Subgroups — C₂×C₅×C₂²⋊A₄ #92133

Order 480.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂⁵×C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×A₄	—	4	5	no	maximal
4	C₂×C₂²⋊A₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁴×C₅	—	3	5	no	—
6	C₂⁴×C₅	—	3	5	no	—
7	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×A₄	—	4	5	no	—
9	C₂²⋊A₄	C₂×C₅	1	1	yes	characteristic, direct product factor
10	C₂³×C₅	—	3	30	no	—
11	C₂³×C₅	—	3	10	no	—
12	C₂³×C₅	—	3	5	no	—
13	C₂³×C₅	—	3	5	no	—
14	C₂³×C₅	A₄	1	5	yes	complemented
15	C₂⁵	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₅	—	16	1	no	—
17	C₂×A₄	—	4	5	no	—
18	C₂²×C₅	—	3	5	no	—
19	C₂²×C₅	—	3	30	no	—
20	C₂²×C₅	—	3	10	no	—
21	C₂²×C₅	—	3	5	no	—
22	C₂²×C₅	C₂×A₄	1	5	yes	complemented
23	C₂⁴	—	3	5	no	—
24	C₂⁴	—	3	5	no	—
25	C₂⁴	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	C₃×C₅	—	16	1	no	Hall
27	A₄	—	4	5	no	—
28	C₂×C₅	—	3	5	no	—
29	C₂×C₅	—	3	5	no	—
30	C₂×C₅	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
31	C₂³	—	3	30	no	—
32	C₂³	—	3	10	no	—
33	C₂³	—	3	5	no	—
34	C₂³	—	3	5	no	—
35	C₂³	C₅×A₄	1	5	yes	complemented
36	C₂×C₃	—	16	1	no	—
37	C₅	C₂×C₂²⋊A₄	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	—	3	5	no	—
39	C₂²	—	3	10	no	—
40	C₂²	—	3	30	no	—
41	C₂²	—	3	5	no	—
42	C₂²	C₂×C₅×A₄	1	5	yes	complemented
43	C₃	—	16	1	no	Sylow
44	C₂	—	3	5	no	—
45	C₂	—	3	5	no	—
46	C₂	C₅×C₂²⋊A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂⁵×C₅	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂²⋊A₄	C₂	direct (N × H)
2. C₂⁵×C₅	C₃	semidirect
4. C₂×C₂²⋊A₄	C₅	direct (N × H)
7. C₂⁴×C₅	C₂×C₃	semidirect
9. C₂²⋊A₄	C₂×C₅	direct (N × H)
14. C₂³×C₅	A₄	semidirect
15. C₂⁵	C₃×C₅	semidirect
22. C₂²×C₅	C₂×A₄	semidirect
25. C₂⁴	C₂×C₃×C₅	semidirect
30. C₂×C₅	C₂²⋊A₄	direct (N × H)
35. C₂³	C₅×A₄	semidirect
37. C₅	C₂×C₂²⋊A₄	direct (N × H)
42. C₂²	C₂×C₅×A₄	semidirect
46. C₂	C₅×C₂²⋊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
C₅×C₂²⋊A₄	2
C₂⁵×C₅	3
C₂×C₅×A₄	4
C₂×C₂²⋊A₄	5

Subgroups — C2×C5×C22⋊A4 #92133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂²⋊A₄ #92133