Subgroups — C₃×C₅₉×#1039 #31799178

Order 17700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#1039	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₅×C₅₉	—	5	6	no	maximal
5	C₂×C₅²×C₅₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₅₉	D₅	1	6	yes	—
7	C₅²×C₅₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₅×C₅₉	—	5	6	no	—
9	C₃×C₅×C₅₉	Dic₅	1	6	yes	complemented
10	C₃×C₄×C₅₉	—	25	1	no	Hall
11	C₂×C₅×C₅₉	C₃×D₅	1	6	yes	—
12	C₂×C₃×C₅₉	C₅⋊D₅	1	1	yes	characteristic
13	C₃×#1039	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₅₉	C₃×Dic₅	1	6	yes	complemented
15	C₄×C₅₉	—	25	1	no	Hall
16	C₃×C₅₉	#1039	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₅²	C₂×C₅₉	1	1	yes	characteristic
18	C₂×C₅₉	C₃×C₅⋊D₅	1	1	yes	characteristic
19	#1039	C₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅²	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
21	C₃×Dic₅	—	5	6	no	—
22	C₅₉	C₃×#1039	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₅²	C₂×C₃×C₅₉	1	1	yes	characteristic
24	C₂×C₃×C₅	D₅×C₅₉	1	6	yes	—
25	C₅²	C₃×C₄×C₅₉	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	5	6	no	—
27	C₃×C₅	Dic₅×C₅₉	1	6	yes	complemented
28	C₃×C₄	—	25	1	no	Hall
29	C₂×C₅	C₃×D₅×C₅₉	1	6	yes	—
30	C₂×C₃	C₅⋊D₅×C₅₉	1	1	yes	characteristic
31	C₅	C₃×Dic₅×C₅₉	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	C₅₉×#1039	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₅⋊D₅×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅₉	C₅⋊D₅
commutator, hypocenter	C₅²	C₃×C₄×C₅₉
Frattini	C₂	C₃×C₅⋊D₅×C₅₉
Fitting, socle, prime radical	C₂×C₃×C₅²×C₅₉	C₂
cosocle	C₂×C₅²	C₂×C₃×C₅₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₅₉

Complements

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

N	H ≅ G/N	type
2. C₅₉×#1039	C₃	direct (N × H)
3. C₃×C₅²×C₅₉	C₄	semidirect
7. C₅²×C₅₉	C₃×C₄	semidirect
9. C₃×C₅×C₅₉	Dic₅	semidirect
13. C₃×#1039	C₅₉	direct (N × H)
14. C₅×C₅₉	C₃×Dic₅	semidirect
16. C₃×C₅₉	#1039	direct (N × H)
19. #1039	C₃×C₅₉	direct (N × H)
20. C₃×C₅²	C₄×C₅₉	semidirect
22. C₅₉	C₃×#1039	direct (N × H)
25. C₅²	C₃×C₄×C₅₉	semidirect
27. C₃×C₅	Dic₅×C₅₉	semidirect
31. C₅	C₃×Dic₅×C₅₉	semidirect
33. C₃	C₅₉×#1039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₅₉	2
C₅₉×#1039	3
C₃×Dic₅×C₅₉	5
C₃×#1039	59

Subgroups — C3×C59×#1039 #31799178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅₉×#1039 #31799178