Subgroups — C₂×C₃×#689 #91660

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₃×Q₈	D₅
hypocenter	C₅	C₂×C₃×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
3. C₃×#689	C₂	direct (N × H)
5. C₂×#689	C₃	direct (N × H)
17. #689	C₂×C₃	direct (N × H)
37. C₂×C₃×C₅	Q₁₆	semidirect
56. C₃×C₅	C₂×Q₁₆	semidirect
62. C₂×C₅	C₃×Q₁₆	semidirect
72. C₂×C₃	#689	direct (N × H)
74. C₅	C₂×C₃×Q₁₆	semidirect
80. C₃	C₂×#689	direct (N × H)
81. C₂	C₃×#689	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×Q₈	2
C₂×C₃×Dic₁₀	2
C₃×#689	2
C₂×C₃×#168	2
C₂×#689	3
C₂×C₃×Q₁₆	5

Subgroups — C2×C3×#689 #91660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#689 #91660