Subgroups — C₂×C₅×AGL(1,𝔽₅) #6058

Order 200.

34 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	C₅×AGL(1,𝔽₅)	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)	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₄×C₅	—	5	1	no	maximal
8	C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₅	—	5	1	no	—
10	C₂×D₅	C₂×C₅	1	1	yes	characteristic
11	AGL(1,𝔽₅)	C₂×C₅	1	2	yes	direct product factor
12	C₄×C₅	—	5	2	no	—
13	C₂×C₅	—	4	1	no	—
14	C₂×C₅	—	5	1	no	—
15	C₂×C₅	—	5	1	no	—
16	C₂×C₅	C₄×C₅	1	1	yes	characteristic, complemented
17	C₂×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
18	D₅	C₄×C₅	1	1	yes	characteristic, complemented
19	D₅	C₂²×C₅	1	1	yes	characteristic
20	C₂×C₄	—	5	1	no	Sylow
21	C₅	—	4	1	no	—
22	C₅	C₂×C₄×C₅	1	1	yes	characteristic, complemented
23	C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
24	C₂²	—	5	1	no	—
25	C₄	—	5	2	no	—
26	C₂	—	5	1	no	—
27	C₂	—	5	1	no	—
28	C₂	C₅×AGL(1,𝔽₅)	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.