Subgroups — A₄×#3928 #14511601

Order 1920.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×#672	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3928	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₈×A₄	C₄	1	1	yes	characteristic
4	C₃×#3928	—	4	1	no	maximal
5	A₄×C₃₂	—	5	1	no	maximal, Hall
6	C₂²×#672	C₂×C₃	1	1	yes	characteristic
7	C₂×#3928	—	3	1	no	—
8	C₂×#3928	—	3	1	no	—
9	C₄×C₅×A₄	C₈	1	1	yes	characteristic
10	C₃×#672	—	4	1	no	—
11	A₄×C₁₆	—	5	1	no	—
12	C₂²×C₅×C₈	C₃×C₄	1	1	yes	characteristic
13	C₂×#672	—	3	1	no	—
14	C₂×#672	—	3	1	no	—
15	#3928	—	3	1	no	—
16	#3928	A₄	1	1	yes	characteristic, direct product factor
17	C₂²×C₃₂	—	5	1	no	Sylow
18	C₂×C₅×A₄	C₁₆	1	1	yes	characteristic
19	C₃×C₅×C₈	—	4	1	no	—
20	C₈×A₄	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₃×C₃₂	—	20	1	no	—
22	C₂²×C₄×C₅	C₃×C₈	1	1	yes	characteristic
23	C₂×C₅×C₈	—	3	1	no	—
24	C₂×C₅×C₈	—	3	1	no	—
25	#672	—	3	1	no	—
26	#672	C₂×A₄	1	1	yes	characteristic
27	C₂²×C₁₆	—	5	1	no	—
28	C₂×C₃₂	—	15	1	no	—
29	C₂×C₃₂	—	15	1	no	—
30	C₅×A₄	C₃₂	1	1	yes	characteristic, complemented
31	C₃×C₄×C₅	—	4	1	no	—
32	C₄×A₄	#170	1	1	yes	characteristic
33	C₃×C₁₆	—	20	1	no	—
34	C₂³×C₅	C₃×C₁₆	1	1	yes	characteristic
35	C₂×C₄×C₅	—	3	1	no	—
36	C₂×C₄×C₅	—	3	1	no	—
37	C₅×C₈	—	3	1	no	—
38	C₅×C₈	C₄×A₄	1	1	yes	characteristic
39	C₂²×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₂×C₁₆	—	15	1	no	—
41	C₂×C₁₆	—	15	1	no	—
42	C₃₂	—	5	1	no	—
43	C₃₂	—	15	1	no	—
44	C₂×C₃×C₅	—	4	1	no	—
45	C₂×A₄	#674	1	1	yes	characteristic
46	C₃×C₈	—	4	1	no	—
47	C₂²×C₅	—	3	1	no	—
48	C₂²×C₅	—	3	1	no	—
49	C₂²×C₅	C₃×C₃₂	1	1	yes	characteristic, complemented
50	C₄×C₅	—	3	1	no	—
51	C₄×C₅	C₈×A₄	1	1	yes	characteristic
52	C₂²×C₄	C₃×#170	1	1	yes	characteristic
53	C₂×C₈	—	3	1	no	—
54	C₂×C₈	—	3	1	no	—
55	C₁₆	—	5	1	no	—
56	C₁₆	—	15	1	no	—
57	C₃×C₅	—	4	1	no	Hall
58	A₄	#3928	1	1	yes	characteristic, direct product factor
59	C₃×C₄	—	4	1	no	—
60	C₂×C₅	—	3	1	no	—
61	C₂×C₅	—	3	1	no	—
62	C₂×C₅	A₄×C₁₆	1	1	yes	characteristic
63	C₂³	C₃×#674	1	1	yes	characteristic
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₈	—	3	1	no	—
67	C₈	A₄×AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₂×C₃	—	4	1	no	—
69	C₅	A₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	3	1	no	—
71	C₂²	—	3	1	no	—
72	C₂²	C₃×#3928	1	1	yes	characteristic, complemented
73	C₄	—	3	1	no	—
74	C₄	A₄×#170	1	1	yes	characteristic
75	C₃	—	4	1	no	Sylow
76	C₂	—	3	1	no	—
77	C₂	—	3	1	no	—
78	C₂	A₄×#674	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	A₄×AGL(1,𝔽₅)
commutator, hypocenter	C₂²×C₅	C₃×C₃₂
Fitting	C₂²×C₅×C₈	C₃×C₄
socle	C₂³×C₅	C₃×C₁₆
prime radical	C₂×C₅×A₄	C₁₆
cosocle	C₂²×#672	C₂×C₃
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#3928	C₃	semidirect
16. #3928	A₄	direct (N × H)
30. C₅×A₄	C₃₂	semidirect
49. C₂²×C₅	C₃×C₃₂	semidirect
58. A₄	#3928	direct (N × H)
69. C₅	A₄×C₃₂	semidirect
72. C₂²	C₃×#3928	semidirect

Maximal subgroups

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

subgroup	index
A₄×#672	2
C₂²×#3928	3
C₃×#3928	4
A₄×C₃₂	5

Subgroups — A4×#3928 #14511601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×#3928 #14511601