Subgroups — C₂×C₅×Dic₁₅ #10597153

Order 600.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₁₅	C₂	direct (N × H)
4. C₂×C₃×C₅²	C₄	semidirect
6. C₂×Dic₁₅	C₅	direct (N × H)
10. C₃×C₅²	C₂×C₄	semidirect
14. Dic₁₅	C₂×C₅	direct (N × H)
16. C₂×C₅²	Dic₃	semidirect
22. C₂×C₃×C₅	Dic₅	semidirect
23. C₂×C₃×C₅	C₄×C₅	semidirect
26. C₅²	C₂×Dic₃	semidirect
34. C₃×C₅	C₂×Dic₅	semidirect
35. C₃×C₅	C₂×C₄×C₅	semidirect
40. C₂×C₅	C₅×Dic₃	semidirect
41. C₂×C₅	Dic₁₅	direct (N × H)
45. C₂×C₃	C₅×Dic₅	semidirect
48. C₅	C₂×C₅×Dic₃	semidirect
49. C₅	C₂×Dic₁₅	direct (N × H)
52. C₃	C₂×C₅×Dic₅	semidirect
53. C₂	C₅×Dic₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅²	2
C₅×Dic₁₅	2
C₂×C₅×Dic₅	3
C₂×Dic₁₅	5
C₂×C₅×Dic₃	5

Subgroups — C2×C5×Dic15 #10597153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×Dic₁₅ #10597153