Subgroups — C₅×C₃⋊#1039 #13093808

Order 1500.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₅×#1039	—	3	1	no	maximal, Hall
3	C₃×C₅³	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#1039	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×Dic₁₅	—	5	6	no	maximal
6	C₂×C₅³	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅²	—	2	12	no	—
8	C₂×C₃×C₅²	D₅	1	6	yes	—
9	C₂×C₃×C₅²	C₂×C₅	1	1	yes	characteristic
10	C₅³	Dic₃	1	1	yes	characteristic, complemented, Sylow
11	#1039	—	3	1	no	—
12	C₅×Dic₅	—	15	6	no	—
13	C₃×C₅²	—	2	12	no	—
14	C₃×C₅²	Dic₅	1	6	yes	complemented
15	C₃×C₅²	C₄×C₅	1	1	yes	characteristic, complemented
16	Dic₁₅	—	5	6	no	—
17	C₅×Dic₃	—	25	1	no	—
18	C₂×C₅²	—	2	12	no	—
19	C₂×C₅²	C₅×D₃	1	1	yes	characteristic
20	C₂×C₅²	D₁₅	1	6	yes	—
21	C₂×C₃×C₅	—	2	12	no	—
22	C₂×C₃×C₅	C₅×D₅	1	6	yes	—
23	C₂×C₃×C₅	C₅⋊D₅	1	1	yes	characteristic
24	C₅²	—	2	12	no	—
25	C₅²	C₅×Dic₃	1	1	yes	characteristic, complemented
26	C₅²	Dic₁₅	1	6	yes	complemented
27	C₄×C₅	—	75	1	no	—
28	Dic₅	—	15	6	no	—
29	C₃×C₅	—	2	12	no	—
30	C₃×C₅	C₅×Dic₅	1	6	yes	complemented
31	C₃×C₅	#1039	1	1	yes	characteristic, complemented
32	Dic₃	—	25	1	no	Hall
33	C₂×C₅	—	2	12	no	—
34	C₂×C₅	C₅×D₁₅	1	6	yes	—
35	C₂×C₅	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
36	C₂×C₃	C₅×C₅⋊D₅	1	1	yes	characteristic
37	C₅	—	2	12	no	—
38	C₅	C₅×Dic₁₅	1	6	yes	complemented
39	C₅	C₃⋊#1039	1	1	yes	characteristic, direct product factor
40	C₄	—	75	1	no	Sylow
41	C₃	C₅×#1039	1	1	yes	characteristic, complemented, Sylow
42	C₂	C₅×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₄×C₅
Frattini	C₂	C₅×C₃⋊(C₅⋊D₅)
Fitting, socle, prime radical	C₂×C₃×C₅³	C₂
cosocle	C₂×C₃×C₅²	C₂×C₅
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅³	C₄	semidirect
4. C₃⋊#1039	C₅	direct (N × H)
10. C₅³	Dic₃	semidirect
14. C₃×C₅²	Dic₅	semidirect
15. C₃×C₅²	C₄×C₅	semidirect
25. C₅²	C₅×Dic₃	semidirect
26. C₅²	Dic₁₅	semidirect
30. C₃×C₅	C₅×Dic₅	semidirect
31. C₃×C₅	#1039	semidirect
38. C₅	C₅×Dic₁₅	semidirect
39. C₅	C₃⋊#1039	direct (N × H)
41. C₃	C₅×#1039	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅³	2
C₅×#1039	3
C₃⋊#1039	5
C₅×Dic₁₅	5

Subgroups — C5×C3⋊#1039 #13093808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#1039 #13093808