Subgroups — Q₈×C₁₁×AGL(1,𝔽₅) #13183340

Order 1760.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₄⋊AGL(1,𝔽₅)	C₂	1	3	yes	maximal
3	C₄×C₁₁×AGL(1,𝔽₅)	C₂	1	3	yes	maximal
4	C₂×C₁₁×AGL(1,𝔽₅)	C₂²	1	3	yes	—
5	C₂×C₁₁×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
6	C₅×Q₈×C₁₁	C₄	1	1	yes	characteristic, complemented
7	C₄×D₅×C₁₁	C₂²	1	3	yes	—
8	C₁₁×Dic₁₀	C₄	1	3	yes	complemented
9	C₄×Q₈×C₁₁	—	5	1	no	maximal, Hall
10	C₂×D₅×C₁₁	C₂³	1	1	yes	characteristic
11	C₁₁×AGL(1,𝔽₅)	—	2	3	no	—
12	C₁₁×AGL(1,𝔽₅)	Q₈	1	2	yes	direct product factor
13	C₄×C₅×C₁₁	C₂×C₄	1	3	yes	—
14	C₁₁×Dic₅	C₂×C₄	1	3	yes	—
15	C₂×Q₈×C₁₁	—	5	1	no	—
16	C₁₁×C₄⋊C₄	—	5	3	no	—
17	C₄²×C₁₁	—	5	3	no	—
18	Q₈×AGL(1,𝔽₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
20	D₅×C₁₁	C₂×Q₈	1	1	yes	characteristic
21	D₅×C₁₁	#41	1	1	yes	characteristic
22	Q₈×C₁₁	—	5	3	no	—
23	Q₈×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
24	C₂×C₄×C₁₁	—	5	1	no	—
25	C₂×C₄×C₁₁	—	5	3	no	—
26	C₂×C₄×C₁₁	—	5	3	no	—
27	Q₈×D₅	C₂×C₁₁	1	1	yes	characteristic
28	C₄⋊AGL(1,𝔽₅)	C₂×C₁₁	1	3	yes	—
29	C₄×AGL(1,𝔽₅)	C₂×C₁₁	1	3	yes	—
30	C₅×C₁₁	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₁₁	—	5	1	no	—
32	C₄×C₁₁	—	5	2	no	—
33	C₄×C₁₁	—	5	3	no	—
34	C₄×C₁₁	—	10	3	no	—
35	C₄×C₁₁	C₂×AGL(1,𝔽₅)	1	3	yes	—
36	C₂×AGL(1,𝔽₅)	C₂²×C₁₁	1	3	yes	—
37	C₂×AGL(1,𝔽₅)	C₂²×C₁₁	1	1	yes	characteristic
38	C₅×Q₈	C₄×C₁₁	1	1	yes	characteristic, complemented
39	C₄×D₅	C₂²×C₁₁	1	3	yes	—
40	Dic₁₀	C₄×C₁₁	1	3	yes	complemented
41	C₄×Q₈	—	5	1	no	Sylow
42	C₂×C₁₁	—	5	1	no	—
43	C₂×C₁₁	—	5	1	no	—
44	C₂×C₁₁	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₂×D₅	C₂³×C₁₁	1	1	yes	characteristic
46	AGL(1,𝔽₅)	—	2	3	no	—
47	AGL(1,𝔽₅)	Q₈×C₁₁	1	2	yes	direct product factor
48	C₄×C₅	C₂×C₄×C₁₁	1	3	yes	—
49	Dic₅	C₂×C₄×C₁₁	1	3	yes	—
50	C₂×Q₈	—	5	1	no	—
51	C₄⋊C₄	—	5	3	no	—
52	C₄²	—	5	3	no	—
53	C₁₁	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
55	D₅	C₂×Q₈×C₁₁	1	1	yes	characteristic
56	D₅	C₁₁×#41	1	1	yes	characteristic
57	Q₈	—	5	3	no	—
58	Q₈	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
59	C₂×C₄	—	5	1	no	—
60	C₂×C₄	—	5	3	no	—
61	C₂×C₄	—	5	3	no	—
62	C₅	C₄×Q₈×C₁₁	1	1	yes	characteristic, complemented, Sylow
63	C₂²	—	5	1	no	—
64	C₄	—	5	2	no	—
65	C₄	—	5	3	no	—
66	C₄	—	10	3	no	—
67	C₄	C₂×C₁₁×AGL(1,𝔽₅)	1	3	yes	—
68	C₂	—	5	1	no	—
69	C₂	—	5	1	no	—
70	C₂	C₂²×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₂	C₂²×C₁₁×AGL(1,𝔽₅)
Fitting	C₅×Q₈×C₁₁	C₄
socle	C₂×C₅×C₁₁	C₂²×C₄
prime radical	C₂×D₅×C₁₁	C₂³
cosocle	C₂×D₅	C₂³×C₁₁
hypercenter	Q₈×C₁₁	AGL(1,𝔽₅)
hypocenter	C₅	C₄×Q₈×C₁₁
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
6. C₅×Q₈×C₁₁	C₄	semidirect
8. C₁₁×Dic₁₀	C₄	semidirect
12. C₁₁×AGL(1,𝔽₅)	Q₈	direct (N × H)
18. Q₈×AGL(1,𝔽₅)	C₁₁	direct (N × H)
23. Q₈×C₁₁	AGL(1,𝔽₅)	direct (N × H)
30. C₅×C₁₁	C₄×Q₈	semidirect
38. C₅×Q₈	C₄×C₁₁	semidirect
40. Dic₁₀	C₄×C₁₁	semidirect
47. AGL(1,𝔽₅)	Q₈×C₁₁	direct (N × H)
53. C₁₁	Q₈×AGL(1,𝔽₅)	direct (N × H)
58. Q₈	C₁₁×AGL(1,𝔽₅)	direct (N × H)
62. C₅	C₄×Q₈×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₅×C₁₁	2
C₁₁×C₄⋊AGL(1,𝔽₅)	2
C₄×C₁₁×AGL(1,𝔽₅)	2
C₄×Q₈×C₁₁	5
Q₈×AGL(1,𝔽₅)	11

Subgroups — Q8×C11×AGL(1,𝔽5) #13183340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×AGL(1,𝔽₅) #13183340