Subgroups — C₂×D₅×C₅₉⋊C₂₉ #46803764

Order 34220.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	D₅×C₅₉⋊C₂₉
commutator, cosocle, hypocenter	C₅×C₅₉	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₅₉	C₂×C₂₉
LCS	G ▷ C₅×C₅₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₅×C₅₉⋊C₂₉	C₂	direct (N × H)
2. C₂×C₅×C₅₉⋊C₂₉	C₂	semidirect
3. C₅×C₅₉⋊C₂₉	C₂²	semidirect
6. C₂×C₅₉⋊C₂₉	D₅	direct (N × H)
7. C₅₉⋊C₂₉	C₂×D₅	direct (N × H)
8. C₂×D₅×C₅₉	C₂₉	semidirect
9. C₂×C₅×C₅₉	C₂×C₂₉	semidirect
10. D₅×C₅₉	C₂×C₂₉	semidirect
12. C₅×C₅₉	C₂²×C₂₉	semidirect
18. C₂×C₅₉	D₅×C₂₉	semidirect
20. C₅₉	C₂×D₅×C₂₉	semidirect
24. C₂×D₅	C₅₉⋊C₂₉	direct (N × H)
25. C₂×C₅	C₂×C₅₉⋊C₂₉	semidirect
26. D₅	C₂×C₅₉⋊C₂₉	direct (N × H)
27. C₅	C₂²×C₅₉⋊C₂₉	semidirect
30. C₂	D₅×C₅₉⋊C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
D₅×C₅₉⋊C₂₉	2
C₂×C₅×C₅₉⋊C₂₉	2
C₂²×C₅₉⋊C₂₉	5
C₂×D₅×C₅₉	29
C₂×D₅×C₂₉	59

Subgroups — C2×D5×C59⋊C29 #46803764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₅₉⋊C₂₉ #46803764