Subgroups — A₄×#168 #91189

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×#168	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×A₄	C₄	1	1	yes	characteristic
4	C₃×#168	—	4	1	no	maximal
5	C₈×A₄	—	5	1	no	maximal, Hall
6	C₂²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
7	C₂×#168	—	3	1	no	—
8	C₂×#168	—	3	1	no	—
9	C₅×A₄	C₈	1	1	yes	characteristic, complemented
10	C₃×C₄×C₅	—	4	1	no	—
11	C₄×A₄	D₅	1	1	yes	characteristic
12	C₂³×C₅	C₃×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅	—	3	1	no	—
14	C₂×C₄×C₅	—	3	1	no	—
15	#168	—	3	1	no	—
16	#168	A₄	1	1	yes	characteristic, direct product factor
17	C₂²×C₈	—	5	1	no	Sylow
18	C₂×C₃×C₅	—	4	1	no	—
19	C₂×A₄	Dic₅	1	1	yes	characteristic
20	C₃×C₈	—	20	1	no	—
21	C₂²×C₅	—	3	1	no	—
22	C₂²×C₅	—	3	1	no	—
23	C₂²×C₅	C₃×C₈	1	1	yes	characteristic, complemented
24	C₄×C₅	—	3	1	no	—
25	C₄×C₅	C₂×A₄	1	1	yes	characteristic
26	C₂²×C₄	C₃×D₅	1	1	yes	characteristic
27	C₂×C₈	—	15	1	no	—
28	C₂×C₈	—	15	1	no	—
29	C₃×C₅	—	4	1	no	Hall
30	A₄	#168	1	1	yes	characteristic, direct product factor
31	C₃×C₄	—	4	1	no	—
32	C₂×C₅	—	3	1	no	—
33	C₂×C₅	—	3	1	no	—
34	C₂×C₅	C₄×A₄	1	1	yes	characteristic
35	C₂³	C₃×Dic₅	1	1	yes	characteristic
36	C₂×C₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₈	—	5	1	no	—
39	C₈	—	15	1	no	—
40	C₂×C₃	—	4	1	no	—
41	C₅	C₈×A₄	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	C₃×#168	1	1	yes	characteristic, complemented
45	C₄	—	3	1	no	—
46	C₄	D₅×A₄	1	1	yes	characteristic
47	C₃	—	4	1	no	Sylow
48	C₂	—	3	1	no	—
49	C₂	—	3	1	no	—
50	C₂	A₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅×A₄
commutator, hypocenter	C₂²×C₅	C₃×C₈
Fitting, cosocle	C₂²×C₄×C₅	C₂×C₃
socle	C₂³×C₅	C₃×C₄
prime radical	C₂×C₅×A₄	C₄
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#168	C₃	semidirect
9. C₅×A₄	C₈	semidirect
16. #168	A₄	direct (N × H)
23. C₂²×C₅	C₃×C₈	semidirect
30. A₄	#168	direct (N × H)
41. C₅	C₈×A₄	semidirect
44. C₂²	C₃×#168	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×A₄	2
C₂²×#168	3
C₃×#168	4
C₈×A₄	5

Subgroups — A4×#168 #91189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×#168 #91189