Subgroups — C₃×#6036 #10597100

Order 600.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×Dic₅	C₂	1	2	yes	maximal, complemented
3	#6036	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅²	C₂²	1	1	yes	characteristic
5	C₃×C₅⋊D₅	C₄	1	2	yes	complemented
6	C₃×C₄×D₅	—	5	2	no	maximal
7	C₂×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
8	C₅×Dic₅	C₂×C₃	1	2	yes	complemented
9	C₃×C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₅	—	5	2	no	—
11	C₂×C₃×D₅	—	10	2	no	—
12	C₃×C₄×C₅	—	5	2	no	—
13	C₃×Dic₅	D₅	1	2	yes	complemented
14	C₂×C₅²	C₂²×C₃	1	1	yes	characteristic
15	C₅⋊D₅	C₃×C₄	1	2	yes	complemented
16	C₄×D₅	—	5	2	no	—
17	C₂×C₃×C₅	—	2	2	no	—
18	C₂×C₃×C₅	C₂×D₅	1	2	yes	—
19	C₃×D₅	—	5	4	no	—
20	C₃×D₅	—	10	4	no	—
21	C₅²	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₄	—	25	1	no	Hall
23	C₂×D₅	—	5	2	no	—
24	C₂×D₅	—	10	2	no	—
25	C₄×C₅	—	5	2	no	—
26	Dic₅	C₃×D₅	1	2	yes	complemented
27	C₃×C₅	—	2	2	no	—
28	C₃×C₅	C₄×D₅	1	2	yes	complemented
29	C₂²×C₃	—	25	1	no	—
30	C₃×C₄	—	5	2	no	—
31	C₂×C₅	—	2	2	no	—
32	C₂×C₅	C₂×C₃×D₅	1	2	yes	—
33	D₅	—	5	4	no	—
34	D₅	—	10	4	no	—
35	C₂×C₄	—	25	1	no	Sylow
36	C₂×C₃	—	25	2	no	—
37	C₂×C₃	D₅²	1	1	yes	characteristic
38	C₅	—	2	2	no	—
39	C₅	C₃×C₄×D₅	1	2	yes	complemented
40	C₂²	—	25	1	no	—
41	C₄	—	5	2	no	—
42	C₃	#6036	1	1	yes	characteristic, direct product factor, Sylow
43	C₂	—	25	2	no	—
44	C₂	C₃×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅²
commutator, hypocenter	C₅²	C₂×C₃×C₄
Frattini	C₂	C₃×D₅²
Fitting, socle	C₂×C₃×C₅²	C₂²
prime radical	C₂×C₃×C₅⋊D₅	C₂
cosocle	C₂×C₅²	C₂²×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×Dic₅	C₂	semidirect
3. #6036	C₃	direct (N × H)
5. C₃×C₅⋊D₅	C₄	semidirect
8. C₅×Dic₅	C₂×C₃	semidirect
9. C₃×C₅²	C₂×C₄	semidirect
13. C₃×Dic₅	D₅	semidirect
15. C₅⋊D₅	C₃×C₄	semidirect
21. C₅²	C₂×C₃×C₄	semidirect
26. Dic₅	C₃×D₅	semidirect
28. C₃×C₅	C₄×D₅	semidirect
39. C₅	C₃×C₄×D₅	semidirect
42. C₃	#6036	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×C₅⋊D₅	2
C₃×C₅×Dic₅	2
#6036	3
C₃×C₄×D₅	5

Subgroups — C3×#6036 #10597100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#6036 #10597100