Subgroups — C₂×#1044 #6061

Order 200.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	#1044	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²	C₄	1	1	yes	characteristic, complemented
4	C₅⋊D₅	C₄	1	1	yes	characteristic, complemented
5	C₅⋊D₅	C₂²	1	1	yes	characteristic
6	C₂×AGL(1,𝔽₅)	—	5	2	no	maximal
7	C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₅	—	5	2	no	—
9	C₂×D₅	—	10	2	no	—
10	AGL(1,𝔽₅)	—	5	4	no	—
11	C₂×C₅	—	2	2	no	—
12	C₂×C₅	AGL(1,𝔽₅)	1	2	yes	complemented
13	D₅	—	5	2	no	—
14	D₅	—	5	2	no	—
15	D₅	—	10	2	no	—
16	D₅	—	10	2	no	—
17	C₂×C₄	—	25	1	no	Sylow
18	C₅	—	2	2	no	—
19	C₅	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
20	C₂²	—	25	1	no	—
21	C₄	—	25	2	no	—
22	C₂	—	25	1	no	—
23	C₂	—	25	1	no	—
24	C₂	#1044	1	1	yes	characteristic, direct product factor

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.