Subgroups — AΓL(1,𝔽₂₅) #11925736

Order 1200.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64480⋊C₂	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597167	C₂	1	1	yes	maximal, characteristic, complemented
4	#6053⋊C₂	—	3	1	no	maximal, Hall
5	#3874⋊C₂	C₄	1	1	yes	characteristic
6	#1043⋊C₃	C₂²	1	1	yes	characteristic
7	#64480	C₄	1	1	yes	characteristic
8	D₅⋊AGL(1,𝔽₅)	—	3	1	no	—
9	#6053	—	3	1	no	—
10	#6053	D₃	1	1	yes	characteristic, complemented
11	(C₅⋊D₅)⋊C₃	C₂×C₄	1	1	yes	characteristic
12	#3874	—	2	1	no	—
13	D₅²	—	3	1	no	—
14	#1044	—	3	1	no	—
15	#1043	C₂×D₃	1	1	yes	characteristic
16	C₅²⋊C₃	M₁₆	1	1	yes	characteristic, complemented, Hall
17	C₅⋊D₅	C₄×D₃	1	1	yes	characteristic
18	C₅×D₅	—	6	1	no	—
19	ΓL(1,𝔽₂₅)	—	25	1	no	maximal, Hall
20	C₂×AGL(1,𝔽₅)	—	30	1	no	—
21	C₅²	ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented, Sylow
22	C₄×D₃	—	25	1	no	—
23	C₃×C₈	—	25	1	no	—
24	C₃⋊C₈	—	25	1	no	—
25	C₂×D₅	—	30	1	no	—
26	AGL(1,𝔽₅)	—	30	1	no	—
27	AGL(1,𝔽₅)	—	30	1	no	—
28	M₁₆	—	75	1	no	Sylow
29	C₂×D₃	—	25	1	no	—
30	C₃×C₄	—	25	1	no	—
31	Dic₃	—	25	1	no	—
32	C₂×C₅	—	30	1	no	—
33	D₅	—	6	1	no	—
34	D₅	—	30	1	no	—
35	C₂×C₄	—	75	1	no	—
36	C₈	—	25	1	no	—
37	C₈	—	75	1	no	—
38	C₂×C₃	—	25	1	no	—
39	D₃	—	50	1	no	—
40	C₅	—	6	1	no	—
41	C₂²	—	75	1	no	—
42	C₄	—	25	1	no	—
43	C₄	—	75	1	no	—
44	C₃	—	25	1	no	Sylow
45	C₂	—	25	1	no	—
46	C₂	—	30	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator	(C₅⋊D₅)⋊C₃	C₂×C₄
Fitting, socle	C₅²	ΓL(1,𝔽₂₅)
prime radical	#3874⋊C₂	C₄
cosocle	#1043⋊C₃	C₂²
hypocenter	C₅²⋊C₃	M₁₆
LCS	G ▷ (C₅⋊D₅)⋊C₃ ▷ C₅²⋊C₃
UCS	C₁

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

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