Subgroups — C₃×C₅×AGL(1,𝔽₅) #64485

Order 300.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅	C₂	1	1	yes	maximal, characteristic
2	C₅×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₄×C₅	—	5	1	no	maximal
6	C₅×D₅	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅	—	5	1	no	—
8	C₃×D₅	C₂×C₅	1	1	yes	characteristic
9	C₅²	C₃×C₄	1	1	yes	characteristic, complemented, Sylow
10	AGL(1,𝔽₅)	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₄×C₅	—	5	1	no	—
12	C₃×C₅	—	4	1	no	—
13	C₃×C₅	C₄×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
15	C₃×C₄	—	5	1	no	Hall
16	C₂×C₅	—	5	1	no	—
17	D₅	C₂×C₃×C₅	1	1	yes	characteristic
18	C₂×C₃	—	5	1	no	—
19	C₅	—	4	1	no	—
20	C₅	C₃×C₄×C₅	1	1	yes	characteristic, complemented
21	C₅	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
22	C₄	—	5	1	no	Sylow
23	C₃	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
24	C₂	—	5	1	no	—

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.