Subgroups — C₃×C₄×Dic₁₀ #91585

Order 480.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#683	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₅	C₂	1	2	yes	maximal
6	C₄×Dic₁₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₅	C₂²	1	2	yes	—
11	C₂×C₃×Dic₅	C₂²	1	2	yes	—
12	C₃×Dic₁₀	C₄	1	4	yes	direct product factor
13	C₃×C₄×Q₈	—	5	1	no	maximal, Hall
14	C₂×Dic₁₀	C₂×C₃	1	1	yes	characteristic
15	C₄²×C₅	C₂×C₃	1	1	yes	characteristic
16	C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic
17	#683	C₂×C₃	1	2	yes	—
18	C₄×Dic₅	C₂×C₃	1	2	yes	—
19	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
20	C₃×C₄×C₅	—	2	1	no	—
21	C₃×C₄×C₅	C₂×C₄	1	2	yes	—
22	C₃×C₄×C₅	Q₈	1	2	yes	complemented
23	C₃×Dic₅	—	2	2	no	—
24	C₃×Dic₅	C₂×C₄	1	4	yes	—
25	C₂×C₃×Q₈	—	5	1	no	—
26	C₃×C₄⋊C₄	—	5	2	no	—
27	C₃×C₄⋊C₄	—	5	1	no	—
28	C₃×C₄²	—	5	2	no	—
29	C₃×C₄²	D₅	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
32	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
33	C₂×Dic₅	C₂²×C₃	1	2	yes	—
34	C₂×Dic₅	C₂²×C₃	1	2	yes	—
35	Dic₁₀	C₃×C₄	1	4	yes	direct product factor
36	C₄×Q₈	—	5	1	no	Sylow
37	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₃×C₅	#41	1	1	yes	characteristic
40	C₃×Q₈	—	5	4	no	—
41	C₂×C₃×C₄	—	5	2	no	—
42	C₂×C₃×C₄	—	5	2	no	—
43	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
44	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
45	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
46	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
47	C₄×C₅	—	2	1	no	—
48	C₄×C₅	C₂×C₃×C₄	1	2	yes	—
49	C₄×C₅	C₃×Q₈	1	2	yes	complemented
50	Dic₅	—	2	2	no	—
51	Dic₅	C₂×C₃×C₄	1	4	yes	—
52	C₂×Q₈	—	5	1	no	—
53	C₄⋊C₄	—	5	2	no	—
54	C₄⋊C₄	—	5	1	no	—
55	C₄²	—	5	2	no	—
56	C₄²	C₃×D₅	1	1	yes	characteristic
57	C₃×C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
58	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
59	C₃×C₄	—	2	1	no	—
60	C₃×C₄	—	5	4	no	—
61	C₃×C₄	—	10	2	no	—
62	C₃×C₄	Dic₁₀	1	2	yes	direct product factor
63	C₃×C₄	C₄×D₅	1	2	yes	—
64	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
65	C₂×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
66	C₂×C₅	C₃×#41	1	1	yes	characteristic
67	Q₈	—	5	4	no	—
68	C₂×C₄	—	5	2	no	—
69	C₂×C₄	—	5	2	no	—
70	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
71	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
72	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
73	C₂×C₃	C₂×Dic₁₀	1	1	yes	characteristic
74	C₂×C₃	C₂×C₄×D₅	1	1	yes	characteristic
75	C₂×C₃	#709	1	1	yes	characteristic
76	C₅	C₃×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
77	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	5	4	no	—
80	C₄	—	10	2	no	—
81	C₄	C₃×Dic₁₀	1	2	yes	direct product factor
82	C₄	C₃×C₄×D₅	1	2	yes	—
83	C₃	C₄×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	C₂×C₃×Dic₁₀	1	1	yes	characteristic
85	C₂	C₂×C₃×C₄×D₅	1	1	yes	characteristic
86	C₂	C₃×#709	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₃×C₄²×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂³
cosocle	C₂²×C₅	C₂³×C₃
hypercenter	C₃×C₄²	D₅
hypocenter	C₅	C₃×C₄×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₁₀	C₃	direct (N × H)
12. C₃×Dic₁₀	C₄	direct (N × H)
22. C₃×C₄×C₅	Q₈	semidirect
35. Dic₁₀	C₃×C₄	direct (N × H)
49. C₄×C₅	C₃×Q₈	semidirect
57. C₃×C₅	C₄×Q₈	semidirect
62. C₃×C₄	Dic₁₀	direct (N × H)
76. C₅	C₃×C₄×Q₈	semidirect
81. C₄	C₃×Dic₁₀	direct (N × H)
83. C₃	C₄×Dic₁₀	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×Dic₁₀	2
C₃×C₄²×C₅	2
C₃×C₄⋊Dic₅	2
C₃×#683	2
C₃×C₄×Dic₅	2
C₄×Dic₁₀	3
C₃×C₄×Q₈	5

Subgroups — C3×C4×Dic10 #91585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×Dic₁₀ #91585