Subgroups — C₅×ΓL(1,𝔽₈)⋊C₄ #88276

Order 420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×ΓL(1,𝔽₈)	C₄	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₈)⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×C₅	—	7	1	no	maximal, Hall
7	C₂×ΓL(1,𝔽₈)	C₂×C₅	1	1	yes	characteristic
8	C₅×C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅	—	7	1	no	—
10	Dic₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	ΓL(1,𝔽₈)	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₄×C₅	—	7	1	no	Hall
13	C₃×C₅	—	7	1	no	Hall
14	C₂×C₇	C₂×C₃×C₅	1	1	yes	characteristic
15	C₃×C₄	—	7	1	no	Hall
16	C₂×C₅	AGL(1,𝔽₇)	1	1	yes	characteristic
17	C₇	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	—	7	1	no	—
19	C₅	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	7	1	no	Sylow
21	C₃	—	7	1	no	Sylow
22	C₂	C₅×AGL(1,𝔽₇)	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.