Subgroups — C₅×D₃×Dic₅ #10597105

Order 600.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×Dic₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅²	C₂²	1	1	yes	characteristic
6	C₅²×D₃	C₄	1	2	yes	complemented
7	C₄×C₅×D₃	—	5	1	no	maximal
8	D₃×Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₅²	—	3	1	no	—
10	C₅×Dic₅	—	3	1	no	—
11	C₅×Dic₅	D₃	1	1	yes	characteristic, direct product factor
12	C₃×C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×D₃	—	2	2	no	—
14	C₂×C₅×D₃	D₅	1	1	yes	characteristic
15	C₂×C₅×D₃	C₂×C₅	1	1	yes	characteristic
16	C₃×C₄×C₅	—	5	1	no	—
17	Dic₁₅	C₂×C₅	1	1	yes	characteristic, complemented
18	C₃×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
19	C₅×Dic₃	—	5	1	no	—
20	C₂×C₅²	—	3	2	no	—
21	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
22	C₂×C₄×C₅	—	15	1	no	—
23	C₂×Dic₅	—	3	1	no	—
24	C₂×C₃×C₅	—	2	2	no	—
25	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
26	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
27	C₅×D₃	—	2	4	no	—
28	C₅×D₃	Dic₅	1	2	yes	direct product factor
29	C₅×D₃	C₄×C₅	1	2	yes	complemented
30	C₅²	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₃	—	5	1	no	Hall
32	C₂²×C₅	—	3	1	no	—
33	C₂²×C₅	—	3	1	no	—
34	C₂²×C₅	—	6	2	no	—
35	C₄×C₅	—	5	1	no	—
36	C₄×C₅	—	15	1	no	—
37	Dic₅	—	3	1	no	—
38	Dic₅	C₅×D₃	1	1	yes	characteristic, direct product factor
39	C₃×C₅	—	2	2	no	—
40	C₃×C₅	C₂×Dic₅	1	1	yes	characteristic, complemented
41	C₃×C₅	C₂×C₄×C₅	1	1	yes	characteristic, complemented
42	C₂×D₃	C₅×D₅	1	1	yes	characteristic
43	C₃×C₄	—	5	1	no	—
44	Dic₃	—	5	1	no	—
45	C₂×C₅	—	2	2	no	—
46	C₂×C₅	—	3	2	no	—
47	C₂×C₅	—	3	2	no	—
48	C₂×C₅	—	6	4	no	—
49	C₂×C₅	D₃×D₅	1	1	yes	characteristic
50	C₂×C₅	C₂×C₅×D₃	1	1	yes	characteristic
51	C₂×C₄	—	15	1	no	Sylow
52	C₂×C₃	C₂×C₅×D₅	1	1	yes	characteristic
53	D₃	C₅×Dic₅	1	2	yes	direct product factor
54	C₅	—	2	2	no	—
55	C₅	D₃×Dic₅	1	1	yes	characteristic, direct product factor
56	C₅	C₄×C₅×D₃	1	1	yes	characteristic, complemented
57	C₂²	—	3	1	no	—
58	C₄	—	5	1	no	—
59	C₄	—	15	1	no	—
60	C₃	C₂×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	3	2	no	—
62	C₂	C₅×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₄×C₅
Frattini	C₂	C₅×D₃×D₅
Fitting, socle	C₂×C₃×C₅²	C₂²
prime radical	C₂×C₅²×D₃	C₂
cosocle	C₂×C₃×C₅	C₂²×C₅
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₁₅	C₂	semidirect
3. C₃×C₅×Dic₅	C₂	semidirect
6. C₅²×D₃	C₄	semidirect
8. D₃×Dic₅	C₅	direct (N × H)
11. C₅×Dic₅	D₃	direct (N × H)
12. C₃×C₅²	C₂×C₄	semidirect
17. Dic₁₅	C₂×C₅	semidirect
18. C₃×Dic₅	C₂×C₅	semidirect
28. C₅×D₃	Dic₅	direct (N × H)
29. C₅×D₃	C₄×C₅	semidirect
30. C₅²	C₄×D₃	semidirect
38. Dic₅	C₅×D₃	direct (N × H)
40. C₃×C₅	C₂×Dic₅	semidirect
41. C₃×C₅	C₂×C₄×C₅	semidirect
53. D₃	C₅×Dic₅	direct (N × H)
55. C₅	D₃×Dic₅	direct (N × H)
56. C₅	C₄×C₅×D₃	semidirect
60. C₃	C₂×C₅×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×D₃	2
C₅×Dic₁₅	2
C₃×C₅×Dic₅	2
C₂×C₅×Dic₅	3
C₄×C₅×D₃	5
D₃×Dic₅	5

Subgroups — C5×D3×Dic5 #10597105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×Dic₅ #10597105