Subgroups — C₂×C₇×C₂₉×D₄₁ #45685646

Order 33292.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×D₄₁	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	C₂×C₂₉×D₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₉×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented
6	C₂₉×D₄₁	C₂×C₇	1	2	yes	direct product factor
7	C₂₉×C₄₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×D₄₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₇×C₂₉	—	41	1	no	maximal, Hall
10	C₂×C₇×C₄₁	C₂×C₂₉	1	1	yes	characteristic, complemented
11	C₇×D₄₁	C₂×C₂₉	1	2	yes	direct product factor
12	C₂×C₇×C₂₉	—	41	2	no	—
13	C₂×C₇×C₂₉	D₄₁	1	1	yes	characteristic, direct product factor
14	C₇×C₄₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
15	C₇×C₂₉	C₂×D₄₁	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₄₁	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₂₉	—	41	1	no	Hall
18	C₂×C₄₁	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
19	D₄₁	C₂×C₇×C₂₉	1	2	yes	direct product factor
20	C₂×C₂₉	—	41	2	no	—
21	C₂×C₂₉	C₇×D₄₁	1	1	yes	characteristic, direct product factor
22	C₄₁	C₂²×C₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₂₉	C₂×C₇×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₇	—	41	1	no	Hall
25	C₂×C₇	—	41	2	no	—
26	C₂×C₇	C₂₉×D₄₁	1	1	yes	characteristic, direct product factor
27	C₇	C₂×C₂₉×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	41	1	no	Sylow
29	C₂	—	41	2	no	—
30	C₂	C₇×C₂₉×D₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₉	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂²×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₉×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₇×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉×D₄₁	C₂	direct (N × H)
2. C₂×C₇×C₂₉×C₄₁	C₂	semidirect
3. C₇×C₂₉×C₄₁	C₂²	semidirect
4. C₂×C₂₉×D₄₁	C₇	direct (N × H)
5. C₂×C₂₉×C₄₁	C₂×C₇	semidirect
6. C₂₉×D₄₁	C₂×C₇	direct (N × H)
7. C₂₉×C₄₁	C₂²×C₇	semidirect
8. C₂×C₇×D₄₁	C₂₉	direct (N × H)
10. C₂×C₇×C₄₁	C₂×C₂₉	semidirect
11. C₇×D₄₁	C₂×C₂₉	direct (N × H)
13. C₂×C₇×C₂₉	D₄₁	direct (N × H)
14. C₇×C₄₁	C₂²×C₂₉	semidirect
15. C₇×C₂₉	C₂×D₄₁	direct (N × H)
16. C₂×D₄₁	C₇×C₂₉	direct (N × H)
18. C₂×C₄₁	C₂×C₇×C₂₉	semidirect
19. D₄₁	C₂×C₇×C₂₉	direct (N × H)
21. C₂×C₂₉	C₇×D₄₁	direct (N × H)
22. C₄₁	C₂²×C₇×C₂₉	semidirect
23. C₂₉	C₂×C₇×D₄₁	direct (N × H)
26. C₂×C₇	C₂₉×D₄₁	direct (N × H)
27. C₇	C₂×C₂₉×D₄₁	direct (N × H)
30. C₂	C₇×C₂₉×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
C₇×C₂₉×D₄₁	2
C₂×C₇×C₂₉×C₄₁	2
C₂×C₂₉×D₄₁	7
C₂×C₇×D₄₁	29
C₂²×C₇×C₂₉	41

Subgroups — C2×C7×C29×D41 #45685646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₉×D₄₁ #45685646