Subgroups — C₃×D₅×Q₁₆ #91634

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×D₅	C₂	1	2	yes	maximal
2	C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#689	C₂	1	2	yes	maximal, complemented
4	C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
6	D₅×Q₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₃×C₄×D₅	—	2	2	no	—
9	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₃×Dic₁₀	—	2	2	no	—
11	C₃×Dic₁₀	C₂²	1	2	yes	—
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₃×#168	C₂²	1	1	yes	characteristic
14	C₂×C₃×Q₁₆	—	5	1	no	maximal, Hall
15	Q₈×D₅	C₂×C₃	1	2	yes	—
16	C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
17	#689	C₂×C₃	1	2	yes	complemented
18	Dic₂₀	C₂×C₃	1	1	yes	characteristic, complemented
19	C₈×D₅	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×D₅	D₄	1	1	yes	characteristic
21	C₃×C₄×C₅	—	2	2	no	—
22	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₃×Dic₅	—	2	2	no	—
24	C₃×Dic₅	D₄	1	1	yes	characteristic
25	C₂×C₃×Q₈	—	5	2	no	—
26	C₃×Q₁₆	—	5	2	no	—
27	C₃×Q₁₆	—	5	1	no	—
28	C₃×Q₁₆	D₅	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₈	—	5	1	no	—
30	C₅×Q₈	C₂²×C₃	1	2	yes	—
31	C₄×D₅	—	2	2	no	—
32	C₄×D₅	C₂²×C₃	1	1	yes	characteristic
33	Dic₁₀	—	2	2	no	—
34	Dic₁₀	C₂²×C₃	1	2	yes	—
35	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
36	#168	C₂²×C₃	1	1	yes	characteristic
37	C₂×Q₁₆	—	5	1	no	Sylow
38	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
39	C₃×D₅	Q₁₆	1	2	yes	direct product factor
40	C₃×Q₈	—	5	2	no	—
41	C₃×Q₈	—	10	2	no	—
42	C₃×Q₈	C₂×D₅	1	2	yes	—
43	C₂×C₃×C₄	—	5	1	no	—
44	C₂×C₃×C₄	—	10	2	no	—
45	C₃×C₈	—	5	1	no	—
46	C₃×C₈	C₂×D₅	1	1	yes	characteristic
47	C₂×D₅	C₃×D₄	1	1	yes	characteristic
48	C₄×C₅	—	2	2	no	—
49	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
50	Dic₅	—	2	2	no	—
51	Dic₅	C₃×D₄	1	1	yes	characteristic
52	C₂×Q₈	—	5	2	no	—
53	Q₁₆	—	5	2	no	—
54	Q₁₆	—	5	1	no	—
55	Q₁₆	C₃×D₅	1	1	yes	characteristic, direct product factor
56	C₂×C₈	—	5	1	no	—
57	C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
58	C₂²×C₃	—	5	1	no	—
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	5	1	no	—
61	C₃×C₄	—	10	2	no	—
62	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
63	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
64	D₅	C₃×Q₁₆	1	2	yes	direct product factor
65	Q₈	—	5	2	no	—
66	Q₈	—	10	2	no	—
67	Q₈	C₂×C₃×D₅	1	2	yes	—
68	C₂×C₄	—	5	1	no	—
69	C₂×C₄	—	10	2	no	—
70	C₈	—	5	1	no	—
71	C₈	C₂×C₃×D₅	1	1	yes	characteristic
72	C₂×C₃	—	5	2	no	—
73	C₂×C₃	D₄×D₅	1	1	yes	characteristic
74	C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	5	1	no	—
76	C₄	—	2	2	no	—
77	C₄	—	5	1	no	—
78	C₄	—	10	2	no	—
79	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
80	C₃	D₅×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	—	5	2	no	—
82	C₂	C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×Q₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×D₅	D₄
hypercenter	C₃×Q₁₆	D₅
hypocenter	C₅	C₂×C₃×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×Q₁₆	C₂	semidirect
3. C₃×#689	C₂	semidirect
4. C₃×Dic₂₀	C₂	semidirect
6. D₅×Q₁₆	C₃	direct (N × H)
16. C₅×Q₁₆	C₂×C₃	semidirect
17. #689	C₂×C₃	semidirect
18. Dic₂₀	C₂×C₃	semidirect
28. C₃×Q₁₆	D₅	direct (N × H)
39. C₃×D₅	Q₁₆	direct (N × H)
55. Q₁₆	C₃×D₅	direct (N × H)
57. C₃×C₅	C₂×Q₁₆	semidirect
64. D₅	C₃×Q₁₆	direct (N × H)
74. C₅	C₂×C₃×Q₁₆	semidirect
80. C₃	D₅×Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×D₅	2
C₃×C₅×Q₁₆	2
C₃×#689	2
C₃×Dic₂₀	2
C₃×C₈×D₅	2
D₅×Q₁₆	3
C₂×C₃×Q₁₆	5

Subgroups — C3×D5×Q16 #91634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×Q₁₆ #91634