Subgroups — C₅×D₃×Q₁₆ #91720

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×Q₈	C₂	1	2	yes	maximal
2	C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#216	C₂	1	2	yes	maximal, complemented
4	C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×Q₁₆	—	3	1	no	maximal, Hall
7	C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₄×C₅×D₃	—	2	2	no	—
9	C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₅×Dic₆	—	2	2	no	—
11	C₅×Dic₆	C₂²	1	2	yes	—
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	D₃×Q₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×Q₈	—	3	2	no	—
16	C₅×Q₁₆	—	3	2	no	—
17	C₅×Q₁₆	—	3	1	no	—
18	C₅×Q₁₆	D₃	1	1	yes	characteristic, direct product factor
19	C₂×C₅×C₈	—	3	1	no	—
20	C₂×C₅×D₃	D₄	1	1	yes	characteristic
21	C₃×C₄×C₅	—	2	2	no	—
22	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₅×Dic₃	—	2	2	no	—
24	C₅×Dic₃	D₄	1	1	yes	characteristic
25	D₃×Q₈	C₂×C₅	1	2	yes	—
26	C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
27	#216	C₂×C₅	1	2	yes	complemented
28	Dic₁₂	C₂×C₅	1	1	yes	characteristic, complemented
29	D₃×C₈	C₂×C₅	1	1	yes	characteristic
30	C₅×Q₈	—	3	2	no	—
31	C₅×Q₈	—	6	2	no	—
32	C₅×Q₈	C₂×D₃	1	2	yes	—
33	C₂×C₄×C₅	—	3	1	no	—
34	C₂×C₄×C₅	—	6	2	no	—
35	C₅×C₈	—	3	1	no	—
36	C₅×C₈	C₂×D₃	1	1	yes	characteristic
37	C₂×Q₁₆	—	3	1	no	Sylow
38	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
39	C₅×D₃	Q₁₆	1	2	yes	direct product factor
40	C₃×Q₈	C₂²×C₅	1	2	yes	—
41	C₄×D₃	—	2	2	no	—
42	C₄×D₃	C₂²×C₅	1	1	yes	characteristic
43	Dic₆	—	2	2	no	—
44	Dic₆	C₂²×C₅	1	2	yes	—
45	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
46	C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
47	C₂²×C₅	—	3	1	no	—
48	C₄×C₅	—	2	2	no	—
49	C₄×C₅	—	3	1	no	—
50	C₄×C₅	—	6	2	no	—
51	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
52	C₂×Q₈	—	3	2	no	—
53	Q₁₆	—	3	2	no	—
54	Q₁₆	—	3	1	no	—
55	Q₁₆	C₅×D₃	1	1	yes	characteristic, direct product factor
56	C₂×C₈	—	3	1	no	—
57	C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
58	C₂×D₃	C₅×D₄	1	1	yes	characteristic
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	C₂³×C₅	1	1	yes	characteristic
61	Dic₃	—	2	2	no	—
62	Dic₃	C₅×D₄	1	1	yes	characteristic
63	C₂×C₅	—	3	2	no	—
64	C₂×C₅	D₃×D₄	1	1	yes	characteristic
65	Q₈	—	3	2	no	—
66	Q₈	—	6	2	no	—
67	Q₈	C₂×C₅×D₃	1	2	yes	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	6	2	no	—
70	C₈	—	3	1	no	—
71	C₈	C₂×C₅×D₃	1	1	yes	characteristic
72	C₂×C₃	C₂×C₅×D₄	1	1	yes	characteristic
73	D₃	C₅×Q₁₆	1	2	yes	direct product factor
74	C₅	D₃×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	—	3	1	no	—
76	C₄	—	2	2	no	—
77	C₄	—	3	1	no	—
78	C₄	—	6	2	no	—
79	C₄	C₂²×C₅×D₃	1	1	yes	characteristic
80	C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	3	2	no	—
82	C₂	C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₃×D₄
commutator, cosocle	C₃×C₄	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×D₃	D₄
hypercenter	C₅×Q₁₆	D₃
hypocenter	C₃	C₂×C₅×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×Q₁₆	C₂	semidirect
3. C₅×#216	C₂	semidirect
4. C₅×Dic₁₂	C₂	semidirect
14. D₃×Q₁₆	C₅	direct (N × H)
18. C₅×Q₁₆	D₃	direct (N × H)
26. C₃×Q₁₆	C₂×C₅	semidirect
27. #216	C₂×C₅	semidirect
28. Dic₁₂	C₂×C₅	semidirect
39. C₅×D₃	Q₁₆	direct (N × H)
55. Q₁₆	C₅×D₃	direct (N × H)
57. C₃×C₅	C₂×Q₁₆	semidirect
73. D₃	C₅×Q₁₆	direct (N × H)
74. C₅	D₃×Q₁₆	direct (N × H)
80. C₃	C₂×C₅×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×Q₈	2
C₃×C₅×Q₁₆	2
C₅×#216	2
C₅×Dic₁₂	2
C₅×D₃×C₈	2
C₂×C₅×Q₁₆	3
D₃×Q₁₆	5

Subgroups — C5×D3×Q16 #91720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×Q₁₆ #91720