Subgroups — (C₁₅₁⋊C₅)⋊AGL(1,𝔽₅) #28419085

Order 15100.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₅₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₅₁⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, complemented
4	Dic₁₅₁⋊C₅	—	5	1	no	maximal
5	D₅×C₁₅₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₁₅₁⋊C₅	—	5	1	no	—
7	C₅×C₁₅₁	C₄×C₅	1	1	yes	characteristic, complemented
8	C₁₅₁⋊C₅	—	4	1	no	—
9	C₁₅₁⋊C₅	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
10	Dic₁₅₁	—	5	1	no	Hall
11	C₂×C₁₅₁	—	5	1	no	—
12	C₁₅₁	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
13	C₅×AGL(1,𝔽₅)	—	151	1	no	maximal, Hall
14	C₅×D₅	—	302	1	no	—
15	C₅²	—	302	1	no	Sylow
16	AGL(1,𝔽₅)	—	151	1	no	—
17	C₄×C₅	—	755	1	no	—
18	C₂×C₅	—	1510	1	no	—
19	D₅	D₁₅₁⋊C₅	1	1	yes	characteristic
20	C₅	—	302	1	no	—
21	C₅	—	604	1	no	—
22	C₅	Dic₁₅₁⋊C₅	1	1	yes	characteristic, complemented
23	C₄	—	755	1	no	Sylow
24	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₅₁	C₄×C₅
prime radical	D₅×C₁₅₁⋊C₅	C₂
cosocle	D₅×C₁₅₁	C₂×C₅
LCS	G ▷ C₅×C₁₅₁
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.