1	1	yes	characteristic, direct product factor
14	C₅×C₄₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₄₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₂₃	C₂×D₄₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₂₃	—	43	1	no	Hall
18	C₂×C₄₃	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
19	D₄₃	C₂×C₅×C₂₃	1	2	yes	direct product factor
20	C₂×C₂₃	—	43	2	no	—
21	C₂×C₂₃	C₅×D₄₃	1	1	yes	characteristic, direct product factor
22	C₄₃	C₂²×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
23	C₂₃	C₂×C₅×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₅	—	43	1	no	Hall
25	C₂×C₅	—	43	2	no	—
26	C₂×C₅	C₂₃×D₄₃	1	1	yes	characteristic, direct product factor
27	C₅	C₂×C₂₃×D₄₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	43	1	no	Sylow
29	C₂	—	43	2	no	—
30	C₂	C₅×C₂₃×D₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₃	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂²×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×D₄₃	C₂	direct (N × H)
2. C₂×C₅×C₂₃×C₄₃	C₂	semidirect
3. C₅×C₂₃×C₄₃	C₂²	semidirect
4. C₂×C₂₃×D₄₃	C₅	direct (N × H)
5. C₂×C₂₃×C₄₃	C₂×C₅	semidirect
6. C₂₃×D₄₃	C₂×C₅	direct (N × H)
7. C₂₃×C₄₃	C₂²×C₅	semidirect
8. C₂×C₅×D₄₃	C₂₃	direct (N × H)
10. C₂×C₅×C₄₃	C₂×C₂₃	semidirect
11. C₅×D₄₃	C₂×C₂₃	direct (N × H)
13. C₂×C₅×C₂₃	D₄₃	direct (N × H)
14. C₅×C₄₃	C₂²×C₂₃	semidirect
15. C₂×D₄₃	C₅×C₂₃	direct (N × H)
16. C₅×C₂₃	C₂×D₄₃	direct (N × H)
18. C₂×C₄₃	C₂×C₅×C₂₃	semidirect
19. D₄₃	C₂×C₅×C₂₃	direct (N × H)
21. C₂×C₂₃	C₅×D₄₃	direct (N × H)
22. C₄₃	C₂²×C₅×C₂₃	semidirect
23. C₂₃	C₂×C₅×D₄₃	direct (N × H)
26. C₂×C₅	C₂₃×D₄₃	direct (N × H)
27. C₅	C₂×C₂₃×D₄₃	direct (N × H)
30. C₂	C₅×C₂₃×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₃×D₄₃	2
C₂×C₅×C₂₃×C₄₃	2
C₂×C₂₃×D₄₃	5
C₂×C₅×D₄₃	23
C₂²×C₅×C₂₃	43

Subgroups — C2×C5×C23×D43 #34089928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂₃×D₄₃ #34089928