Subgroups — C₂×C₅×C₄₁×D₄₁ #46777472

Order 33620.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₁×D₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₄₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₁²	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₁×D₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₄₁²	C₂×C₅	1	1	yes	characteristic, complemented
6	C₄₁×D₄₁	C₂×C₅	1	2	yes	direct product factor
7	C₄₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₅×C₄₁	—	41	1	no	maximal
9	C₂×C₅×D₄₁	C₄₁	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₅×C₄₁	—	2	20	no	—
11	C₂×C₅×C₄₁	—	41	2	no	—
12	C₂×C₅×C₄₁	D₄₁	1	1	yes	characteristic, direct product factor
13	C₂×C₅×C₄₁	C₂×C₄₁	1	1	yes	characteristic, complemented
14	C₅×D₄₁	C₂×C₄₁	1	2	yes	direct product factor
15	C₅×C₄₁	—	2	20	no	—
16	C₅×C₄₁	C₂×D₄₁	1	1	yes	characteristic, direct product factor
17	C₅×C₄₁	C₂²×C₄₁	1	1	yes	characteristic, complemented
18	C₂²×C₄₁	—	41	1	no	—
19	C₂×D₄₁	C₅×C₄₁	1	1	yes	characteristic, direct product factor
20	C₂×C₄₁	—	2	20	no	—
21	C₂×C₄₁	—	41	2	no	—
22	C₂×C₄₁	C₅×D₄₁	1	1	yes	characteristic, direct product factor
23	C₂×C₄₁	C₂×C₅×C₄₁	1	1	yes	characteristic, complemented
24	D₄₁	C₂×C₅×C₄₁	1	2	yes	direct product factor
25	C₄₁	—	2	20	no	—
26	C₄₁	C₂×C₅×D₄₁	1	1	yes	characteristic, direct product factor
27	C₄₁	C₂²×C₅×C₄₁	1	1	yes	characteristic, complemented
28	C₂²×C₅	—	41	1	no	Hall
29	C₂×C₅	—	41	2	no	—
30	C₂×C₅	C₄₁×D₄₁	1	1	yes	characteristic, direct product factor
31	C₅	C₂×C₄₁×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²	—	41	1	no	Sylow
33	C₂	—	41	2	no	—
34	C₂	C₅×C₄₁×D₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₄₁	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂²×C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₄₁²	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₅×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₁×D₄₁	C₂	direct (N × H)
2. C₂×C₅×C₄₁²	C₂	semidirect
3. C₅×C₄₁²	C₂²	semidirect
4. C₂×C₄₁×D₄₁	C₅	direct (N × H)
5. C₂×C₄₁²	C₂×C₅	semidirect
6. C₄₁×D₄₁	C₂×C₅	direct (N × H)
7. C₄₁²	C₂²×C₅	semidirect
9. C₂×C₅×D₄₁	C₄₁	direct (N × H)
12. C₂×C₅×C₄₁	D₄₁	direct (N × H)
13. C₂×C₅×C₄₁	C₂×C₄₁	semidirect
14. C₅×D₄₁	C₂×C₄₁	direct (N × H)
16. C₅×C₄₁	C₂×D₄₁	direct (N × H)
17. C₅×C₄₁	C₂²×C₄₁	semidirect
19. C₂×D₄₁	C₅×C₄₁	direct (N × H)
22. C₂×C₄₁	C₅×D₄₁	direct (N × H)
23. C₂×C₄₁	C₂×C₅×C₄₁	semidirect
24. D₄₁	C₂×C₅×C₄₁	direct (N × H)
26. C₄₁	C₂×C₅×D₄₁	direct (N × H)
27. C₄₁	C₂²×C₅×C₄₁	semidirect
30. C₂×C₅	C₄₁×D₄₁	direct (N × H)
31. C₅	C₂×C₄₁×D₄₁	direct (N × H)
34. C₂	C₅×C₄₁×D₄₁	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×C₄₁×D₄₁	2
C₂×C₅×C₄₁²	2
C₂×C₄₁×D₄₁	5
C₂²×C₅×C₄₁	41
C₂×C₅×D₄₁	41

Subgroups — C2×C5×C41×D41 #46777472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₄₁×D₄₁ #46777472