Subgroups — Dic₁₀₀ #87710

Order 400.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₀	C₂	1	2	yes	maximal
2	C₈×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂₅	C₂²	1	1	yes	characteristic
4	Dic₂₅	—	2	2	no	—
5	Dic₂₀	—	5	1	no	maximal
6	C₂×C₂₅	D₄	1	1	yes	characteristic
7	Dic₁₀	—	5	2	no	—
8	C₅×C₈	D₅	1	1	yes	characteristic
9	C₂₅	Q₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₄×C₅	C₂×D₅	1	1	yes	characteristic
11	Dic₅	—	10	2	no	—
12	Q₁₆	—	25	1	no	Sylow
13	C₂×C₅	D₂₀	1	1	yes	characteristic
14	Q₈	—	25	2	no	—
15	C₈	D₂₅	1	1	yes	characteristic
16	C₅	Dic₂₀	1	1	yes	characteristic
17	C₄	—	50	2	no	—
18	C₄	C₂×D₂₅	1	1	yes	characteristic
19	C₂	D₁₀₀	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. C₂₅	Q₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.