Subgroups — #41001977

Order 26900.

26 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	1	no	maximal
4	Dic₁₃₄₅	—	5	1	no	maximal
5	C₂×C₅×C₂₆₉	—	5	1	no	—
6	D₅×C₂₆₉	D₅	1	1	yes	characteristic
7	C₅×C₂₆₉	—	4	1	no	—
8	C₅×C₂₆₉	Dic₅	1	1	yes	characteristic, complemented
9	C₅×C₂₆₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
10	Dic₂₆₉	—	25	1	no	Hall
11	C₂×C₂₆₉	—	5	1	no	—
12	C₂₆₉	#1042	1	1	yes	characteristic, complemented, Sylow
13	#1042	—	269	1	no	maximal, Hall
14	C₅×D₅	D₂₆₉	1	1	yes	characteristic
15	C₅²	Dic₂₆₉	1	1	yes	characteristic, complemented, Sylow
16	AGL(1,𝔽₅)	—	1345	1	no	—
17	Dic₅	—	1345	1	no	—
18	C₂×C₅	—	5	1	no	—
19	D₅	D₁₃₄₅	1	1	yes	characteristic
20	C₅	—	4	1	no	—
21	C₅	Dic₁₃₄₅	1	1	yes	characteristic, complemented
22	C₅	#19129042	1	1	yes	characteristic, complemented
23	C₄	—	6725	1	no	Sylow
24	C₂	—	5	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.