Subgroups — #37562895

Order 24100.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₂₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₂₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#18012539	—	5	1	no	maximal
4	#18012537	—	5	1	no	maximal
5	D₁₂₀₅	D₅	1	1	yes	characteristic
6	C₅×D₂₄₁	—	5	1	no	—
7	C₅×C₂₄₁	—	4	1	no	—
8	C₅×C₂₄₁	Dic₅	1	1	yes	characteristic, complemented
9	C₅×C₂₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
10	#11757210	—	25	1	no	Hall
11	D₂₄₁	—	5	1	no	—
12	C₂₄₁	#1042	1	1	yes	characteristic, complemented, Sylow
13	#1042	—	241	1	no	maximal, Hall
14	C₅×D₅	—	241	1	no	—
15	C₅²	#11757210	1	1	yes	characteristic, complemented, Sylow
16	AGL(1,𝔽₅)	—	1205	1	no	—
17	Dic₅	—	1205	1	no	—
18	C₂×C₅	—	1205	1	no	—
19	D₅	—	241	1	no	—
20	C₅	—	4	1	no	—
21	C₅	#18012537	1	1	yes	characteristic, complemented
22	C₅	#18012539	1	1	yes	characteristic, complemented
23	C₄	—	6025	1	no	Sylow
24	C₂	—	1205	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₂₄₁	C₄
prime radical, cosocle	C₅×D₁₂₀₅	C₂
LCS	G ▷ C₅²×C₂₄₁
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.