Subgroups — C₃×Q₈×AGL(1,𝔽₅) #91980

Order 480.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊AGL(1,𝔽₅)	C₂	1	3	yes	maximal
3	C₃×C₄×AGL(1,𝔽₅)	C₂	1	3	yes	maximal
4	Q₈×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×AGL(1,𝔽₅)	C₂²	1	3	yes	—
6	C₂×C₃×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
7	C₃×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
8	C₃×C₄×D₅	C₂²	1	3	yes	—
9	C₃×Dic₁₀	C₄	1	3	yes	complemented
10	C₃×C₄×Q₈	—	5	1	no	maximal, Hall
11	Q₈×D₅	C₂×C₃	1	1	yes	characteristic
12	C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	3	yes	—
13	C₄×AGL(1,𝔽₅)	C₂×C₃	1	3	yes	—
14	C₂×C₃×D₅	C₂³	1	1	yes	characteristic
15	C₃×AGL(1,𝔽₅)	—	2	3	no	—
16	C₃×AGL(1,𝔽₅)	Q₈	1	2	yes	direct product factor
17	C₃×C₄×C₅	C₂×C₄	1	3	yes	—
18	C₃×Dic₅	C₂×C₄	1	3	yes	—
19	C₂×C₃×Q₈	—	5	1	no	—
20	C₃×C₄⋊C₄	—	5	3	no	—
21	C₃×C₄²	—	5	3	no	—
22	C₂×AGL(1,𝔽₅)	C₂²×C₃	1	3	yes	—
23	C₂×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
24	C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
25	C₄×D₅	C₂²×C₃	1	3	yes	—
26	Dic₁₀	C₃×C₄	1	3	yes	complemented
27	C₄×Q₈	—	5	1	no	Sylow
28	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
29	C₃×D₅	C₂×Q₈	1	1	yes	characteristic
30	C₃×D₅	#41	1	1	yes	characteristic
31	C₃×Q₈	—	5	3	no	—
32	C₃×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₄	—	5	1	no	—
34	C₂×C₃×C₄	—	5	3	no	—
35	C₂×C₃×C₄	—	5	3	no	—
36	C₂×D₅	C₂³×C₃	1	1	yes	characteristic
37	AGL(1,𝔽₅)	—	2	3	no	—
38	AGL(1,𝔽₅)	C₃×Q₈	1	2	yes	direct product factor
39	C₄×C₅	C₂×C₃×C₄	1	3	yes	—
40	Dic₅	C₂×C₃×C₄	1	3	yes	—
41	C₂×Q₈	—	5	1	no	—
42	C₄⋊C₄	—	5	3	no	—
43	C₄²	—	5	3	no	—
44	C₃×C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	—	5	1	no	—
46	C₃×C₄	—	5	2	no	—
47	C₃×C₄	—	5	3	no	—
48	C₃×C₄	—	10	3	no	—
49	C₃×C₄	C₂×AGL(1,𝔽₅)	1	3	yes	—
50	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
51	D₅	C₂×C₃×Q₈	1	1	yes	characteristic
52	D₅	C₃×#41	1	1	yes	characteristic
53	Q₈	—	5	3	no	—
54	Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	5	1	no	—
56	C₂×C₄	—	5	3	no	—
57	C₂×C₄	—	5	3	no	—
58	C₂×C₃	—	5	1	no	—
59	C₂×C₃	—	5	1	no	—
60	C₂×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
61	C₅	C₃×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²	—	5	1	no	—
63	C₄	—	5	2	no	—
64	C₄	—	5	3	no	—
65	C₄	—	10	3	no	—
66	C₄	C₂×C₃×AGL(1,𝔽₅)	1	3	yes	—
67	C₃	Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	5	1	no	—
69	C₂	—	5	1	no	—
70	C₂	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×Q₈	C₄
socle	C₂×C₃×C₅	C₂²×C₄
prime radical	C₂×C₃×D₅	C₂³
cosocle	C₂×D₅	C₂³×C₃
hypercenter	C₃×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₄×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
4. Q₈×AGL(1,𝔽₅)	C₃	direct (N × H)
7. C₃×C₅×Q₈	C₄	semidirect
9. C₃×Dic₁₀	C₄	semidirect
16. C₃×AGL(1,𝔽₅)	Q₈	direct (N × H)
24. C₅×Q₈	C₃×C₄	semidirect
26. Dic₁₀	C₃×C₄	semidirect
32. C₃×Q₈	AGL(1,𝔽₅)	direct (N × H)
38. AGL(1,𝔽₅)	C₃×Q₈	direct (N × H)
44. C₃×C₅	C₄×Q₈	semidirect
54. Q₈	C₃×AGL(1,𝔽₅)	direct (N × H)
61. C₅	C₃×C₄×Q₈	semidirect
67. C₃	Q₈×AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×D₅	2
C₃×C₄⋊AGL(1,𝔽₅)	2
C₃×C₄×AGL(1,𝔽₅)	2
Q₈×AGL(1,𝔽₅)	3
C₃×C₄×Q₈	5

Subgroups — C3×Q8×AGL(1,𝔽5) #91980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Q₈×AGL(1,𝔽₅) #91980