Subgroups — C₂²×C₃²×C₄₁⋊C₅ #20301607

Order 7380.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄₁⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₄₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₄₁⋊C₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃²×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₄₁⋊C₅	C₂×C₃	1	12	yes	direct product factor
6	C₂²×C₄₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₄₁	C₂×C₅	1	3	yes	complemented
8	C₃×C₄₁⋊C₅	C₂²×C₃	1	4	yes	direct product factor
9	C₂²×C₃×C₄₁	C₃×C₅	1	4	yes	complemented
10	C₂×C₄₁⋊C₅	C₂×C₃²	1	3	yes	direct product factor
11	C₃²×C₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₄₁	C₂×C₃×C₅	1	12	yes	complemented
13	C₄₁⋊C₅	C₂²×C₃²	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₃²×C₅	—	41	1	no	maximal, Hall
15	C₂²×C₄₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₁	C₂²×C₃×C₅	1	4	yes	complemented
17	C₂×C₃²×C₅	—	41	3	no	—
18	C₂×C₄₁	C₂×C₃²×C₅	1	3	yes	complemented
19	C₂²×C₃×C₅	—	41	4	no	—
20	C₃²×C₅	—	41	1	no	Hall
21	C₄₁	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₃²	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	—	41	12	no	—
24	C₂²×C₅	—	41	1	no	Hall
25	C₂×C₃²	C₂×C₄₁⋊C₅	1	3	yes	direct product factor
26	C₃×C₅	—	41	4	no	—
27	C₂²×C₃	C₃×C₄₁⋊C₅	1	4	yes	direct product factor
28	C₂×C₅	—	41	3	no	—
29	C₃²	C₂²×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₃×C₄₁⋊C₅	1	12	yes	direct product factor
31	C₅	—	41	1	no	Sylow
32	C₂²	C₃²×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₄₁⋊C₅	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₄₁⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃²	C₄₁⋊C₅
commutator, hypocenter	C₄₁	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂²×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₄₁⋊C₅	C₂	direct (N × H)
2. C₂²×C₃×C₄₁⋊C₅	C₃	direct (N × H)
3. C₃²×C₄₁⋊C₅	C₂²	direct (N × H)
4. C₂²×C₃²×C₄₁	C₅	semidirect
5. C₂×C₃×C₄₁⋊C₅	C₂×C₃	direct (N × H)
6. C₂²×C₄₁⋊C₅	C₃²	direct (N × H)
7. C₂×C₃²×C₄₁	C₂×C₅	semidirect
8. C₃×C₄₁⋊C₅	C₂²×C₃	direct (N × H)
9. C₂²×C₃×C₄₁	C₃×C₅	semidirect
10. C₂×C₄₁⋊C₅	C₂×C₃²	direct (N × H)
11. C₃²×C₄₁	C₂²×C₅	semidirect
12. C₂×C₃×C₄₁	C₂×C₃×C₅	semidirect
13. C₄₁⋊C₅	C₂²×C₃²	direct (N × H)
15. C₂²×C₄₁	C₃²×C₅	semidirect
16. C₃×C₄₁	C₂²×C₃×C₅	semidirect
18. C₂×C₄₁	C₂×C₃²×C₅	semidirect
21. C₄₁	C₂²×C₃²×C₅	semidirect
22. C₂²×C₃²	C₄₁⋊C₅	direct (N × H)
25. C₂×C₃²	C₂×C₄₁⋊C₅	direct (N × H)
27. C₂²×C₃	C₃×C₄₁⋊C₅	direct (N × H)
29. C₃²	C₂²×C₄₁⋊C₅	direct (N × H)
30. C₂×C₃	C₂×C₃×C₄₁⋊C₅	direct (N × H)
32. C₂²	C₃²×C₄₁⋊C₅	direct (N × H)
33. C₃	C₂²×C₃×C₄₁⋊C₅	direct (N × H)
34. C₂	C₂×C₃²×C₄₁⋊C₅	direct (N × H)

Subgroups — C22×C32×C41⋊C5 #20301607

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃²×C₄₁⋊C₅ #20301607