Subgroups — #41001989

Order 26900.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₂₆₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₂₆₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19129042	—	5	2	no	maximal
4	D₅×C₂₆₉	—	5	2	no	—
5	D₅×C₂₆₉	—	10	2	no	—
6	C₅×C₂₆₉	—	2	2	no	—
7	C₅×C₂₆₉	AGL(1,𝔽₅)	1	2	yes	complemented
8	Dic₂₆₉	—	25	1	no	Hall
9	C₂×C₂₆₉	—	25	1	no	—
10	C₂₆₉	#1044	1	1	yes	characteristic, complemented, Sylow
11	#1044	—	269	1	no	maximal, Hall
12	C₅⋊D₅	D₂₆₉	1	1	yes	characteristic
13	C₅²	Dic₂₆₉	1	1	yes	characteristic, complemented, Sylow
14	AGL(1,𝔽₅)	—	1345	2	no	—
15	D₅	—	5	2	no	—
16	D₅	—	10	2	no	—
17	C₅	—	2	2	no	—
18	C₅	#19129042	1	2	yes	complemented
19	C₄	—	6725	1	no	Sylow
20	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₂₆₉	C₄
prime radical, cosocle	C₅⋊D₅×C₂₆₉	C₂
LCS	G ▷ C₅²×C₂₆₉
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.