Subgroups — C₂³×C₅×A₄ #92132

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	7	yes	maximal, direct product factor
2	C₂⁵×C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂³×C₃×C₅	—	4	1	no	maximal
4	C₂×C₅×A₄	C₂²	1	7	yes	direct product factor
5	C₂³×A₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂⁴×C₅	—	3	7	no	—
7	C₂⁴×C₅	—	3	1	no	—
8	C₂⁴×C₅	C₂×C₃	1	7	yes	complemented
9	C₂²×C₃×C₅	—	4	7	no	—
10	C₅×A₄	C₂³	1	1	yes	characteristic, direct product factor
11	C₂²×A₄	C₂×C₅	1	7	yes	direct product factor
12	C₂³×C₅	—	3	21	no	—
13	C₂³×C₅	—	3	14	no	—
14	C₂³×C₅	—	3	7	no	—
15	C₂³×C₅	—	3	7	no	—
16	C₂³×C₅	A₄	1	1	yes	characteristic, direct product factor
17	C₂³×C₅	C₂²×C₃	1	7	yes	complemented
18	C₂⁵	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₅	—	4	7	no	—
20	C₂³×C₃	—	4	1	no	—
21	C₂×A₄	C₂²×C₅	1	7	yes	direct product factor
22	C₂²×C₅	—	3	7	no	—
23	C₂²×C₅	—	3	14	no	—
24	C₂²×C₅	—	3	21	no	—
25	C₂²×C₅	—	3	7	no	—
26	C₂²×C₅	C₂×A₄	1	7	yes	direct product factor
27	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic, complemented
28	C₂⁴	—	3	7	no	—
29	C₂⁴	—	3	1	no	—
30	C₂⁴	C₂×C₃×C₅	1	7	yes	complemented
31	C₃×C₅	—	4	1	no	Hall
32	C₂²×C₃	—	4	7	no	—
33	A₄	C₂³×C₅	1	1	yes	characteristic, direct product factor
34	C₂×C₅	—	3	7	no	—
35	C₂×C₅	—	3	1	no	—
36	C₂×C₅	C₂²×A₄	1	7	yes	direct product factor
37	C₂³	—	3	21	no	—
38	C₂³	—	3	14	no	—
39	C₂³	—	3	7	no	—
40	C₂³	—	3	7	no	—
41	C₂³	C₅×A₄	1	1	yes	characteristic, direct product factor
42	C₂³	C₂²×C₃×C₅	1	7	yes	complemented
43	C₂×C₃	—	4	7	no	—
44	C₅	C₂³×A₄	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²	—	3	7	no	—
46	C₂²	—	3	14	no	—
47	C₂²	—	3	7	no	—
48	C₂²	—	3	21	no	—
49	C₂²	C₂×C₅×A₄	1	7	yes	direct product factor
50	C₂²	C₂³×C₃×C₅	1	1	yes	characteristic, complemented
51	C₃	—	4	1	no	Sylow
52	C₂	—	3	1	no	—
53	C₂	—	3	7	no	—
54	C₂	C₂²×C₅×A₄	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₅	A₄
commutator, cosocle, hypocenter	C₂²	C₂³×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂⁵×C₅	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×A₄	C₂	direct (N × H)
2. C₂⁵×C₅	C₃	semidirect
4. C₂×C₅×A₄	C₂²	direct (N × H)
5. C₂³×A₄	C₅	direct (N × H)
8. C₂⁴×C₅	C₂×C₃	semidirect
10. C₅×A₄	C₂³	direct (N × H)
11. C₂²×A₄	C₂×C₅	direct (N × H)
16. C₂³×C₅	A₄	direct (N × H)
17. C₂³×C₅	C₂²×C₃	semidirect
18. C₂⁵	C₃×C₅	semidirect
21. C₂×A₄	C₂²×C₅	direct (N × H)
26. C₂²×C₅	C₂×A₄	direct (N × H)
27. C₂²×C₅	C₂³×C₃	semidirect
30. C₂⁴	C₂×C₃×C₅	semidirect
33. A₄	C₂³×C₅	direct (N × H)
36. C₂×C₅	C₂²×A₄	direct (N × H)
41. C₂³	C₅×A₄	direct (N × H)
42. C₂³	C₂²×C₃×C₅	semidirect
44. C₅	C₂³×A₄	direct (N × H)
49. C₂²	C₂×C₅×A₄	direct (N × H)
50. C₂²	C₂³×C₃×C₅	semidirect
54. C₂	C₂²×C₅×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
C₂⁵×C₅	3
C₂³×C₃×C₅	4
C₂³×A₄	5

Subgroups — C23×C5×A4 #92132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×A₄ #92132