Subgroups — ((C₅⋊D₅)⋊C₅)⋊C₂ #92541

Order 500.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6953	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₅⋊D₅)⋊C₅	C₂	1	2	yes	maximal, complemented
3	H(3,𝔽₅)	C₂²	1	1	yes	characteristic, complemented, Sylow
4	D₅²	—	5	2	no	maximal
5	C₅⋊D₅	D₅	1	2	yes	complemented
6	C₅×D₅	—	5	2	no	—
7	C₅×D₅	—	5	2	no	—
8	C₅×D₅	—	10	2	no	—
9	C₅²	—	2	2	no	—
10	C₅²	C₂×D₅	1	2	yes	complemented
11	C₂×D₅	—	25	1	no	—
12	C₂×D₅	—	25	2	no	—
13	C₂×C₅	—	25	2	no	—
14	C₂×C₅	—	25	1	no	—
15	D₅	—	5	2	no	—
16	D₅	—	5	2	no	—
17	D₅	—	10	2	no	—
18	D₅	—	25	2	no	—
19	C₅	—	5	2	no	—
20	C₅	—	10	2	no	—
21	C₅	D₅²	1	1	yes	characteristic
22	C₂²	—	125	1	no	Sylow
23	C₂	—	25	1	no	—
24	C₂	—	25	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	H(3,𝔽₅)	C₂²
Frattini, socle	C₅	D₅²
LCS	G ▷ H(3,𝔽₅)
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.