Subgroups — D₅₀₀ #11758621

Order 1000.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂₅	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₂₅	C₂²	1	1	yes	characteristic
4	D₁₂₅	—	2	2	no	—
5	D₁₀₀	—	5	1	no	maximal
6	C₁₂₅	D₄	1	1	yes	characteristic, complemented, Sylow
7	C₂×D₂₅	—	5	2	no	—
8	C₄×C₂₅	D₅	1	1	yes	characteristic
9	C₂×C₂₅	C₂×D₅	1	1	yes	characteristic
10	D₂₅	—	10	2	no	—
11	D₂₀	—	25	1	no	—
12	C₂₅	D₂₀	1	1	yes	characteristic
13	C₂×D₅	—	25	2	no	—
14	C₄×C₅	D₂₅	1	1	yes	characteristic
15	C₂×C₅	C₂×D₂₅	1	1	yes	characteristic
16	D₅	—	50	2	no	—
17	D₄	—	125	1	no	Sylow
18	C₅	D₁₀₀	1	1	yes	characteristic
19	C₂²	—	125	2	no	—
20	C₄	D₁₂₅	1	1	yes	characteristic, complemented
21	C₂	—	250	2	no	—
22	C₂	C₂×D₁₂₅	1	1	yes	characteristic

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.