Subgroups — C₂×C₇×C₃₁⋊C₂₅ #24925739

Order 10850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇×C₃₁	C₅	1	1	yes	maximal, characteristic
3	C₂×C₃₁⋊C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic
5	C₃₁⋊C₂₅	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₇×C₃₁	C₂₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇×C₂₅	—	31	1	no	maximal, Hall
8	C₂×C₅×C₃₁	C₅×C₇	1	1	yes	characteristic
9	C₇×C₃₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₇×C₂₅	—	31	1	no	Hall
11	C₅×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic
12	C₂×C₅×C₇	ΓL(1,𝔽₃₂)	1	1	yes	characteristic
13	C₂×C₃₁	C₇×C₂₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₂₅	—	31	1	no	Hall
15	C₅×C₇	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
16	C₃₁	C₂×C₇×C₂₅	1	1	yes	characteristic, complemented, Sylow
17	C₂₅	—	31	1	no	Sylow
18	C₂×C₇	C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
20	C₇	C₂×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₂×C₇×ΓL(1,𝔽₃₂)	1	1	yes	characteristic
22	C₂	C₇×C₃₁⋊C₂₅	1	1	yes	characteristic, direct product factor, 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.