Subgroups — D₅×C₂₉×D₅₉ #46803777

Order 34220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₂₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₂₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₂₉×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₉×D₅₉	—	5	1	no	maximal, Hall
6	C₂×C₂₉×C₅₉	—	5	1	no	—
7	C₂₉×D₅₉	—	5	1	no	—
8	C₂₉×D₅₉	D₅	1	1	yes	characteristic, direct product factor
9	C₂₉×C₅₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×D₅₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₂₉₅	C₂×C₂₉	1	1	yes	characteristic, complemented
12	C₅×D₅₉	C₂×C₂₉	1	1	yes	characteristic, complemented
13	D₅×C₅₉	C₂×C₂₉	1	1	yes	characteristic, complemented
14	C₂×D₅×C₂₉	—	59	1	no	maximal, Hall
15	C₅×C₅₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₂₉	—	59	1	no	—
17	D₅×C₂₉	—	59	1	no	—
18	D₅×C₂₉	D₅₉	1	1	yes	characteristic, direct product factor
19	C₂×D₅₉	—	5	1	no	Hall
20	C₅×C₂₉	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅₉	—	5	1	no	—
22	D₅₉	—	5	1	no	—
23	D₅₉	D₅×C₂₉	1	1	yes	characteristic, direct product factor
24	C₂²×C₂₉	—	295	1	no	Hall
25	C₅₉	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₂₉	—	5	1	no	—
27	C₂×C₂₉	—	295	1	no	—
28	C₂×C₂₉	—	59	1	no	—
29	C₂₉	D₅×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×D₅	—	59	1	no	Hall
31	C₂×C₅	—	59	1	no	—
32	D₅	—	59	1	no	—
33	D₅	C₂₉×D₅₉	1	1	yes	characteristic, direct product factor
34	C₅	C₂×C₂₉×D₅₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	295	1	no	Sylow
36	C₂	—	5	1	no	—
37	C₂	—	295	1	no	—
38	C₂	—	59	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₅×D₅₉
commutator, cosocle, hypocenter	C₅×C₅₉	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₂₉×C₅₉	C₂²
LCS	G ▷ C₅×C₅₉
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₂₉₅	C₂	semidirect
2. D₅×C₂₉×C₅₉	C₂	semidirect
3. C₅×C₂₉×D₅₉	C₂	semidirect
4. C₅×C₂₉×C₅₉	C₂²	semidirect
8. C₂₉×D₅₉	D₅	direct (N × H)
9. C₂₉×C₅₉	C₂×D₅	semidirect
10. D₅×D₅₉	C₂₉	direct (N × H)
11. D₂₉₅	C₂×C₂₉	semidirect
12. C₅×D₅₉	C₂×C₂₉	semidirect
13. D₅×C₅₉	C₂×C₂₉	semidirect
15. C₅×C₅₉	C₂²×C₂₉	semidirect
18. D₅×C₂₉	D₅₉	direct (N × H)
20. C₅×C₂₉	C₂×D₅₉	semidirect
23. D₅₉	D₅×C₂₉	direct (N × H)
25. C₅₉	C₂×D₅×C₂₉	semidirect
29. C₂₉	D₅×D₅₉	direct (N × H)
33. D₅	C₂₉×D₅₉	direct (N × H)
34. C₅	C₂×C₂₉×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×D₂₉₅	2
D₅×C₂₉×C₅₉	2
C₅×C₂₉×D₅₉	2
C₂×C₂₉×D₅₉	5
D₅×D₅₉	29
C₂×D₅×C₂₉	59

Subgroups — D5×C29×D59 #46803777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₂₉×D₅₉ #46803777