Subgroups — C₂×C₇×C₉×C₄₁⋊C₅ #38788898

Order 25830.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇×C₄₁⋊C₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₉×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₇×C₄₁⋊C₅	C₂×C₃	1	1	yes	characteristic
5	C₂×C₉×C₄₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇×C₄₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₉×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₉×C₄₁⋊C₅	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₄₁	C₃×C₅	1	1	yes	characteristic
10	C₇×C₄₁⋊C₅	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₄₁⋊C₅	C₃×C₇	1	1	yes	characteristic
12	C₃×C₇×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₂×C₉×C₄₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₇×C₉	—	41	1	no	maximal, Hall
15	C₃×C₄₁⋊C₅	C₂×C₃×C₇	1	1	yes	characteristic
16	C₂×C₇×C₄₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₁⋊C₅	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₉×C₄₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
19	C₅×C₇×C₉	—	41	1	no	Hall
20	C₇×C₄₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₄₁	C₃×C₅×C₇	1	1	yes	characteristic
22	C₂×C₃×C₅×C₇	—	41	1	no	—
23	C₄₁⋊C₅	C₂×C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₇×C₉	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₄₁	C₂×C₃×C₅×C₇	1	1	yes	characteristic
26	C₃×C₅×C₇	—	41	1	no	—
27	C₂×C₅×C₉	—	41	1	no	Hall
28	C₂×C₄₁	C₅×C₇×C₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₇	—	41	1	no	Hall
30	C₇×C₉	C₂×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₉	—	41	1	no	Hall
32	C₂×C₃×C₇	C₃×C₄₁⋊C₅	1	1	yes	characteristic
33	C₄₁	C₂×C₅×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	—	41	1	no	Hall
35	C₂×C₃×C₅	—	41	1	no	—
36	C₃×C₇	C₂×C₃×C₄₁⋊C₅	1	1	yes	characteristic
37	C₂×C₉	C₇×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	—	41	1	no	—
39	C₂×C₇	C₉×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₅	—	41	1	no	Hall
41	C₉	C₂×C₇×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₂×C₉×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₃×C₇×C₄₁⋊C₅	1	1	yes	characteristic
44	C₅	—	41	1	no	Sylow
45	C₃	C₂×C₃×C₇×C₄₁⋊C₅	1	1	yes	characteristic
46	C₂	C₇×C₉×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇×C₉	C₄₁⋊C₅
commutator, hypocenter	C₄₁	C₂×C₅×C₇×C₉
Frattini	C₃	C₂×C₃×C₇×C₄₁⋊C₅
Fitting	C₂×C₇×C₉×C₄₁	C₅
socle	C₂×C₃×C₇×C₄₁	C₃×C₅
prime radical	C₂×C₃×C₇×C₄₁⋊C₅	C₃
cosocle	C₃×C₄₁	C₂×C₃×C₅×C₇
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₇×C₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₄₁⋊C₅	C₂	direct (N × H)
3. C₂×C₇×C₉×C₄₁	C₅	semidirect
5. C₂×C₉×C₄₁⋊C₅	C₇	direct (N × H)
6. C₂×C₇×C₄₁⋊C₅	C₉	direct (N × H)
7. C₇×C₉×C₄₁	C₂×C₅	semidirect
8. C₉×C₄₁⋊C₅	C₂×C₇	direct (N × H)
10. C₇×C₄₁⋊C₅	C₂×C₉	direct (N × H)
13. C₂×C₉×C₄₁	C₅×C₇	semidirect
16. C₂×C₇×C₄₁	C₅×C₉	semidirect
17. C₂×C₄₁⋊C₅	C₇×C₉	direct (N × H)
18. C₉×C₄₁	C₂×C₅×C₇	semidirect
20. C₇×C₄₁	C₂×C₅×C₉	semidirect
23. C₄₁⋊C₅	C₂×C₇×C₉	direct (N × H)
24. C₂×C₇×C₉	C₄₁⋊C₅	direct (N × H)
28. C₂×C₄₁	C₅×C₇×C₉	semidirect
30. C₇×C₉	C₂×C₄₁⋊C₅	direct (N × H)
33. C₄₁	C₂×C₅×C₇×C₉	semidirect
37. C₂×C₉	C₇×C₄₁⋊C₅	direct (N × H)
39. C₂×C₇	C₉×C₄₁⋊C₅	direct (N × H)
41. C₉	C₂×C₇×C₄₁⋊C₅	direct (N × H)
42. C₇	C₂×C₉×C₄₁⋊C₅	direct (N × H)
46. C₂	C₇×C₉×C₄₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₄₁⋊C₅	2
C₂×C₃×C₇×C₄₁⋊C₅	3
C₂×C₇×C₉×C₄₁	5
C₂×C₉×C₄₁⋊C₅	7
C₂×C₅×C₇×C₉	41

Subgroups — C2×C7×C9×C41⋊C5 #38788898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₉×C₄₁⋊C₅ #38788898