Subgroups — C₂×A₄×Dic₅ #91968

Order 480.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×A₄	C₂	1	1	yes	maximal, characteristic
2	A₄×Dic₅	C₂	1	2	yes	maximal, direct product factor
3	C₂³×Dic₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₅×A₄	C₄	1	2	yes	complemented
5	C₂×C₅×A₄	C₂²	1	1	yes	characteristic
6	C₂×C₃×Dic₅	—	4	1	no	maximal
7	C₂×C₄×A₄	—	5	1	no	maximal, Hall
8	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic
9	C₂²×Dic₅	—	3	1	no	—
10	C₂²×Dic₅	—	3	1	no	—
11	C₂²×Dic₅	—	3	2	no	—
12	C₂²×Dic₅	C₂×C₃	1	2	yes	complemented
13	C₂²×C₃×C₅	—	4	1	no	—
14	C₅×A₄	C₂×C₄	1	1	yes	characteristic, complemented
15	C₃×Dic₅	—	4	2	no	—
16	C₂²×A₄	D₅	1	1	yes	characteristic
17	C₄×A₄	—	5	2	no	—
18	C₂³×C₅	—	3	1	no	—
19	C₂³×C₅	—	3	2	no	—
20	C₂³×C₅	—	3	1	no	—
21	C₂³×C₅	C₃×C₄	1	2	yes	complemented
22	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
23	C₂×Dic₅	—	3	2	no	—
24	C₂×Dic₅	—	3	1	no	—
25	C₂×Dic₅	—	3	2	no	—
26	C₂×Dic₅	—	3	2	no	—
27	C₂×Dic₅	—	3	2	no	—
28	C₂×Dic₅	A₄	1	1	yes	characteristic, direct product factor
29	C₂³×C₄	—	5	1	no	Sylow
30	C₂×C₃×C₅	—	4	2	no	—
31	C₂×C₃×C₅	—	4	1	no	—
32	C₂×A₄	Dic₅	1	2	yes	direct product factor
33	C₂×A₄	C₂×D₅	1	1	yes	characteristic
34	C₂×C₃×C₄	—	20	1	no	—
35	C₂²×C₅	—	3	2	no	—
36	C₂²×C₅	—	3	1	no	—
37	C₂²×C₅	—	3	2	no	—
38	C₂²×C₅	—	3	2	no	—
39	C₂²×C₅	—	3	2	no	—
40	C₂²×C₅	—	3	1	no	—
41	C₂²×C₅	—	3	1	no	—
42	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
43	C₂²×C₅	C₂×A₄	1	1	yes	characteristic
44	Dic₅	—	3	2	no	—
45	Dic₅	C₂×A₄	1	2	yes	direct product factor
46	C₂⁴	C₃×D₅	1	1	yes	characteristic
47	C₂²×C₄	—	5	2	no	—
48	C₂²×C₄	—	15	1	no	—
49	C₂²×C₄	—	15	2	no	—
50	C₂²×C₄	—	15	1	no	—
51	C₃×C₅	—	4	1	no	Hall
52	C₂²×C₃	—	4	1	no	—
53	A₄	C₂×Dic₅	1	1	yes	characteristic, direct product factor
54	C₃×C₄	—	20	2	no	—
55	C₂×C₅	—	3	2	no	—
56	C₂×C₅	—	3	1	no	—
57	C₂×C₅	—	3	1	no	—
58	C₂×C₅	C₄×A₄	1	2	yes	complemented
59	C₂×C₅	C₂²×A₄	1	1	yes	characteristic
60	C₂³	—	3	1	no	—
61	C₂³	—	3	2	no	—
62	C₂³	—	3	1	no	—
63	C₂³	C₃×Dic₅	1	2	yes	complemented
64	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
65	C₂×C₄	—	5	1	no	—
66	C₂×C₄	—	15	2	no	—
67	C₂×C₄	—	15	2	no	—
68	C₂×C₄	—	15	2	no	—
69	C₂×C₄	—	15	1	no	—
70	C₂×C₄	—	15	2	no	—
71	C₂×C₃	—	4	2	no	—
72	C₂×C₃	—	4	1	no	—
73	C₅	C₂×C₄×A₄	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	3	2	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	3	2	no	—
77	C₂²	—	3	2	no	—
78	C₂²	—	3	2	no	—
79	C₂²	—	3	1	no	—
80	C₂²	—	3	1	no	—
81	C₂²	C₂×C₃×Dic₅	1	1	yes	characteristic, complemented
82	C₂²	D₅×A₄	1	1	yes	characteristic
83	C₄	—	5	2	no	—
84	C₄	—	15	2	no	—
85	C₃	—	4	1	no	Sylow
86	C₂	—	3	1	no	—
87	C₂	—	3	2	no	—
88	C₂	—	3	1	no	—
89	C₂	A₄×Dic₅	1	2	yes	direct product factor
90	C₂	C₂×D₅×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₅×A₄
commutator, hypocenter	C₂²×C₅	C₂×C₃×C₄
Frattini	C₂	C₂×D₅×A₄
Fitting, socle	C₂⁴×C₅	C₂×C₃
prime radical	C₂²×C₅×A₄	C₂
cosocle	C₂³×C₅	C₂²×C₃
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. A₄×Dic₅	C₂	direct (N × H)
3. C₂³×Dic₅	C₃	semidirect
4. C₂×C₅×A₄	C₄	semidirect
12. C₂²×Dic₅	C₂×C₃	semidirect
14. C₅×A₄	C₂×C₄	semidirect
21. C₂³×C₅	C₃×C₄	semidirect
28. C₂×Dic₅	A₄	direct (N × H)
32. C₂×A₄	Dic₅	direct (N × H)
42. C₂²×C₅	C₂×C₃×C₄	semidirect
45. Dic₅	C₂×A₄	direct (N × H)
53. A₄	C₂×Dic₅	direct (N × H)
58. C₂×C₅	C₄×A₄	semidirect
63. C₂³	C₃×Dic₅	semidirect
73. C₅	C₂×C₄×A₄	semidirect
81. C₂²	C₂×C₃×Dic₅	semidirect
89. C₂	A₄×Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×A₄	2
A₄×Dic₅	2
C₂³×Dic₅	3
C₂×C₃×Dic₅	4
C₂×C₄×A₄	5

Subgroups — C2×A4×Dic5 #91968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×A₄×Dic₅ #91968