Subgroups — C₂×C₅×C₇×D₅₉ #22551908

Order 8260.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₅₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×D₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₇×C₅₉	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×D₅₉	C₂×C₅	1	2	yes	direct product factor
8	C₂×C₅×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented
9	C₅×D₅₉	C₂×C₇	1	2	yes	direct product factor
10	C₇×C₅₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₅₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₅₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₅×C₇	—	59	1	no	maximal, Hall
14	C₂×C₅₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
15	D₅₉	C₂×C₅×C₇	1	2	yes	direct product factor
16	C₂×C₅×C₇	—	59	2	no	—
17	C₂×C₅×C₇	D₅₉	1	1	yes	characteristic, direct product factor
18	C₅₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
19	C₅×C₇	C₂×D₅₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₇	—	59	1	no	Hall
21	C₂²×C₅	—	59	1	no	Hall
22	C₂×C₇	—	59	2	no	—
23	C₂×C₇	C₅×D₅₉	1	1	yes	characteristic, direct product factor
24	C₂×C₅	—	59	2	no	—
25	C₂×C₅	C₇×D₅₉	1	1	yes	characteristic, direct product factor
26	C₇	C₂×C₅×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₅	C₂×C₇×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	59	1	no	Sylow
29	C₂	—	59	2	no	—
30	C₂	C₅×C₇×D₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₅₉
commutator, hypocenter	C₅₉	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₅₉	C₂
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₂×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₅₉	C₂	direct (N × H)
2. C₂×C₅×C₇×C₅₉	C₂	semidirect
3. C₅×C₇×C₅₉	C₂²	semidirect
4. C₂×C₇×D₅₉	C₅	direct (N × H)
5. C₂×C₅×D₅₉	C₇	direct (N × H)
6. C₂×C₇×C₅₉	C₂×C₅	semidirect
7. C₇×D₅₉	C₂×C₅	direct (N × H)
8. C₂×C₅×C₅₉	C₂×C₇	semidirect
9. C₅×D₅₉	C₂×C₇	direct (N × H)
10. C₇×C₅₉	C₂²×C₅	semidirect
11. C₅×C₅₉	C₂²×C₇	semidirect
12. C₂×D₅₉	C₅×C₇	direct (N × H)
14. C₂×C₅₉	C₂×C₅×C₇	semidirect
15. D₅₉	C₂×C₅×C₇	direct (N × H)
17. C₂×C₅×C₇	D₅₉	direct (N × H)
18. C₅₉	C₂²×C₅×C₇	semidirect
19. C₅×C₇	C₂×D₅₉	direct (N × H)
23. C₂×C₇	C₅×D₅₉	direct (N × H)
25. C₂×C₅	C₇×D₅₉	direct (N × H)
26. C₇	C₂×C₅×D₅₉	direct (N × H)
27. C₅	C₂×C₇×D₅₉	direct (N × H)
30. C₂	C₅×C₇×D₅₉	direct (N × H)

Subgroups — C2×C5×C7×D59 #22551908

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×D₅₉ #22551908