Subgroups — D₅×C₂₃×D₄₁ #34038219

Order 18860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₂₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×D₄₁	—	5	1	no	maximal, Hall
6	C₂×C₂₃×C₄₁	—	5	1	no	—
7	C₂₃×D₄₁	—	5	1	no	—
8	C₂₃×D₄₁	D₅	1	1	yes	characteristic, direct product factor
9	C₂₃×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×D₄₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×D₅×C₂₃	—	41	1	no	maximal, Hall
12	D₂₀₅	C₂×C₂₃	1	1	yes	characteristic, complemented
13	C₅×D₄₁	C₂×C₂₃	1	1	yes	characteristic, complemented
14	D₅×C₄₁	C₂×C₂₃	1	1	yes	characteristic, complemented
15	C₂×C₅×C₂₃	—	41	1	no	—
16	D₅×C₂₃	—	41	1	no	—
17	D₅×C₂₃	D₄₁	1	1	yes	characteristic, direct product factor
18	C₅×C₄₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₄₁	—	5	1	no	Hall
20	C₅×C₂₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₂₃	—	205	1	no	Hall
22	C₂×C₄₁	—	5	1	no	—
23	D₄₁	—	5	1	no	—
24	D₄₁	D₅×C₂₃	1	1	yes	characteristic, direct product factor
25	C₂×C₂₃	—	5	1	no	—
26	C₂×C₂₃	—	41	1	no	—
27	C₂×C₂₃	—	205	1	no	—
28	C₄₁	C₂×D₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₂₃	D₅×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₅	—	41	1	no	Hall
31	C₂×C₅	—	41	1	no	—
32	D₅	—	41	1	no	—
33	D₅	C₂₃×D₄₁	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₂₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	205	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	41	1	no	—
38	C₂	—	205	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₅×D₄₁
commutator, cosocle, hypocenter	C₅×C₄₁	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₄₁	C₂²
LCS	G ▷ C₅×C₄₁
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₂₀₅	C₂	semidirect
2. D₅×C₂₃×C₄₁	C₂	semidirect
3. C₅×C₂₃×D₄₁	C₂	semidirect
4. C₅×C₂₃×C₄₁	C₂²	semidirect
8. C₂₃×D₄₁	D₅	direct (N × H)
9. C₂₃×C₄₁	C₂×D₅	semidirect
10. D₅×D₄₁	C₂₃	direct (N × H)
12. D₂₀₅	C₂×C₂₃	semidirect
13. C₅×D₄₁	C₂×C₂₃	semidirect
14. D₅×C₄₁	C₂×C₂₃	semidirect
17. D₅×C₂₃	D₄₁	direct (N × H)
18. C₅×C₄₁	C₂²×C₂₃	semidirect
20. C₅×C₂₃	C₂×D₄₁	semidirect
24. D₄₁	D₅×C₂₃	direct (N × H)
28. C₄₁	C₂×D₅×C₂₃	semidirect
29. C₂₃	D₅×D₄₁	direct (N × H)
33. D₅	C₂₃×D₄₁	direct (N × H)
34. C₅	C₂×C₂₃×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×D₂₀₅	2
D₅×C₂₃×C₄₁	2
C₅×C₂₃×D₄₁	2
C₂×C₂₃×D₄₁	5
D₅×D₄₁	23
C₂×D₅×C₂₃	41

Subgroups — D5×C23×D41 #34038219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₂₃×D₄₁ #34038219