Subgroups — C₃×D₅×Dic₃ #67128

Order 360.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₅	—	3	1	no	maximal
5	D₅×Dic₃	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
7	C₃²×D₅	C₄	1	2	yes	complemented
8	C₂×C₃×Dic₃	—	5	1	no	maximal, Hall
9	C₂×C₃×D₅	—	2	1	no	—
10	C₂×C₃×D₅	D₃	1	1	yes	characteristic
11	C₂×C₃×D₅	C₂×C₃	1	1	yes	characteristic
12	C₃×C₄×C₅	—	3	1	no	—
13	Dic₁₅	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×Dic₅	—	3	1	no	—
15	C₅×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
16	C₃²×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
17	C₄×D₅	—	3	1	no	Hall
18	C₂²×C₃²	—	5	1	no	—
19	C₃×Dic₃	—	5	1	no	—
20	C₃×Dic₃	D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₅	—	2	1	no	—
22	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
23	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
24	C₃×D₅	—	2	2	no	—
25	C₃×D₅	Dic₃	1	2	yes	direct product factor
26	C₃×D₅	C₃×C₄	1	2	yes	complemented
27	C₂×C₃×C₄	—	15	1	no	—
28	C₂×Dic₃	—	5	1	no	—
29	C₂×D₅	C₃×D₃	1	1	yes	characteristic
30	C₄×C₅	—	3	1	no	—
31	Dic₅	—	3	1	no	—
32	C₂×C₃²	—	5	2	no	—
33	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
34	C₃×C₅	—	2	1	no	—
35	C₃×C₅	C₂×Dic₃	1	1	yes	characteristic, complemented
36	C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
37	C₂²×C₃	—	5	1	no	—
38	C₂²×C₃	—	5	1	no	—
39	C₂²×C₃	—	10	1	no	—
40	C₃×C₄	—	3	1	no	—
41	C₃×C₄	—	15	1	no	—
42	Dic₃	—	5	1	no	—
43	Dic₃	C₃×D₅	1	1	yes	characteristic, direct product factor
44	C₂×C₅	C₂×C₃×D₃	1	1	yes	characteristic
45	D₅	C₃×Dic₃	1	2	yes	direct product factor
46	C₃²	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄	—	15	1	no	Sylow
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	5	2	no	—
50	C₂×C₃	—	5	2	no	—
51	C₂×C₃	—	10	2	no	—
52	C₂×C₃	D₃×D₅	1	1	yes	characteristic
53	C₂×C₃	C₂×C₃×D₅	1	1	yes	characteristic
54	C₅	C₂×C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
55	C₂²	—	5	1	no	—
56	C₄	—	3	1	no	—
57	C₄	—	15	1	no	—
58	C₃	—	2	1	no	—
59	C₃	D₅×Dic₃	1	1	yes	characteristic, direct product factor
60	C₃	C₃×C₄×D₅	1	1	yes	characteristic, complemented
61	C₂	—	5	2	no	—
62	C₂	C₃×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₃×C₄
Frattini	C₂	C₃×D₃×D₅
Fitting, socle	C₂×C₃²×C₅	C₂²
prime radical	C₂×C₃²×D₅	C₂
cosocle	C₂×C₃×C₅	C₂²×C₃
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₁₅	C₂	semidirect
3. C₃×C₅×Dic₃	C₂	semidirect
5. D₅×Dic₃	C₃	direct (N × H)
7. C₃²×D₅	C₄	semidirect
13. Dic₁₅	C₂×C₃	semidirect
15. C₅×Dic₃	C₂×C₃	semidirect
16. C₃²×C₅	C₂×C₄	semidirect
20. C₃×Dic₃	D₅	direct (N × H)
25. C₃×D₅	Dic₃	direct (N × H)
26. C₃×D₅	C₃×C₄	semidirect
35. C₃×C₅	C₂×Dic₃	semidirect
36. C₃×C₅	C₂×C₃×C₄	semidirect
43. Dic₃	C₃×D₅	direct (N × H)
45. D₅	C₃×Dic₃	direct (N × H)
46. C₃²	C₄×D₅	semidirect
54. C₅	C₂×C₃×Dic₃	semidirect
59. C₃	D₅×Dic₃	direct (N × H)
60. C₃	C₃×C₄×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₅	2
C₃×Dic₁₅	2
C₃×C₅×Dic₃	2
C₃×C₄×D₅	3
D₅×Dic₃	3
C₂×C₃×Dic₃	5

Subgroups — C3×D5×Dic3 #67128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×Dic₃ #67128