Subgroups — C₃×C₇×AGL(1,𝔽₅) #88295

Order 420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅	C₂	1	1	yes	maximal, characteristic
2	C₇×AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₄×C₇	—	5	1	no	maximal, Hall
5	C₇×D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×AGL(1,𝔽₅)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇	—	5	1	no	—
8	C₅×C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇	—	5	1	no	Hall
11	C₃×C₇	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
12	AGL(1,𝔽₅)	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇	—	5	1	no	—
15	C₃×C₄	—	5	1	no	Hall
16	D₅	C₂×C₃×C₇	1	1	yes	characteristic
17	C₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃	—	5	1	no	—
19	C₅	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	5	1	no	Sylow
21	C₃	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
22	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.