Subgroups — C₅×C₁₃×D₂₀₅ #40998564

Order 26650.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₀₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×C₁₃×D₄₁	—	5	1	no	maximal
4	C₅×C₁₃×C₄₁	—	2	2	no	—
5	C₅×C₁₃×C₄₁	D₅	1	1	yes	characteristic, complemented
6	C₅×C₁₃×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅×D₂₀₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₃×D₄₁	—	5	1	no	Hall
9	C₅²×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₅×C₁₃	—	41	1	no	maximal, Hall
11	C₁₃×C₄₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
12	D₂₀₅	C₅×C₁₃	1	1	yes	characteristic, direct product factor
13	C₅×D₄₁	—	5	1	no	—
14	C₅²×C₁₃	D₄₁	1	1	yes	characteristic, complemented, Hall
15	C₅×C₄₁	—	2	2	no	—
16	C₅×C₄₁	D₅×C₁₃	1	1	yes	characteristic, complemented
17	C₅×C₄₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
18	C₂×C₅×C₁₃	—	205	1	no	—
19	D₅×C₁₃	—	41	1	no	—
20	D₄₁	—	5	1	no	Hall
21	C₅×C₁₃	—	2	2	no	—
22	C₅×C₁₃	C₅×D₄₁	1	1	yes	characteristic, complemented
23	C₅×C₁₃	D₂₀₅	1	1	yes	characteristic, direct product factor
24	C₅×D₅	—	41	1	no	Hall
25	C₄₁	C₅×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	205	1	no	Hall
27	C₅²	C₁₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
28	C₁₃	C₅×D₂₀₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅	—	205	1	no	—
30	D₅	—	41	1	no	—
31	C₅	—	2	2	no	—
32	C₅	C₅×C₁₃×D₄₁	1	1	yes	characteristic, complemented
33	C₅	C₁₃×D₂₀₅	1	1	yes	characteristic, direct product factor
34	C₂	—	205	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₂₀₅
commutator, cosocle, hypocenter	C₅×C₄₁	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₄₁	C₂
LCS	G ▷ C₅×C₄₁
UCS	C₁ ◁ C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₃×C₄₁	C₂	semidirect
2. C₁₃×D₂₀₅	C₅	direct (N × H)
5. C₅×C₁₃×C₄₁	D₅	semidirect
6. C₅×C₁₃×C₄₁	C₂×C₅	semidirect
7. C₅×D₂₀₅	C₁₃	direct (N × H)
9. C₅²×C₄₁	C₂×C₁₃	semidirect
11. C₁₃×C₄₁	C₅×D₅	semidirect
12. D₂₀₅	C₅×C₁₃	direct (N × H)
14. C₅²×C₁₃	D₄₁	semidirect
16. C₅×C₄₁	D₅×C₁₃	semidirect
17. C₅×C₄₁	C₂×C₅×C₁₃	semidirect
22. C₅×C₁₃	C₅×D₄₁	semidirect
23. C₅×C₁₃	D₂₀₅	direct (N × H)
25. C₄₁	C₅×D₅×C₁₃	semidirect
27. C₅²	C₁₃×D₄₁	semidirect
28. C₁₃	C₅×D₂₀₅	direct (N × H)
32. C₅	C₅×C₁₃×D₄₁	semidirect
33. C₅	C₁₃×D₂₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₁₃×C₄₁	2
C₁₃×D₂₀₅	5
C₅×C₁₃×D₄₁	5
C₅×D₂₀₅	13
C₅×D₅×C₁₃	41

Subgroups — C5×C13×D205 #40998564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×D₂₀₅ #40998564