Subgroups — ΓL(1,𝔽₈)×C₂₅×C₄₇ #37590521

Order 24675.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×ΓL(1,𝔽₈)×C₄₇	C₅	1	1	yes	maximal, characteristic
3	C₃×C₂₅×C₄₇	—	7	1	no	maximal, Hall
4	C₅×C₇×C₄₇	C₃×C₅	1	1	yes	characteristic
5	C₂₅×C₄₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
6	ΓL(1,𝔽₈)×C₄₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₄₇	—	7	1	no	—
8	ΓL(1,𝔽₈)×C₂₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₄₇	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₄₇	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₇×C₂₅	C₃×C₄₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄₇	—	7	1	no	Hall
13	C₅×ΓL(1,𝔽₈)	C₅×C₄₇	1	1	yes	characteristic
14	C₃×C₂₅	—	7	1	no	Hall
15	C₄₇	ΓL(1,𝔽₈)×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₅×C₇	C₃×C₅×C₄₇	1	1	yes	characteristic
17	C₂₅	ΓL(1,𝔽₈)×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	ΓL(1,𝔽₈)	C₂₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅	—	7	1	no	—
20	C₇	C₃×C₂₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₅×ΓL(1,𝔽₈)×C₄₇	1	1	yes	characteristic
22	C₃	—	7	1	no	Sylow

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.