Subgroups — Dic₅×D₁₅ #10597118

Order 600.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×Dic₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅²	C₂²	1	1	yes	characteristic
6	C₅×D₁₅	C₄	1	2	yes	complemented
7	C₄×D₁₅	—	5	1	no	maximal
8	D₃×Dic₅	—	5	1	no	maximal
9	C₂×C₅×D₅	—	3	1	no	—
10	#1039	—	3	1	no	—
11	C₅×Dic₅	D₃	1	1	yes	characteristic, complemented
12	C₃×C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₁₅	D₅	1	1	yes	characteristic
14	C₂×C₅×D₃	—	5	1	no	—
15	C₃×C₄×C₅	—	5	1	no	—
16	Dic₁₅	—	5	1	no	—
17	Dic₁₅	—	5	1	no	—
18	Dic₁₅	—	10	2	no	—
19	C₃×Dic₅	D₅	1	1	yes	characteristic, complemented
20	C₂×C₅²	C₂×D₃	1	1	yes	characteristic
21	C₅×D₅	—	3	2	no	—
22	C₂×Dic₅	—	15	1	no	—
23	C₄×D₅	—	15	1	no	—
24	C₂×C₃×C₅	—	2	2	no	—
25	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
26	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
27	D₁₅	Dic₅	1	2	yes	direct product factor
28	C₅×D₃	—	5	2	no	—
29	C₅²	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
30	C₄×D₃	—	25	1	no	Hall
31	C₂²×C₅	—	15	1	no	—
32	C₂×D₅	—	3	1	no	—
33	C₄×C₅	—	5	1	no	—
34	Dic₅	—	15	1	no	—
35	Dic₅	—	15	1	no	—
36	Dic₅	—	30	2	no	—
37	Dic₅	D₁₅	1	1	yes	characteristic, direct product factor
38	C₃×C₅	—	2	2	no	—
39	C₃×C₅	C₄×D₅	1	1	yes	characteristic, complemented
40	C₃×C₅	C₂×Dic₅	1	1	yes	characteristic, complemented
41	C₂×D₃	—	5	1	no	—
42	C₃×C₄	—	5	1	no	—
43	Dic₃	—	25	1	no	—
44	C₂×C₅	—	2	2	no	—
45	C₂×C₅	—	15	2	no	—
46	C₂×C₅	D₃×D₅	1	1	yes	characteristic
47	C₂×C₅	C₂×D₁₅	1	1	yes	characteristic
48	D₅	—	3	2	no	—
49	C₂×C₄	—	75	1	no	Sylow
50	C₂×C₃	D₅²	1	1	yes	characteristic
51	D₃	—	5	2	no	—
52	C₅	—	2	2	no	—
53	C₅	D₃×Dic₅	1	1	yes	characteristic, complemented
54	C₅	C₄×D₁₅	1	1	yes	characteristic, complemented
55	C₂²	—	15	1	no	—
56	C₄	—	5	1	no	—
57	C₄	—	75	1	no	—
58	C₃	D₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	15	2	no	—
60	C₂	D₅×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₁₅
commutator, hypocenter	C₃×C₅²	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₅²	C₂²
prime radical	C₂×C₅×D₁₅	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊#1039	C₂	semidirect
3. C₃×C₅×Dic₅	C₂	semidirect
6. C₅×D₁₅	C₄	semidirect
11. C₅×Dic₅	D₃	semidirect
12. C₃×C₅²	C₂×C₄	semidirect
19. C₃×Dic₅	D₅	semidirect
27. D₁₅	Dic₅	direct (N × H)
29. C₅²	C₄×D₃	semidirect
37. Dic₅	D₁₅	direct (N × H)
39. C₃×C₅	C₄×D₅	semidirect
40. C₃×C₅	C₂×Dic₅	semidirect
53. C₅	D₃×Dic₅	semidirect
54. C₅	C₄×D₁₅	semidirect
58. C₃	D₅×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₁₅	2
C₃⋊#1039	2
C₃×C₅×Dic₅	2
D₅×Dic₅	3
C₄×D₁₅	5
D₃×Dic₅	5

Subgroups — Dic5×D15 #10597118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×D₁₅ #10597118