Subgroups — D₅×C₄₃×D₂₃ #34089918

Order 19780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×D₁₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₃×D₂₃	—	5	1	no	maximal, Hall
6	C₂×C₂₃×C₄₃	—	5	1	no	—
7	C₄₃×D₂₃	—	5	1	no	—
8	C₄₃×D₂₃	D₅	1	1	yes	characteristic, direct product factor
9	C₂₃×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	C₂×D₅×C₄₃	—	23	1	no	maximal, Hall
11	D₅×D₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₄₃	—	23	1	no	—
13	D₅×C₄₃	—	23	1	no	—
14	D₅×C₄₃	D₂₃	1	1	yes	characteristic, direct product factor
15	D₁₁₅	C₂×C₄₃	1	1	yes	characteristic, complemented
16	C₅×D₂₃	C₂×C₄₃	1	1	yes	characteristic, complemented
17	D₅×C₂₃	C₂×C₄₃	1	1	yes	characteristic, complemented
18	C₅×C₄₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₄₃	—	115	1	no	Hall
20	C₅×C₂₃	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₂₃	—	5	1	no	Hall
22	C₂×C₄₃	—	5	1	no	—
23	C₂×C₄₃	—	23	1	no	—
24	C₂×C₄₃	—	115	1	no	—
25	C₂×C₂₃	—	5	1	no	—
26	D₂₃	—	5	1	no	—
27	D₂₃	D₅×C₄₃	1	1	yes	characteristic, direct product factor
28	C₄₃	D₅×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂₃	C₂×D₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₅	—	23	1	no	Hall
31	C₂×C₅	—	23	1	no	—
32	D₅	—	23	1	no	—
33	D₅	C₄₃×D₂₃	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₄₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	115	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	23	1	no	—
38	C₂	—	115	1	no	—

	subgroup	G/H
center, hypercenter	C₄₃	D₅×D₂₃
commutator, cosocle, hypocenter	C₅×C₂₃	C₂²×C₄₃
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₄₃	C₂²
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₄₃

Complements

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

N	H ≅ G/N	type
1. C₄₃×D₁₁₅	C₂	semidirect
2. D₅×C₂₃×C₄₃	C₂	semidirect
3. C₅×C₄₃×D₂₃	C₂	semidirect
4. C₅×C₂₃×C₄₃	C₂²	semidirect
8. C₄₃×D₂₃	D₅	direct (N × H)
9. C₂₃×C₄₃	C₂×D₅	semidirect
11. D₅×D₂₃	C₄₃	direct (N × H)
14. D₅×C₄₃	D₂₃	direct (N × H)
15. D₁₁₅	C₂×C₄₃	semidirect
16. C₅×D₂₃	C₂×C₄₃	semidirect
17. D₅×C₂₃	C₂×C₄₃	semidirect
18. C₅×C₄₃	C₂×D₂₃	semidirect
20. C₅×C₂₃	C₂²×C₄₃	semidirect
27. D₂₃	D₅×C₄₃	direct (N × H)
28. C₄₃	D₅×D₂₃	direct (N × H)
29. C₂₃	C₂×D₅×C₄₃	semidirect
33. D₅	C₄₃×D₂₃	direct (N × H)
34. C₅	C₂×C₄₃×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×D₁₁₅	2
D₅×C₂₃×C₄₃	2
C₅×C₄₃×D₂₃	2
C₂×C₄₃×D₂₃	5
C₂×D₅×C₄₃	23
D₅×D₂₃	43

Subgroups — D5×C43×D23 #34089918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₄₃×D₂₃ #34089918