Subgroups — C₅×D₃×D₄₀₁ #37562637

Order 24060.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₄₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₄₀₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₄₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₄₀₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₄₀₁	—	3	1	no	—
8	C₅×D₄₀₁	—	3	1	no	—
9	C₅×D₄₀₁	D₃	1	1	yes	characteristic, direct product factor
10	D₁₂₀₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×D₄₀₁	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₄₀₁	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₄₀₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₄₀₁	—	3	1	no	Hall
15	C₃×C₄₀₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₄₀₁	—	3	1	no	—
17	D₄₀₁	—	3	1	no	—
18	D₄₀₁	C₅×D₃	1	1	yes	characteristic, direct product factor
19	C₄₀₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅×D₃	—	401	1	no	maximal, Hall
21	C₂×C₃×C₅	—	401	1	no	—
22	C₅×D₃	—	401	1	no	—
23	C₅×D₃	D₄₀₁	1	1	yes	characteristic, direct product factor
24	C₂²×C₅	—	1203	1	no	Hall
25	C₃×C₅	C₂×D₄₀₁	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	401	1	no	Hall
27	C₂×C₅	—	3	1	no	—
28	C₂×C₅	—	401	1	no	—
29	C₂×C₅	—	1203	1	no	—
30	C₂×C₃	—	401	1	no	—
31	D₃	—	401	1	no	—
32	D₃	C₅×D₄₀₁	1	1	yes	characteristic, direct product factor
33	C₅	D₃×D₄₀₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	1203	1	no	Sylow
35	C₃	C₂×C₅×D₄₀₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	401	1	no	—
38	C₂	—	1203	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃×D₄₀₁
commutator, cosocle, hypocenter	C₃×C₄₀₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₄₀₁	C₂²
LCS	G ▷ C₃×C₄₀₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₂₀₃	C₂	semidirect
2. C₅×D₃×C₄₀₁	C₂	semidirect
3. C₃×C₅×D₄₀₁	C₂	semidirect
5. C₃×C₅×C₄₀₁	C₂²	semidirect
6. D₃×D₄₀₁	C₅	direct (N × H)
9. C₅×D₄₀₁	D₃	direct (N × H)
10. D₁₂₀₃	C₂×C₅	semidirect
11. C₃×D₄₀₁	C₂×C₅	semidirect
12. D₃×C₄₀₁	C₂×C₅	semidirect
13. C₅×C₄₀₁	C₂×D₃	semidirect
15. C₃×C₄₀₁	C₂²×C₅	semidirect
18. D₄₀₁	C₅×D₃	direct (N × H)
19. C₄₀₁	C₂×C₅×D₃	semidirect
23. C₅×D₃	D₄₀₁	direct (N × H)
25. C₃×C₅	C₂×D₄₀₁	semidirect
32. D₃	C₅×D₄₀₁	direct (N × H)
33. C₅	D₃×D₄₀₁	direct (N × H)
35. C₃	C₂×C₅×D₄₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₂₀₃	2
C₅×D₃×C₄₀₁	2
C₃×C₅×D₄₀₁	2
C₂×C₅×D₄₀₁	3
D₃×D₄₀₁	5
C₂×C₅×D₃	401

Subgroups — C5×D3×D401 #37562637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₄₀₁ #37562637