Subgroups — A₄×Dic₁₁⋊C₅ #72276515

Order 2640.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	A₄×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented
4	C₃×Dic₁₁⋊C₅	—	4	1	no	maximal
5	A₄×Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂³×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
7	C₂×Dic₁₁⋊C₅	—	3	1	no	—
8	C₂×Dic₁₁⋊C₅	—	3	1	no	—
9	C₂×C₃×C₁₁⋊C₅	—	4	1	no	—
10	C₂×C₁₁×A₄	C₂×C₅	1	1	yes	characteristic
11	C₄×C₅×A₄	—	11	1	no	maximal, Hall
12	C₂²×C₁₁⋊C₅	—	3	1	no	—
13	C₂²×C₁₁⋊C₅	—	3	1	no	—
14	C₂²×C₁₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented
15	Dic₁₁⋊C₅	—	3	1	no	—
16	Dic₁₁⋊C₅	A₄	1	1	yes	characteristic, direct product factor
17	C₂²×Dic₁₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
18	C₃×C₁₁⋊C₅	—	4	1	no	Hall
19	C₁₁×A₄	C₄×C₅	1	1	yes	characteristic, complemented
20	C₃×Dic₁₁	—	4	1	no	—
21	C₂×C₅×A₄	—	11	1	no	—
22	C₂×C₁₁⋊C₅	—	3	1	no	—
23	C₂×C₁₁⋊C₅	—	3	1	no	—
24	C₂×C₁₁⋊C₅	C₂×A₄	1	1	yes	characteristic
25	C₂³×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic
26	C₂×Dic₁₁	—	3	1	no	—
27	C₂×Dic₁₁	—	3	1	no	—
28	C₂²×C₄×C₅	—	11	1	no	Hall
29	C₂×C₃×C₁₁	—	4	1	no	—
30	C₅×A₄	—	11	1	no	—
31	C₃×C₄×C₅	—	44	1	no	—
32	C₁₁⋊C₅	C₄×A₄	1	1	yes	characteristic, complemented, Hall
33	C₄×A₄	—	11	1	no	Hall
34	C₂²×C₁₁	—	3	1	no	—
35	C₂²×C₁₁	—	3	1	no	—
36	C₂²×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented
37	Dic₁₁	—	3	1	no	—
38	Dic₁₁	C₅×A₄	1	1	yes	characteristic, complemented
39	C₂³×C₅	—	11	1	no	—
40	C₂×C₄×C₅	—	33	1	no	—
41	C₂×C₄×C₅	—	33	1	no	—
42	C₃×C₁₁	—	4	1	no	Hall
43	C₂×C₃×C₅	—	44	1	no	—
44	C₂×A₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic
45	C₂×C₁₁	—	3	1	no	—
46	C₂×C₁₁	—	3	1	no	—
47	C₂×C₁₁	C₂×C₅×A₄	1	1	yes	characteristic
48	C₂²×C₅	—	11	1	no	—
49	C₂²×C₅	—	33	1	no	—
50	C₂²×C₅	—	33	1	no	—
51	C₄×C₅	—	11	1	no	—
52	C₄×C₅	—	33	1	no	—
53	C₂²×C₄	—	11	1	no	Sylow
54	C₃×C₅	—	44	1	no	Hall
55	A₄	Dic₁₁⋊C₅	1	1	yes	characteristic, direct product factor
56	C₃×C₄	—	44	1	no	—
57	C₁₁	C₄×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₅	—	11	1	no	—
59	C₂×C₅	—	33	1	no	—
60	C₂×C₅	—	33	1	no	—
61	C₂³	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
62	C₂×C₄	—	33	1	no	—
63	C₂×C₄	—	33	1	no	—
64	C₂×C₃	—	4	1	no	—
65	C₅	—	11	1	no	Sylow
66	C₂²	—	3	1	no	—
67	C₂²	—	3	1	no	—
68	C₂²	C₃×Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
69	C₄	—	11	1	no	—
70	C₄	—	33	1	no	—
71	C₃	—	4	1	no	Sylow
72	C₂	—	3	1	no	—
73	C₂	—	3	1	no	—
74	C₂	A₄×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×AGL(1,𝔽₁₁)
commutator, hypocenter	C₂²×C₁₁	C₃×C₄×C₅
Fitting, socle, cosocle	C₂³×C₁₁	C₂×C₃×C₅
prime radical	C₂×A₄×C₁₁⋊C₅	C₂
LCS	G ▷ C₂²×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₁⋊C₅	C₃	semidirect
3. A₄×C₁₁⋊C₅	C₄	semidirect
5. A₄×Dic₁₁	C₅	semidirect
14. C₂²×C₁₁⋊C₅	C₃×C₄	semidirect
16. Dic₁₁⋊C₅	A₄	direct (N × H)
17. C₂²×Dic₁₁	C₃×C₅	semidirect
19. C₁₁×A₄	C₄×C₅	semidirect
32. C₁₁⋊C₅	C₄×A₄	semidirect
36. C₂²×C₁₁	C₃×C₄×C₅	semidirect
38. Dic₁₁	C₅×A₄	semidirect
55. A₄	Dic₁₁⋊C₅	direct (N × H)
57. C₁₁	C₄×C₅×A₄	semidirect
68. C₂²	C₃×Dic₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×A₄×C₁₁⋊C₅	2
C₂²×Dic₁₁⋊C₅	3
C₃×Dic₁₁⋊C₅	4
A₄×Dic₁₁	5
C₄×C₅×A₄	11

Subgroups — A4×Dic11⋊C5 #72276515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×Dic₁₁⋊C₅ #72276515