Subgroups — AGL(1,𝔽₅)×#170 #11717299

Order 800.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊#170	C₂	1	1	yes	maximal, characteristic
2	D₅×#170	C₂	1	1	yes	maximal, characteristic
3	Dic₅×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
4	C₂×#1042	C₄	1	1	yes	characteristic
5	C₂×C₅×AGL(1,𝔽₅)	C₄	1	1	yes	characteristic
6	D₅×Dic₅	C₂²	1	1	yes	characteristic
7	#6034	C₄	1	1	yes	characteristic, complemented
8	#6033	C₄	1	1	yes	characteristic, complemented
9	#6032	C₄	1	1	yes	characteristic, complemented
10	C₅×#170	C₄	1	1	yes	characteristic, complemented
11	C₄×#170	—	5	1	no	maximal
12	C₈×AGL(1,𝔽₅)	—	5	1	no	maximal
13	C₂×C₅×D₅	C₂×C₄	1	1	yes	characteristic
14	#1042	C₈	1	2	yes	complemented
15	C₅×AGL(1,𝔽₅)	C₈	1	2	yes	complemented
16	#1039	C₂×C₄	1	1	yes	characteristic
17	C₅×Dic₅	C₂×C₄	1	1	yes	characteristic
18	C₂×#170	—	5	1	no	—
19	C₂×#170	—	5	1	no	—
20	C₄×AGL(1,𝔽₅)	—	5	1	no	—
21	D₅⋊C₈	—	5	1	no	—
22	C₄×Dic₅	—	5	1	no	—
23	C₈×D₅	—	5	1	no	—
24	C₂×C₅²	C₄²	1	1	yes	characteristic
25	C₅×D₅	C₂×C₈	1	1	yes	characteristic
26	C₅×D₅	C₂×C₈	1	1	yes	characteristic
27	C₂×AGL(1,𝔽₅)	—	5	1	no	—
28	C₂×AGL(1,𝔽₅)	AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₂×C₄×C₅	—	5	1	no	—
30	C₂×Dic₅	—	5	1	no	—
31	C₂×Dic₅	—	5	1	no	—
32	C₄×D₅	—	5	1	no	—
33	#170	—	5	1	no	—
34	#170	—	5	1	no	—
35	#170	—	5	1	no	—
36	#170	—	5	1	no	—
37	#170	—	5	1	no	—
38	#170	—	20	1	no	—
39	#170	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
40	C₅×C₈	—	5	1	no	—
41	#168	—	5	1	no	—
42	C₄×C₈	—	25	1	no	Sylow
43	C₅²	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₅	—	5	1	no	—
45	C₂×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
46	AGL(1,𝔽₅)	—	5	2	no	—
47	AGL(1,𝔽₅)	#170	1	2	yes	direct product factor
48	C₄×C₅	—	5	2	no	—
49	C₄×C₅	—	5	1	no	—
50	Dic₅	—	5	2	no	—
51	Dic₅	—	5	1	no	—
52	Dic₅	—	5	1	no	—
53	Dic₅	—	20	1	no	—
54	Dic₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂×C₈	—	25	1	no	—
56	C₂×C₈	—	25	1	no	—
57	C₄²	—	25	1	no	—
58	C₂×C₅	—	4	1	no	—
59	C₂×C₅	—	5	1	no	—
60	C₂×C₅	—	5	1	no	—
61	C₂×C₅	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
62	C₂×C₅	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
63	D₅	D₅⋊C₈	1	1	yes	characteristic
64	D₅	C₂×#170	1	1	yes	characteristic
65	C₂×C₄	—	5	1	no	—
66	C₂×C₄	—	25	1	no	—
67	C₂×C₄	—	25	1	no	—
68	C₈	—	5	1	no	—
69	C₈	—	25	1	no	—
70	C₈	—	25	1	no	—
71	C₈	—	25	1	no	—
72	C₅	—	4	1	no	—
73	C₅	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
74	C₅	C₄×#170	1	1	yes	characteristic, complemented
75	C₂²	—	5	1	no	—
76	C₄	—	5	2	no	—
77	C₄	—	5	1	no	—
78	C₄	—	25	2	no	—
79	C₄	—	25	1	no	—
80	C₂	—	5	1	no	—
81	C₂	—	5	1	no	—
82	C₂	AGL(1,𝔽₅)²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	AGL(1,𝔽₅)²
commutator, hypocenter	C₅²	C₄×C₈
Fitting, socle	C₂×C₅²	C₄²
prime radical	C₂×C₅×D₅	C₂×C₄
cosocle	D₅×Dic₅	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
7. #6034	C₄	semidirect
8. #6033	C₄	semidirect
9. #6032	C₄	semidirect
10. C₅×#170	C₄	semidirect
14. #1042	C₈	semidirect
15. C₅×AGL(1,𝔽₅)	C₈	semidirect
39. #170	AGL(1,𝔽₅)	direct (N × H)
43. C₅²	C₄×C₈	semidirect
47. AGL(1,𝔽₅)	#170	direct (N × H)
73. C₅	C₈×AGL(1,𝔽₅)	semidirect
74. C₅	C₄×#170	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊#170	2
D₅×#170	2
Dic₅×AGL(1,𝔽₅)	2
C₄×#170	5
C₈×AGL(1,𝔽₅)	5

Subgroups — AGL(1,𝔽5)×#170 #11717299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#170 #11717299