Subgroups — AGL(1,𝔽₅)×#10597244 #27130903

Order 12100.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#10597244	C₂	1	1	yes	maximal, characteristic
2	C₅×#10597244	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁²×AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, complemented
4	C₄×#10597244	—	5	1	no	maximal
5	D₅×C₁₁²	C₂×C₅	1	1	yes	characteristic
6	C₂×#10597244	—	5	1	no	—
7	AGL(1,𝔽₅)×C₁₁⋊C₅	—	11	2	no	maximal
8	C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
9	#10597244	—	4	1	no	—
10	#10597244	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
11	D₅×C₁₁⋊C₅	—	11	2	no	—
12	C₄×C₁₁²	—	5	1	no	Hall
13	C₅×C₁₁⋊C₅	—	11	2	no	—
14	C₂×C₁₁²	—	5	1	no	—
15	C₁₁×AGL(1,𝔽₅)	—	5	2	no	—
16	C₁₁×AGL(1,𝔽₅)	C₁₁⋊C₅	1	2	yes	complemented
17	C₄×C₁₁⋊C₅	—	55	2	no	—
18	C₁₁²	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	D₅×C₁₁	—	5	2	no	—
20	D₅×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	—
21	C₂×C₁₁⋊C₅	—	55	2	no	—
22	C₅×AGL(1,𝔽₅)	—	121	1	no	Hall
23	C₅×C₁₁	—	5	2	no	—
24	C₅×C₁₁	C₄×C₁₁⋊C₅	1	2	yes	complemented
25	C₁₁⋊C₅	—	11	2	no	—
26	C₁₁⋊C₅	—	44	2	no	—
27	C₅×D₅	—	121	1	no	—
28	C₄×C₁₁	—	5	2	no	—
29	C₄×C₁₁	—	25	2	no	—
30	C₅²	—	121	1	no	Sylow
31	C₂×C₁₁	—	5	2	no	—
32	C₂×C₁₁	—	25	2	no	—
33	AGL(1,𝔽₅)	#10597244	1	1	yes	characteristic, direct product factor
34	C₄×C₅	—	605	1	no	—
35	C₁₁	—	5	2	no	—
36	C₁₁	AGL(1,𝔽₅)×C₁₁⋊C₅	1	2	yes	complemented
37	C₂×C₅	—	605	1	no	—
38	D₅	C₂×#10597244	1	1	yes	characteristic
39	C₅	—	121	1	no	—
40	C₅	—	484	1	no	—
41	C₅	C₄×#10597244	1	1	yes	characteristic, complemented
42	C₄	—	5	1	no	Sylow
43	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₁²	C₄×C₅
prime radical	D₅×#10597244	C₂
cosocle	D₅×C₁₁²	C₂×C₅
LCS	G ▷ C₅×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅×#10597244	C₄	semidirect
3. C₁₁²×AGL(1,𝔽₅)	C₅	semidirect
8. C₅×C₁₁²	C₄×C₅	semidirect
10. #10597244	AGL(1,𝔽₅)	direct (N × H)
16. C₁₁×AGL(1,𝔽₅)	C₁₁⋊C₅	semidirect
18. C₁₁²	C₅×AGL(1,𝔽₅)	semidirect
24. C₅×C₁₁	C₄×C₁₁⋊C₅	semidirect
33. AGL(1,𝔽₅)	#10597244	direct (N × H)
36. C₁₁	AGL(1,𝔽₅)×C₁₁⋊C₅	semidirect
41. C₅	C₄×#10597244	semidirect

Maximal subgroups

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

subgroup	index
D₅×#10597244	2
C₁₁²×AGL(1,𝔽₅)	5
C₄×#10597244	5
AGL(1,𝔽₅)×C₁₁⋊C₅	11

Subgroups — AGL(1,𝔽5)×#10597244 #27130903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#10597244 #27130903