Subgroups — C₂×D₇×C₂₉×C₄₁ #45685649

Order 33292.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×C₂₉×C₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₂₉×C₄₁	—	7	1	no	maximal, Hall
5	C₂×C₂₉×C₄₁	—	7	2	no	—
6	C₂×C₂₉×C₄₁	D₇	1	1	yes	characteristic, direct product factor
7	C₂₉×C₄₁	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×D₇×C₄₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₇×C₂₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₄₁	C₂×C₂₉	1	1	yes	characteristic, complemented
11	D₇×C₄₁	C₂×C₂₉	1	2	yes	direct product factor
12	C₂×C₇×C₂₉	C₂×C₄₁	1	1	yes	characteristic, complemented
13	D₇×C₂₉	C₂×C₄₁	1	2	yes	direct product factor
14	C₇×C₄₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
15	C₇×C₂₉	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₄₁	—	7	1	no	Hall
17	C₂²×C₂₉	—	7	1	no	Hall
18	C₂×C₄₁	—	7	2	no	—
19	C₂×C₄₁	D₇×C₂₉	1	1	yes	characteristic, direct product factor
20	C₂×C₂₉	—	7	2	no	—
21	C₂×C₂₉	D₇×C₄₁	1	1	yes	characteristic, direct product factor
22	C₄₁	C₂×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂₉	C₂×D₇×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₇	C₂₉×C₄₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	C₂×C₂₉×C₄₁	1	1	yes	characteristic, complemented
26	D₇	C₂×C₂₉×C₄₁	1	2	yes	direct product factor
27	C₇	C₂²×C₂₉×C₄₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	7	1	no	Sylow
29	C₂	—	7	2	no	—
30	C₂	D₇×C₂₉×C₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₉×C₄₁	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₂₉×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₉×C₄₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₂₉×C₄₁

Complements

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

N	H ≅ G/N	type
1. D₇×C₂₉×C₄₁	C₂	direct (N × H)
2. C₂×C₇×C₂₉×C₄₁	C₂	semidirect
3. C₇×C₂₉×C₄₁	C₂²	semidirect
6. C₂×C₂₉×C₄₁	D₇	direct (N × H)
7. C₂₉×C₄₁	C₂×D₇	direct (N × H)
8. C₂×D₇×C₄₁	C₂₉	direct (N × H)
9. C₂×D₇×C₂₉	C₄₁	direct (N × H)
10. C₂×C₇×C₄₁	C₂×C₂₉	semidirect
11. D₇×C₄₁	C₂×C₂₉	direct (N × H)
12. C₂×C₇×C₂₉	C₂×C₄₁	semidirect
13. D₇×C₂₉	C₂×C₄₁	direct (N × H)
14. C₇×C₄₁	C₂²×C₂₉	semidirect
15. C₇×C₂₉	C₂²×C₄₁	semidirect
19. C₂×C₄₁	D₇×C₂₉	direct (N × H)
21. C₂×C₂₉	D₇×C₄₁	direct (N × H)
22. C₄₁	C₂×D₇×C₂₉	direct (N × H)
23. C₂₉	C₂×D₇×C₄₁	direct (N × H)
24. C₂×D₇	C₂₉×C₄₁	direct (N × H)
25. C₂×C₇	C₂×C₂₉×C₄₁	semidirect
26. D₇	C₂×C₂₉×C₄₁	direct (N × H)
27. C₇	C₂²×C₂₉×C₄₁	semidirect
30. C₂	D₇×C₂₉×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
D₇×C₂₉×C₄₁	2
C₂×C₇×C₂₉×C₄₁	2
C₂²×C₂₉×C₄₁	7
C₂×D₇×C₄₁	29
C₂×D₇×C₂₉	41

Subgroups — C2×D7×C29×C41 #45685649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×C₂₉×C₄₁ #45685649