Subgroups — A₄⋊#3926 #14511539

Order 1920.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₄×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#3926	—	3	1	no	maximal, Hall
3	C₅×C₈×A₄	C₄	1	1	yes	characteristic
4	C₃⋊#3926	—	4	1	no	maximal
5	A₄⋊C₃₂	—	5	1	no	maximal, Hall
6	C₂²×C₅×C₁₆	D₃	1	1	yes	characteristic
7	C₂×#3926	—	3	1	no	—
8	C₂×#3926	—	3	1	no	—
9	C₄×C₅×A₄	C₈	1	1	yes	characteristic
10	C₃×C₅×C₁₆	—	4	1	no	—
11	A₄×C₁₆	D₅	1	1	yes	characteristic
12	C₂²×C₅×C₈	Dic₃	1	1	yes	characteristic
13	C₂×C₅×C₁₆	—	3	1	no	—
14	C₂×C₅×C₁₆	—	3	1	no	—
15	#3926	—	6	1	no	—
16	#3926	—	6	1	no	—
17	C₂²⋊C₃₂	—	15	1	no	Sylow
18	C₂×C₅×A₄	C₁₆	1	1	yes	characteristic
19	C₃×C₅×C₈	—	4	1	no	—
20	C₈×A₄	Dic₅	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	C₅×C₁₆	—	3	1	no	—
26	C₅×C₁₆	S₄	1	1	yes	characteristic
27	C₂²×C₁₆	D₁₅	1	1	yes	characteristic
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	#168	1	1	yes	characteristic
33	C₃×C₁₆	—	4	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	SL(2,ℤ/4)	1	1	yes	characteristic
39	C₂²×C₈	Dic₁₅	1	1	yes	characteristic
40	C₂×C₁₆	—	3	1	no	—
41	C₂×C₁₆	—	3	1	no	—
42	C₃₂	—	30	1	no	—
43	C₃₂	—	30	1	no	—
44	C₂×C₃×C₅	—	4	1	no	—
45	C₂×A₄	#672	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	A₄⋊C₈	1	1	yes	characteristic
52	C₂²×C₄	C₃⋊#168	1	1	yes	characteristic
53	C₂×C₈	—	3	1	no	—
54	C₂×C₈	—	3	1	no	—
55	C₁₆	—	3	1	no	—
56	C₁₆	C₅⋊S₄	1	1	yes	characteristic
57	C₃×C₅	—	4	1	no	Hall
58	A₄	#3926	1	1	yes	characteristic, complemented
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⋊#672	1	1	yes	characteristic
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₈	—	3	1	no	—
67	C₈	A₄⋊Dic₅	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⋊#3926	1	1	yes	characteristic, complemented
73	C₄	—	3	1	no	—
74	C₄	A₄⋊#168	1	1	yes	characteristic
75	C₃	—	4	1	no	Sylow
76	C₂	—	3	1	no	—
77	C₂	—	3	1	no	—
78	C₂	A₄⋊#672	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	C₅⋊S₄
commutator, hypocenter	C₅×A₄	C₃₂
Fitting	C₂²×C₅×C₁₆	D₃
socle	C₂³×C₅	C₃⋊C₁₆
prime radical	C₂×C₅×A₄	C₁₆
cosocle	C₅×A₄×C₁₆	C₂
LCS	G ▷ C₅×A₄
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
30. C₅×A₄	C₃₂	semidirect
49. C₂²×C₅	C₃⋊C₃₂	semidirect
58. A₄	#3926	semidirect
69. C₅	A₄⋊C₃₂	semidirect
72. C₂²	C₃⋊#3926	semidirect

Maximal subgroups

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

subgroup	index
C₅×A₄×C₁₆	2
C₂²⋊#3926	3
C₃⋊#3926	4
A₄⋊C₃₂	5

Subgroups — A4⋊#3926 #14511539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄⋊#3926 #14511539