Subgroups — D₄×C₂₅ #6023

Order 200.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₅	C₂	1	2	yes	maximal, complemented
2	C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₅	—	2	2	no	—
4	C₂×C₂₅	C₂²	1	1	yes	characteristic
5	C₅×D₄	C₅	1	1	yes	maximal, characteristic
6	C₂₅	D₄	1	1	yes	characteristic, direct product factor, Sylow
7	C₂²×C₅	C₂×C₅	1	2	yes	—
8	C₄×C₅	C₂×C₅	1	1	yes	characteristic
9	C₂×C₅	—	2	2	no	—
10	C₂×C₅	C₂²×C₅	1	1	yes	characteristic
11	D₄	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₅	C₅×D₄	1	1	yes	characteristic
13	C₂²	C₂×C₂₅	1	2	yes	complemented
14	C₄	C₂×C₂₅	1	1	yes	characteristic, complemented
15	C₂	—	2	2	no	—
16	C₂	C₂²×C₂₅	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.