Subgroups — C₃²×C₇×D₅×C₄₁ #38788973

Order 25830.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₅×C₄₁	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₇×C₄₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇×C₄₁	C₂×C₃	1	4	yes	complemented
5	C₃²×D₅×C₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₅×C₄₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₇×C₄₁	D₅	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₅×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇×C₄₁	—	5	4	no	—
10	C₅×C₇×C₄₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₄₁	C₃×C₇	1	4	yes	direct product factor
12	C₃×C₇×C₄₁	C₃×D₅	1	4	yes	direct product factor
13	C₂×C₃²×C₄₁	—	5	1	no	Hall
14	C₃²×C₇×D₅	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₁	C₂×C₃×C₇	1	4	yes	complemented
16	C₂×C₇×C₄₁	—	5	1	no	Hall
17	D₅×C₄₁	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₄₁	C₇×D₅	1	1	yes	characteristic, direct product factor, Hall
19	C₃²×C₅×C₇	C₂×C₄₁	1	1	yes	characteristic, complemented, Hall
20	C₇×C₄₁	C₃²×D₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₄₁	—	5	4	no	—
22	C₃×C₇×D₅	C₃×C₄₁	1	4	yes	direct product factor
23	C₅×C₄₁	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃²×C₇	—	5	1	no	Hall
25	C₃×C₄₁	C₃×C₇×D₅	1	4	yes	direct product factor
26	C₃×C₅×C₇	C₂×C₃×C₄₁	1	4	yes	complemented
27	C₃²×D₅	C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₄₁	—	5	1	no	Hall
29	C₇×D₅	C₃²×C₄₁	1	1	yes	characteristic, direct product factor, Hall
30	C₃²×C₇	D₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
31	C₃²×C₅	C₂×C₇×C₄₁	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₇	—	5	4	no	—
33	C₄₁	C₃²×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₅×C₇	C₂×C₃²×C₄₁	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	C₃×C₇×C₄₁	1	4	yes	direct product factor
36	C₃×C₇	C₃×D₅×C₄₁	1	4	yes	direct product factor
37	C₂×C₃²	—	5	1	no	Hall
38	C₃×C₅	C₂×C₃×C₇×C₄₁	1	4	yes	complemented
39	C₂×C₇	—	5	1	no	Hall
40	D₅	C₃²×C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
41	C₃²	C₇×D₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃²×D₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	5	4	no	—
44	C₅	C₂×C₃²×C₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×C₇×D₅×C₄₁	1	4	yes	direct product factor
46	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇×C₄₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃²×C₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₄₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₇×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₄₁	C₂	semidirect
2. C₃×C₇×D₅×C₄₁	C₃	direct (N × H)
4. C₃×C₅×C₇×C₄₁	C₂×C₃	semidirect
5. C₃²×D₅×C₄₁	C₇	direct (N × H)
6. C₇×D₅×C₄₁	C₃²	direct (N × H)
7. C₃²×C₇×C₄₁	D₅	direct (N × H)
8. C₃²×C₅×C₄₁	C₂×C₇	semidirect
10. C₅×C₇×C₄₁	C₂×C₃²	semidirect
11. C₃×D₅×C₄₁	C₃×C₇	direct (N × H)
12. C₃×C₇×C₄₁	C₃×D₅	direct (N × H)
14. C₃²×C₇×D₅	C₄₁	direct (N × H)
15. C₃×C₅×C₄₁	C₂×C₃×C₇	semidirect
17. D₅×C₄₁	C₃²×C₇	direct (N × H)
18. C₃²×C₄₁	C₇×D₅	direct (N × H)
19. C₃²×C₅×C₇	C₂×C₄₁	semidirect
20. C₇×C₄₁	C₃²×D₅	direct (N × H)
22. C₃×C₇×D₅	C₃×C₄₁	direct (N × H)
23. C₅×C₄₁	C₂×C₃²×C₇	semidirect
25. C₃×C₄₁	C₃×C₇×D₅	direct (N × H)
26. C₃×C₅×C₇	C₂×C₃×C₄₁	semidirect
27. C₃²×D₅	C₇×C₄₁	direct (N × H)
29. C₇×D₅	C₃²×C₄₁	direct (N × H)
30. C₃²×C₇	D₅×C₄₁	direct (N × H)
31. C₃²×C₅	C₂×C₇×C₄₁	semidirect
33. C₄₁	C₃²×C₇×D₅	direct (N × H)
34. C₅×C₇	C₂×C₃²×C₄₁	semidirect
35. C₃×D₅	C₃×C₇×C₄₁	direct (N × H)
36. C₃×C₇	C₃×D₅×C₄₁	direct (N × H)
38. C₃×C₅	C₂×C₃×C₇×C₄₁	semidirect
40. D₅	C₃²×C₇×C₄₁	direct (N × H)
41. C₃²	C₇×D₅×C₄₁	direct (N × H)
42. C₇	C₃²×D₅×C₄₁	direct (N × H)
44. C₅	C₂×C₃²×C₇×C₄₁	semidirect
45. C₃	C₃×C₇×D₅×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₄₁	2
C₃×C₇×D₅×C₄₁	3
C₂×C₃²×C₇×C₄₁	5
C₃²×D₅×C₄₁	7
C₃²×C₇×D₅	41

Subgroups — C32×C7×D5×C41 #38788973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₅×C₄₁ #38788973