Subgroups — C₂²×D₅×A₄ #92126

Order 480.

356 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, complemented
2	C₂×D₅×A₄	C₂	1	6	yes	maximal, direct product factor
3	C₂⁴×D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂²×C₃×D₅	—	4	1	no	maximal
5	C₂×C₅×A₄	C₂²	1	3	yes	complemented
6	D₅×A₄	C₂²	1	4	yes	direct product factor
7	C₂³×A₄	—	5	1	no	maximal, Hall
8	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂³×D₅	—	3	1	no	—
10	C₂³×D₅	—	3	1	no	—
11	C₂³×D₅	—	3	6	no	—
12	C₂³×D₅	C₂×C₃	1	6	yes	complemented
13	C₂²×C₃×C₅	—	4	1	no	—
14	C₂×C₃×D₅	—	4	6	no	—
15	C₅×A₄	C₂³	1	1	yes	characteristic, complemented
16	C₂²×A₄	—	5	6	no	—
17	C₂²×A₄	D₅	1	1	yes	characteristic, direct product factor
18	C₂³×C₅	—	3	3	no	—
19	C₂³×C₅	—	3	1	no	—
20	C₂³×C₅	C₂²×C₃	1	3	yes	complemented
21	C₂²×D₅	—	3	6	no	—
22	C₂²×D₅	—	3	8	no	—
23	C₂²×D₅	—	3	1	no	—
24	C₂²×D₅	—	3	6	no	—
25	C₂²×D₅	—	3	6	no	—
26	C₂²×D₅	—	3	6	no	—
27	C₂²×D₅	—	3	12	no	—
28	C₂²×D₅	A₄	1	1	yes	characteristic, direct product factor
29	C₂²×D₅	C₂²×C₃	1	4	yes	complemented
30	C₂⁵	—	5	1	no	Sylow
31	C₂×C₃×C₅	—	4	3	no	—
32	C₃×D₅	—	4	4	no	—
33	C₂³×C₃	—	20	1	no	—
34	C₂×A₄	—	5	4	no	—
35	C₂×A₄	C₂×D₅	1	3	yes	direct product factor
36	C₂²×C₅	—	3	3	no	—
37	C₂²×C₅	—	3	2	no	—
38	C₂²×C₅	—	3	3	no	—
39	C₂²×C₅	—	3	3	no	—
40	C₂²×C₅	C₂×A₄	1	1	yes	characteristic, complemented
41	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic, complemented
42	C₂×D₅	—	3	12	no	—
43	C₂×D₅	—	3	6	no	—
44	C₂×D₅	—	3	12	no	—
45	C₂×D₅	—	3	4	no	—
46	C₂×D₅	—	3	4	no	—
47	C₂×D₅	C₂×A₄	1	6	yes	direct product factor
48	C₂⁴	—	5	6	no	—
49	C₂⁴	—	15	1	no	—
50	C₂⁴	—	15	6	no	—
51	C₂⁴	—	15	1	no	—
52	C₂⁴	C₃×D₅	1	1	yes	characteristic, complemented
53	C₃×C₅	—	4	1	no	Hall
54	C₂²×C₃	—	4	1	no	—
55	C₂²×C₃	—	20	6	no	—
56	A₄	C₂²×D₅	1	1	yes	characteristic, direct product factor
57	C₂×C₅	—	3	3	no	—
58	C₂×C₅	—	3	1	no	—
59	C₂×C₅	C₂²×A₄	1	3	yes	complemented
60	D₅	—	3	4	no	—
61	D₅	C₂²×A₄	1	4	yes	direct product factor
62	C₂³	—	3	3	no	—
63	C₂³	—	3	1	no	—
64	C₂³	—	5	1	no	—
65	C₂³	—	5	4	no	—
66	C₂³	—	15	6	no	—
67	C₂³	—	15	6	no	—
68	C₂³	—	15	12	no	—
69	C₂³	—	15	6	no	—
70	C₂³	—	15	8	no	—
71	C₂³	—	15	6	no	—
72	C₂³	—	15	1	no	—
73	C₂³	C₂×C₃×D₅	1	3	yes	complemented
74	C₂×C₃	—	4	3	no	—
75	C₂×C₃	—	20	4	no	—
76	C₅	C₂³×A₄	1	1	yes	characteristic, complemented, Sylow
77	C₂²	—	3	3	no	—
78	C₂²	—	3	2	no	—
79	C₂²	—	3	3	no	—
80	C₂²	—	3	3	no	—
81	C₂²	—	5	6	no	—
82	C₂²	—	15	4	no	—
83	C₂²	—	15	12	no	—
84	C₂²	—	15	4	no	—
85	C₂²	—	15	12	no	—
86	C₂²	—	15	6	no	—
87	C₂²	D₅×A₄	1	1	yes	characteristic, direct product factor
88	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
89	C₃	—	4	1	no	Sylow
90	C₂	—	3	1	no	—
91	C₂	—	3	3	no	—
92	C₂	—	5	4	no	—
93	C₂	—	15	4	no	—
94	C₂	C₂×D₅×A₄	1	3	yes	direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×A₄	C₂	semidirect
2. C₂×D₅×A₄	C₂	direct (N × H)
3. C₂⁴×D₅	C₃	semidirect
5. C₂×C₅×A₄	C₂²	semidirect
6. D₅×A₄	C₂²	direct (N × H)
8. C₂⁴×C₅	C₂×C₃	semidirect
12. C₂³×D₅	C₂×C₃	semidirect
15. C₅×A₄	C₂³	semidirect
17. C₂²×A₄	D₅	direct (N × H)
20. C₂³×C₅	C₂²×C₃	semidirect
28. C₂²×D₅	A₄	direct (N × H)
29. C₂²×D₅	C₂²×C₃	semidirect
35. C₂×A₄	C₂×D₅	direct (N × H)
40. C₂²×C₅	C₂×A₄	semidirect
41. C₂²×C₅	C₂³×C₃	semidirect
47. C₂×D₅	C₂×A₄	direct (N × H)
52. C₂⁴	C₃×D₅	semidirect
56. A₄	C₂²×D₅	direct (N × H)
59. C₂×C₅	C₂²×A₄	semidirect
61. D₅	C₂²×A₄	direct (N × H)
73. C₂³	C₂×C₃×D₅	semidirect
76. C₅	C₂³×A₄	semidirect
87. C₂²	D₅×A₄	direct (N × H)
88. C₂²	C₂²×C₃×D₅	semidirect
94. C₂	C₂×D₅×A₄	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
C₂×D₅×A₄	2
C₂⁴×D₅	3
C₂²×C₃×D₅	4
C₂³×A₄	5

Subgroups — C22×D5×A4 #92126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₅×A₄ #92126